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date: 14 July 2020

Tornadoes and Their Parent Convective Storms

Abstract and Keywords

In the past four decades much has been discovered about tornado formation and structure from observations, laboratory models, and numerical-simulation experiments. Observations include nearby movies and photographs of tornadoes, fixed-site, airborne, and ground-based mobile Doppler radar remote measurements, and in situ measurements using instrumented probes. Laboratory models are vortex chambers and numerical-simulations are based on the governing fluid dynamical equations. However, questions remain: How and why do tornadoes form? and How does the wind field associated with them vary in space and time? Recent studies of tornadoes based on observations, particularly by radar, are detailed. The major aspects of numerically simulating a tornado and its formation are reviewed, and the dynamics of tornado formation and structure based on both observations and laboratory and numerical-simulation experiments are described. Finally, future avenues of research and suggested instrument development for furthering our knowledge are discussed.

Introduction

Tornadoes are intense columns of rotating air, ~100 m to 1 km in diameter, pendant from convective clouds (Bluestein, 2013). They occur in many locations around the globe and sometimes in land-falling tropical cyclones (Novlan & Gray, 1974) but are most common in the central United States during the spring (Davies-Jones, Trapp, & Bluestein, 2001). Tornadoes over water are called waterspouts (Bluestein, 1999b). The minimum wind speed in tornadoes is generally that considered high enough to sustain damage. In the absence of direct measurements, tornado wind speeds are estimated from damage using the enhanced Fujita scale (Marshall, 2004) (Table 1) and supplemented when possible by data from mobile Doppler radars (Snyder & Bluestein, 2014). Tornadoes are of great interest to society because they are capable of inflicting intense damage, injuries, and loss of life. The most important scientific questions about tornadoes are as follows:

1. 1. How and why do they form?

2. 2. How does the wind field associated with them vary in space and time?

Table 1. The Fujita and Enhanced Fujita Scales for Estimating Wind Speeds in Tornadoes Based on Damage

Fujita Scale

Enhanced Fujita Scale

Fujita Scale

Fastest 1/4-mile wind speed, mph

3-Second gust speed, mph

Enhanced Fujita Scale

3-Second gust speed, mph

F0

40–72

45–78

EF0

65–85

F1

73–112

79–117

EF1

86–109

F2

113–157

118–161

EF2

110–137

F3

158–207

162–209

EF3

138–167

F4

208–260

210–261

EF4

168–199

F5

261–318

262–317

EF5

200–234

Answers to the first question will help us forecast them more accurately and add to our general scientific knowledge. The most important problems to be solved are determining the source(s) of vorticity (twice the angular velocity of a fluid parcel about its center of rotation) in tornadoes and how vorticity, which may have a significant horizontal component, is transformed into a vertical column of rapidly rotating air. The source(s) of vorticity may exist prior to storm formation, independent of the parent storm, or be produced by the storm itself. Answers to the second are of interest to structural engineers who want to design buildings capable of sustaining minimal damage when tornadoes strike.

In the next section, recent studies of tornadoes based on observations, particularly by radar, are detailed. In the third section we review the major aspects of numerically simulating a tornado and its formation. The dynamics of tornado formation and structure based on both observations and laboratory and numerical-simulation experiments are then described in the fourth section. There is a fifth and final section on future avenues of research and suggested instrument development for furthering our knowledge.

Observations of Tornadoes and Their Parent Storms and Observation Technology

Photogrammetric Analyses, Radar Observations, and Visual Observations

Quantitative estimates of wind speeds normal to the line of sight in tornadoes have been obtained from photogrammetric analyses of pieces of flying debris that can be tracked from frame to frame in movies (Hoecker, 1960). Doppler radar is used to estimate the component of the wind in the line-of-sight direction (the “Doppler wind component”). Photographs and other visual observations of tornadoes in storms are used to relate cloud structure in the parent storm to the location of tornadoes, without any correlating radar observations (Fujita, 1960). Condensation funnels are frequently found in tornadoes but may not be visible if the boundary layer, that part of the atmosphere that is affected by the Earth’s surface, is too dry and/or the pressure drop in them is not large enough. Or tornadoes may be hidden behind an opaque curtain of precipitation (Bluestein, 2013). Since flying debris is not always visible, because airborne debris either are simply not present or are hidden by a condensation funnel or precipitation, photogrammetric estimates of wind speeds in tornadoes have been of only limited usefulness. In addition, one must make the assumption that debris motion follows air motion, which, owing to the drag induced by debris, is not completely valid (Dowell, Alexander, Wurman, & Wicker, 2005).

Supercells, long-lived convective storms, which are most commonly found in midlatitudes, are characterized by a rotating updraft which has a large component of propagation normal to the pressure-weighted mean wind in the troposphere (Browning, 1964, 1965a, 1965b; Browning & Donaldson, 1963; Browning & Ludlam, 1962) and are the most prolific producers of strong tornadoes. Ordinary cells, on the other hand, persist only for about the time it takes an air parcel to ascend from the cloud base to the top of the storm and then fall back to the ground (~40–50 minutes) and do not generally have rotating updrafts (Browning, 1986; Weisman & Klemp, 1986). Supercells are also sometimes found in the outer rainbands of tropical cyclones (Eastin & Link, 2009) and in land-falling tropical cyclones (McCaul, 1991; Novlan & Gray, 1974; Suzuki, Hiroshi, Hisao, & Hiroshi, 2000).

Figure 1. (a) Mobile, 3-cm wavelength, Doppler radar data (University of Massachusetts X-Pol) for a tornadic supercell near Greensburg, Kansas, on May 4, 2007 (Tanamachi et al., 2012). (top) Radar reflectivity factor (dBZ). A hook echo and weak-echo hole are evident. (bottom) Dealiased Doppler velocity (m s–1). The black circular ring marks the cyclonic shear vortex signature. Range rings are shown every 5 km. (b) Zoomed-in view of a tornado at low levels from the University of Oklahoma mobile Doppler radar RaXPol (Rapid-scan X-band Polarimetric) (Pazmany, Mead, Bluestein, Snyder, & Houser, 2013) near Shawnee, Oklahoma, on May 19, 2013. (top left) Radar reflectivity factor Z (dBZ) showing a “debris ball”; (top right) differential reflectivity (ZDR) showing low values indicative of debris; (bottom left) undealiased Doppler velocity (m s–1) showing a cyclonic vortex shear signature; (bottom right) copolar cross-correlation coefficient ρhv showing low values, indicative of debris. Range rings are shown every 1 km.

Figure 2. Vertical cross section through the weak-echo hole and bounded weak-echo region (BWER; or “vault”) of the tornadic supercell shown in Figure 1.

The intensity of radar echoes in convective storms is typically measured logarithmically, owing to the high dynamic range of the intensity of backscattered radiation from distant precipitation. The radar reflectivity factor (Z) for Rayleigh scatterers (when the diameter of the scatterers is small compared to the wavelength of the radiation) is proportional to the sum of the sixth power of the diameter of all the scatterers in the radar volume, so a relatively high Z could be caused by relatively few large hydrometeors or by many small hydrometeors. Information about the drop-size spectrum is therefore not known from Z alone. The reflectivity factor is also affected by the wetness of the surface and other “microphysical” properties of the scatterers. The supercell radar echo often has a hook-shaped appendage on its right rear flank (with respect to the direction of storm motion), which is indicative of rotation (Figure 1a). The strong updraft in a supercell is marked at low levels by a weak-echo region and aloft by a bounded weak-echo region, created because the residence time of small cloud particles in the updraft is too short for larger, precipitation-size scatterers to form (Browning, 1965a) (Figure 2).

Figure 3. (a) Idealized visual model (top, based on Moller [1978]) and actual photograph (bottom) of a tornadic supercell as viewed from its right flank. The photograph (© Howard B. Bluestein) was taken in Goshen County, Wyoming, on June 5, 2009, during VORTEX2. (b) Idealized model of a tornadic supercell (from Lemon & Doswell, 1979). The thick solid line is the outline of the radar echo. The locations of the rear-flank downdraft (RFD), forward-flank downdraft (FFD), and main updraft (UD) are stippled and outlined by dashed lines. The arrows indicate the direction of the low-level winds. The cold front symbol denotes the rear-flank gust front.

From a network of Doppler radars the two-dimensional wind field on the storm scale can be synthesized on tilted planes from line-of-sight measurements made from different viewing angles; from these two-dimensional wind fields, the three-dimensional wind is estimated using as a constraint the conservation of mass and estimates of terminal fall velocity of hydrometeors based on measurements of the intensity of backscattered signal (Armijo, 1969; Brandes, 1977a, 1977b, 1978, 1981; Heymsfield, 1978; Ray et al., 1975). A radar and visual (“storm chasers” [Bluestein, 1999a] provided the photographs) idealized model of supercells with tornadoes (Moller, 1978; Moller, Doswell, Foster, & Woodall, 1994) is seen in Figure 3. Tornadoes in supercells tend to be found near the wall cloud, a lowered cloud base underneath the main, rotating, cumulonimbus cloud, which is characterized by an updraft. Downdrafts are found in two locations: The forward-flank downdraft (FFD), where precipitation falls downstream at upper levels from the anvil, and the rear-flank downdraft (RFD), upstream with respect to storm-relative flow at midlevels. The RFD bulges outward as a gust front, a line along which the wind shifts from storm-relative inflow to sometimes cooler storm-relative outflow. Tornadoes tend to be found in and near the mesocyclone at the tip of the RFD gust front and are flanked by a downdraft and an updraft (Lemon & Doswell, 1979). The FFD is not typically marked by a well-defined wind shift on its right flank, as depicted in the Lemon and Doswell model. The storm-scale (mesocyclones ~O [2.5–10 km]) features associated with tornadoes (tornadoes are ~O [100 m–1 km]) appear to be a small-scale analog of the synoptic-scale cyclone that forms at the intersection of a cold front and a warm front.

Tornadoes also occur in ordinary-cell convective storms (Bluestein, 1985; Wakimoto & Wilson, 1989). These tornadoes form from vorticity in the boundary layer along wind-shift lines that preceded the formation and development of the parent convective storms, unlike the tornadoes that form in supercells from vorticity that is produced by the storm itself. These types of tornadoes are overall not as intense as those that form in supercells. They are challenging to detect because they sometimes appear before any radar echoes from precipitation have formed.

Figure 4. Depiction of a tornado within a line of convective storms just southwest of Norman, Oklahoma, during the early morning of April 2, 2010. (top panel) Radar reflectivity factor (dBZ) showing a hook echo; (bottom panel) Doppler velocity (m s–1) showing a cyclonic vortex shear signature (circled). Data from a 3-cm wavelength mesoscale network radar (from Mahale et al., 2012). Range rings shown every 5 km.

Tornadoes are also found in quasi-linear mesoscale convective systems or rainbands along local bulges in lines of deep convection (Figure 4) (Bluestein, 2013; Mahale, Brotzge, & Bluestein, 2012; Trapp, Tessendorf, Godfrey, & Brooks, 2005b). These tornadoes are also overall not as intense as supercell tornadoes and account for roughly 20% of all tornadoes reported in the United States; they present a challenge to observe because they are frequently not visible owing to intervening precipitation.

In Situ Measurements

Mechanically scanning radars typically take at least several minutes or more to scan the lower half of a storm or tornado. This update time is sufficient to document changes in storm features, whose advective time scale (the time it takes an air parcel to pass into and out of a feature in a storm) is ~O (10 km/10 m s–1 ~ 1000 s ~ tens of minutes). A scanning radar’s update time is constrained by the necessity for the radar beam to dwell on volumes for a sufficiently long time to acquire enough samples to estimate the Doppler wind field with high accuracy. In addition, the beam is smeared considerably if the mechanical scanning rate is high.

Many research radars and the WSR-88D network radars in the United States now have dual-polarization capability (Doviak, Bringi, Ryzhkov, Zahrai, & Zrnic, 2000). From dual-polarization radar data, one can deduce information about the nature of the scatterers in a storm (Romine, Burgess, & Wilhelmson, 2008; Straka, Zrnic, & Ryzhkov, 2000; Van Den Broeke, Straka, & Rasmussen, 2008; Zrnic & Ryzhkov, 1999). The quantities differential reflectivity (ZDR) and copolar cross-correlation coefficient are often used,

$Display mathematics$
(1)

where ZH and ZV are the radar reflectivity factors for the horizontally and vertically polarized beams, respectively. Large raindrops, which become oblate as they fall, are characterized by high ZDR, while small raindrops are characterized by low ZDR. When short-wavelength radars are used and/or when scatterer sizes are large, scattering is in the Mie range, where resonance effects complicate the relationship between scatter size and reflectivity such that there is not a monotonic relationship between Z and the sizes and density of the scatterers. The copolar cross correlation coefficient is determined by

$Display mathematics$
(2)

where Sxy is the transmitted (x) and backscattered (y) complex signal strength. There are a number of scientific justifications for using polarimetric radar data.

Cold-Pool Potential

The evaporation and sublimation rates of water vapor into the air and the resultant cooling rates are functions of the types of hydrometeors present and the humidity of the air into which the hydrometeors are falling or suspended. Therefore, knowledge of the three-dimensional distribution of the types of hydrometeors is significant in determining the intensity of surface cold pools underneath convective storms (French, Burgess, Mansell, & Wicker, 2014b), which plays a role in the formation of low-level mesocyclones in supercells (Markowski & Richardson, 2014).

Tumbling debris in tornadoes is not characterized by any preferred orientation, so debris is characterized by low ZDR and ρηv (Bluestein et al., 2007a; Bluestein, Snyder, & Houser, 2015; Ryzhkov, Schuur, Burgess, & Zrnić, 2005; Snyder, Bluestein, Zhang, & Frasier, 2010; Wurman et al., 2013). A region of low ZDR and ρηv when a TVS is present is called a tornado debris signature (TDS) (Figure 1b); ρηv is usually a better indicator of tornado debris than ZDR. The TDS is an additional useful product for locating tornadoes. Since surveillance radars (such as the WSR-88D) are often far enough away from tornadoes that a TVS cannot be detected near the ground, the TDS provides independent evidence that there is a tornado because damage is being inflicted.

Identification of Strong Updrafts

Figure 5. A ZDR (db) tower in a supercell as detected by a 10-cm Doppler radar

(from Kumjian & Ryzhkov, 2008).

When a strong updraft lofts raindrops above the freezing level, there is a column of relatively high ZDR (Kumjian & Ryzhkov, 2008; Snyder, Bluestein, Venkatesh, & Frasier, 2013) (Figure 5). Since Doppler radars typically scan at relatively low elevation angles (constrained by the range to the radar and the height of the radar echoes), most of the velocity component detected is horizontal so that vertical velocity must be inferred (from mass continuity constraints when there is multiple-Doppler synthesis of the two-dimensional wind). Independent confirmation of a strong updraft is therefore useful, especially when only single-Doppler data are available and it is not possible to estimate vertical velocity (Snyder, Ryzhkov, Kumjian, & Picca, 2014).

Identification of Storm Rotation

Figure 6. A ZDR (db) arc along the right forward flank at low levels in a supercell as detected by a 10-cm Doppler radar

(from Kumjian & Ryzhkov, 2008).

A narrow band of relatively high ZDR as a result of size sorting of precipitation particles is often found along the forward flank of supercells (Kumjian & Ryzhkov, 2008). The ZDR arc (Figure 6) can be thought of as an indicator of the magnitude of the storm-relative mean wind, which typically is large for supercells that rotate and propagate off the environmental hodograph (Dawson, Mansell, & Kumjian, 2015).

Simulations of Tornadoes and Their Parent Storms

Modeling of Convective Storms

In order to understand tornadogenesis, it is necessary to perform controlled experiments. Since it is not possible to do a controlled experiment in nature, simulation experiments are needed in which one can vary the state of the atmosphere prior to tornadogenesis. Since many of the processes responsible for the formation and evolution of convective storms and tornadoes are highly nonlinear, understanding of tornadogenesis can come only through numerical simulations. Understanding is enhanced, however, by analytical solutions for highly idealized processes. Finally, numerical models may be used to predict storm formation and evolution. Observations are needed as a guide for what is to be expected as outcomes. The overall method for predicting meteorological variables, that is, extrapolating them into the future, is now outlined (Klemp & Wilhelmson, 1978; Schlesinger, 1975).

The governing equations in Cartesian coordinates for convective storms include the three-dimensional equation of motion:

$Display mathematics$
(3)

where is the density of the “basic state” (average value over the domain, which extends far beyond the convective storm); p¢ is the deviation of the pressure from the basic state pressure; the buoyancy terms involving water vapor and condensate suspended in the air, g is the acceleration of gravity and θ is the potential temperature, with primed and averaged quantities representing the deviation from the basic state and the basic state itself, respectively; and F represents sub-grid-scale mixing/turbulence. Various techniques have been used to parameterize sub-grid-scale turbulence based on grid-scale measurements, most of which make use of the assumption that the grid scale of the model is within the inertial subrange (Klemp & Wilhelmson, 1978), where kinetic energy is produced at larger scales and cascaded down through eddies to the smaller scales of molecules, where it is dissipated as heat at the same rate as it is transported downscale from the eddies. Potential temperature is determined by $θ=T(p/po)R/Cp$, where T is the temperature; po is the pressure at the reference level, usually 1000 hPa; R is the gas constant; and Cp is the specific heat at constant pressure. When simulations are carried on for time periods in excess of just a few hours, it is necessary to include the effects of the rotation of the Earth about its axis via the Coriolis force (not shown in Equation 3). Electrical forces could also be included but for simplicity are not included here. Most observational evidence does not support the inclusion of electrical forces (Davies-Jones, 1986) for simulating tornadoes.

The conservation of mass may be expressed in flux form by the following fully compressible continuity equation:

$Display mathematics$
(4)

Equations for conservation of water substance are used separately for water vapor, cloud particles, and precipitation particles of a number of different kinds (e.g., raindrops, ice crystals, hail).

The prognostic equations for v are given in terms of the right-hand side of Equation 3, which is a function of the three-dimensional wind field, temperature, and density. Each component of the wind is extrapolated into the future using finite-difference schemes. The relation between the grid spacing and the duration of the time step is chosen so that the numerical integration is computationally stable. Pressure, which appears as a horizontal gradient on the right-hand side of Equation 3, is found by forming a diagnostic, Poisson, pressure equation by computing a divergence equation from the individual components of Equation 3 and using the incompressible form of the equation of continuity (4) (Ogura & Phillips, 1962) (the time derivative term involving density is neglected) to eliminate the time derivative terms, to arrive at the following (Rotunno & Klemp, 1982, 1985):

$Display mathematics$
(5)

The terms on the right-hand side of Equation 5 are computed from the three-dimensional distribution of the wind, temperature, and density. Sound waves are allowed by the fully compressible continuity equation, and these must be accounted for when necessary.

The thermodynamic equation is given by

$Display mathematics$
(6)

where Ql, Qr, and QF are the diabatic heating rates due to changes in the phase of water substance (Kessler, 1969; evaporation, condensation, sublimation, melting, etc.), radiation, and sub-grid-scale diffusion of heat.

Boundary conditions are chosen so that vertical velocity is zero at the ground (the kinematic boundary condition: there is no exchange of air across the surface) and at high levels well above cloud top. At the surface (z = 0), the free-slip boundary condition is usually imposed (i.e., ). Using the free-slip lower boundary condition, there is no surface friction. If the more realistic no-slip lower boundary condition (u = 0 and v = 0 at z = 0) were applied, then the vertical grid spacing would have to approach zero near the surface. So all models that use the free-slip boundary condition, while appropriate for studying tornadogenesis, are not appropriate for studying the structural engineering impacts of tornadoes. A compromise, the semi-slip lower boundary condition (Kuo, 1971; Taylor, 1915), is sometimes used, for which $v=K∂v/∂z$ and K > 0. Lateral boundary conditions are also applied so that disturbances propagating into the domain are reflected minimally.

For fundamental studies, the environment is usually assumed to be horizontally homogeneous, for simplicity, and a single sounding is used to define the environment. However, it is recognized that convective storms frequently form along surface boundaries, where the environment is not homogeneous, so changes in the environment must be taken into account (Richardson, Droegemeier, & Davies-Jones, 2007), especially when a storm crosses or moves away from a boundary (Atkins, Weisman, & Wicker, 1999; Markowski, Rasmussen, & Straka, 1998). For actual numerical weather prediction, the environment is allowed to be inhomogeneous. Initializing the model for idealized experiments requires artificially triggering a storm by releasing a buoyant bubble (or a spatial distribution of buoyant bubbles) at low levels or imposing a region of negatively buoyant air near the surface, which then forces air upward at its periphery. Initializing the model for numerical weather prediction is complex, involving the use of many types of data as initial conditions (data from rawinsondes, radars, satellites, surface-observing instruments, etc.) and, in the case of four-dimensional “data assimilation,” the blending of both the observational data and model data as a function of time (Talagrand, 1997). Techniques have also been developed for combining real data and model data to obtain analyses of meteorological variables for the diagnosis of physical processes (Marquis, Richardson, Markowski, Dowell, & Wurman, 2012).

Numerical-simulation experiments for studying the behavior of convective storms usually involves grid spacings of ~100 m to 1 km. The smaller grid spacing is required for the most accurate representation of storms. Tornadoes, which are smaller in horizontal scale, are not represented explicitly in the models. Simulations with grid spacing as low as ~50 m show remarkable detail and can reproduce tornado-like vortices (Orf, Wilhelmson, Wicker, Lee, & Finley, 2014).

To model tornadoes, laboratory models have been used to study tornado behavior (Ward, 1972), with the model tornado completely divorced from its parent storm. In particular, laboratory models, vortex chambers, have been used to model what happens when a rapidly rotating vortex interacts with the ground (Church, Snow, & Agee, 1977). Numerical-model analogs of laboratory models have been used to study idealized vortices interacting with the ground (Rotunno, 1977, 1979), without the need to make measurements with instruments, which can disrupt the airflow, of all the variables at each point in the vortex chamber. There are two main types of models: the Ward chamber (Ward, 1972) and the Fiedler chamber (Fiedler, 1995; Trapp & Fiedler, 1995). In the former, air is sucked out of the chamber at the top by an exhaust fan and in at the bottom; the relative amount of air that flows around the vortex compared to that which flows radially inward is controlled by vanes. A measure of the relative amount of “swirl” (azimuthal flow) to radial inflow is called the swirl ratio (Church, Snow, Baker, & Agee, 1979). In the latter model, which is virtual (not physical), a fixed source of buoyancy is imposed in the chamber and air is circulated within the chamber. In the Ward chamber, the exhaust fan plays the role of the updraft in the parent storm; in the Fiedler chamber, the buoyant bubble plays the role of the updraft. The effects of the parent storm are modeled through the boundary conditions. Recently, a physical simulator has been constructed that more closely simulates tornado-like flow by scaling the physical dimensions/properties of the simulator to the flow in tornadoes as measured by Doppler radar (Refan, 2014).

The equation of motion for the radial wind component in cylindrical coordinates for axisymmetric flow is

$Display mathematics$
(7)

where u, v, and w are the radial, azimuthal, and vertical components of the wind, respectively, and ν is the eddy coefficient of viscosity. When –v2/r is brought to the right-hand side of the equation and the sign reversed, it is the (outward) acceleration due to the centrifugal force; is the radial acceleration due to the radial pressure-gradient force; and the last term is the radial acceleration due to sub-grid-scale mixing and turbulence. The thermodynamic equation is not considered when, for simplicity, the atmosphere is incompressible.

To model tornado behavior more accurately, large-eddy simulation (LES) models are used (Lewellen, Lewellen, & Sykes, 1997), for which the spatial resolution is high enough to reproduce the largest eddies in the inertial subrange. For tornadoes, the spatial resolution is ~O (1 m).

Dynamics of Tornadoes and Their Parent Storms

The dynamics of supercells (Klemp, 1987) may be explained through the three-dimensional vorticity equation (Rotunno, 1981):

$Display mathematics$
(8)

Vorticity may be advected from one place to another, tilted from one axis to another, and amplified or suppressed by the stretching or shrinking of a fluid segment (first term on the right-hand side); generated or dissipated baroclinically (second term on the right-hand side); and generated or dissipated by sub-grid-scale mixing (third term on the right-hand side).

To find out how vorticity is generated in a supercell, backward trajectories are computed from the mesocylone/tornado and then the terms in the vorticity equation are calculated (Rotunno & Klemp, 1985). This procedure can be difficult because the trajectories are sensitive to the origination points when the wind field is strong and there are sharp gradients, as are found in strong vortices (Dahl, Parker, & Wicker, 2012). Also, near the ground, trajectories are sensitive to the choice of lower boundary condition and parameterization of sub-grid-scale mixing/turbulence, along with the vertical increment used near the ground. Finally, air converging into a mesocylone or tornado can originate from different air masses (Rotunno & Klemp, 1985).

Circulation analysis is a macroscale alternative to vorticity analysis, which involves finite material surfaces, while vorticity analysis involves infinitesimal air parcels (Rotunno & Klemp, 1985). Circulation

$Display mathematics$
(9)

where l is a unit vector tangent to the material curve about which the line integral is computed and pointing in the counterclockwise direction, where for vertical vortices, the vorticity

$Display mathematics$
(10)

where A is the area enclosed by the closed circuit. For a circular circuit about a vertical vortex such as a mesocyclone or a tornado exhibiting axisymmetry,

$Display mathematics$
(11)

where Γ is angular momentum (per unit mass) at the radius of the circular circuit. In a barotropic atmosphere that is inviscid (no sub-grid-scale mixing/turbulence), circulation is conserved following air motion (DC/Dt = 0). In a baroclinic atmosphere, circulation may be generated or dissipated (V. Bjerknes’s first circulation theorem). The mechanisms for the formation of a tornado are therefore sometimes categorized as being purely barotropic or purely baroclinic.

The Origin of the Midlevel Mesocyclone in a Supercell

From observations (Brandes, 1984) and numerical simulations (Klemp & Wilhelmson, 1978; Schlesinger, 1975) we have learned that counterrotating vortices are produced at midlevels in a supercell by the tilting, along the flanks of the main updraft in a buoyant updraft, of horizontal vorticity associated with vertical shear of the environmental wind onto the vertical axis (Figure 7, top). This environmental vertical shear is largely a consequence of the pole-to-equator temperature gradient in the troposphere, though, on the synoptic-scale, by the thermal-wind relation (Bluestein, 1992):

$Display mathematics$
(12)

Figure 7. (top) Illustration of the production of a cyclonic–anticyclonic couplet at midlevels by the tilting of the horizontal vortex line (line along which the three-dimensional vorticity vector points) associated with vertical shear in the environment (vertical variation of the winds indicated by wind vectors at the rear left) by a storm’s buoyant updraft. Upward-directed arrows depict upward accelerations induced by the vertical perturbation pressure gradient forces below each midlevel vortex. (bottom) As in the top panel but at a later time as the updraft splits.

From Klemp (1987).

where vg is the geostrophic wind. In the boundary layer, vertical shear may have a significant contribution from sub-grid-scale mixing (surface friction).

The diagnostic pressure equation (5) may be expressed as (Klemp & Rotunno, 1983; Rotunno & Klemp, 1982, 1985)

$Display mathematics$
(13)

in which the wind field has been decomposed into a mean (ˉ) part, representative of a horizontally homogeneous environment and a perturbation (¢) part, representative of the storm, and

$Display mathematics$
(14)

$Display mathematics$
(15)

$Display mathematics$
(16)

where′ and ω′ represent the three-dimensional perturbation deformation and perturbation vorticity, respectively, such that

$Display mathematics$
(17)

$Display mathematics$
(18)

and where

the x component of vorticity,

the y component of vorticity and

. the z component of vorticity

The first term on the right-hand side of Equation 13 is the linear, dynamic term (p¢L); the second term is the nonlinear, dynamic term (p¢NL); the third term is the buoyancy term (p¢B); and the fourth term is the sub-grid-scale mixing term (p¢F), where

$Display mathematics$
(19)

and

$Display mathematics$
(20)

Figure 8. Idealized, semicircular hodograph plotted from the surface (0) to some level above height h. Wind vector at a level below h is shown in red, along with the vorticity vector (dashed) and vertical shear vector (solid). “u” and “v” are the components of wind in the x (zonal) and y (meridional) direstions, respectively.

In the first, linear, dynamic term, the vertical shear vector of the mean wind may be plotted as a hodograph, the locus of points marked by the wind in the environment at each level (Figure 8).

The two counterrotating vortices that are produced at midlevels are each associated with a relative minimum in p¢ according the vorticity part of the nonlinear, dynamic term. Below each vortex, then, there is an upward-directed perturbation pressure-gradient force that lifts air upward and splits the updraft into a cyclonically rotating, right-“moving” (with respect to the mean shear) part and an anticyclonically rotating, left-“moving” part, as is observed in nature (Charba & Sasaki, 1971; Fujita & Grandoso, 1968) (Figure 7, bottom): Each updraft propagates away from the original updraft. Precipitation can fall in between the updrafts but not into the updrafts themselves; consequently, the updrafts are not suppressed as they can be in ordinary-cell convection, when the vertical shear is relatively weak. Since simulated storms split even when no precipitation is allowed, evaporatively cooled pools of air near the ground are not necessary for off-shear propagation.

There is a relative minimum (maximum) in p¢ on the downshear (upshear) side of the updraft according to the linear part of the dynamic term. The linear term is responsible for favoring a right-moving (left-moving) updraft when the environmental hodograph (the vertical shear vector is tangent to the hodograph) turns in clockwise (counterclockwise) manner with height. In nature, owing to the boundary layer, in which the wind veers with height and increases in speed with height, most hodographs favor right-moving, cyclonically rotating supercells (Figure 9). On very rare occasions, mirror- image, left-moving, anticyclonically rotating supercells (Hammond, 1967) produce anticyclonic tornadoes (Bluestein, 2013; Bunkers & Stoppkotte, 2007).

Figure 9. Illustration of how an upward (downward)–directed perturbation pressure gradient force (dashed vectors) on the right (left) flanks of an updraft (cylinder marked as w > 0) occurs when the vertical shear vector (solid) turns in a clockwise manner with height.

From Bluestein (2013).

The dynamic perturbation pressure-gradient forces typically contribute approximately half of the updraft strength, and buoyancy contributes the other half (Weisman & Rotunno, 2000). In the lower several kilometers of the atmosphere, the dynamic perturbation pressure-gradient force may contribute more to vertical acceleration than buoyancy, which is especially true in supercells in landfalling tropical cyclones, where convective available potential energy (CAPE) is relatively low (McCaul & Weisman, 1996). (We ignore, for simplicity, the contribution from sub-grid-scale mixing/turbulence.)

As noted earlier, the generation of rotation in a convective storm allows the updraft to survive much longer than an updraft in a nonrotating convective storm because, owing to updraft propagation, precipitation does not fall into it and destroy the updraft by negating the buoyancy. Supercell formation can occur in an environment of moderate to strong deep-layer shear and modest to strong CAPE, where

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and where LFC is the level of free convection (height at which an upward forced air parcel first becomes positively buoyant) and EL is the equilibrium level (height at which the buoyancy returns to zero, i.e., the height at which the temperature of the air parcel in the cloud is no longer warmer than its environment). High lapse rates (large vertical derivatives of temperature) associated with relatively warm air below and cool air aloft and high moisture content in the boundary layer contribute to high CAPE.

From the inviscid form of the vertical equation of motion (3) expressed as,

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where p′ = pd′ + pb′ and pd′ and pb′ are the perturbation pressures associated with the wind field (dynamic) and buoyancy, respectively. If both the dynamic and buoyancy parts of the perturbation pressure are ignored, then

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This equation is valid when a thermal bubble is at rest (as it is before being “released”) and when the bubble is much wider than it is deep and mixing can be ignored. In general, however, Equation 23 yields an upper bound to vertical velocity because downward-directed buoyancy perturbation pressure-gradient forces (thermals bubbles cannot be too flattened), precipitation loading, and entrainment of nonbuoyant air into the bubble act to decrease w: CAPE is a crude measure of the potential for updraft intensity.

The tendency of an updraft to rotate therefore depends on the strength of the midlevel updraft caused by buoyancy and the magnitude of deep shear (also noted observationally by Rasmussen [2003] and Rasmussen & Blanchard [1998]). Supercell behavior depends on the propagation of updrafts in the direction normal to the vertical shear through upward-directed perturbation pressure-gradient forces underneath the vortices generated by tilting. A necessary condition for supercell formation is that the bulk Richardson number

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is relatively low, where U is the magnitude of the storm-relative inflow and is related to the vertical wind shear. R cannot be too low though, for example, when CAPE is very low, because the updraft strength is too weak; R cannot be too high, for example, when U is small, because the dynamic, upward-directed perturbation pressure gradients underneath midlevel vortices are too weak (Weisman & Klemp, 1982, 1984).

Other conditions that affect whether a supercell rather than an ordinary cell form include the geometry of the boundary along which convective storms may form, the orientation of the tropospheric-mean vertical wind shear with respect to the boundary (Bluestein & Weisman, 2000), and the humidity. Neighboring storm interactions (e.g., collisions) and interactions with boundaries can also affect storm behavior (Bluestein & Weisman, 2000). Also, mesoscale variability can affect storm evolution (Richardson et al., 2007).

There are two paradigms of supercell behavior, the vertical shear perspective and the helicity perspective (Weisman & Rotunno, 2000). In the former, it is the vertical shear that is responsible for producing midlevel rotation along the flanks of the updraft, which leads to propagation of updrafts away from the direction of the vertical shear vector. In the latter, it is the propagation that leads to rotation.

The helicity paradigm is motivated by the finding that when there is streamwise vorticity$(v−c)•ω>0;c$ is the storm motion vector so that v – c is the storm-relative wind vector—vertical vorticity and vertical velocity are correlated in a dry, inviscid atmosphere for small displacements from the mean state (Davies-Jones, 1984). For example, the linearized vertical vorticity equation for steady flow with an updraft propagating in the –y direction (at c = –cy) and mean vertical shear in the +x direction $(∂u¯/∂z)$ is

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The integral of Equation 25 with respect to y leads to

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So, $∂u¯/∂z>0$ and when $w>0,ζ>0$ and when $w<0,ζ<0$.

When vertical vorticity is correlated with vertical motion, convergence underneath an updraft acts to increase vorticity through stretching, which is a nonlinear process; thus, propagation leads to rotation (the mesocyclone). This analysis, however, does not explain how c is maintained. The storm-relative environmental helicity (SREH) is determined as

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in which forecasters often use h = 3 km. High SREH is thought to be indicative of a high probability of storm rotation and tornadoes. A problem with the helicity paradigm is that it depends on the reference frame, that is, it is not Galilean invariant. The storm-relative motion must be known. SREH may be computed from an environmental hodograph and the storm-motion vector as twice the area swept out by the storm-relative wind vector between the surface and height (h). High SREH is favored by long hodographs having strong clockwise curvature. For no storm motion, SREH increases with synoptic-scale horizontal temperature advection—$SREH(c=0)≡H~−v•∇hT$—the latter tending to be greatest where the temperature gradient is highest, that is, near surface boundaries.

The inviscid form of the vertical equation of motion (22) may be expressed as

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where is the Bernoulli term and is the Lamb term (Weisman & Rotunno, 2000). The Lamb term is small for highly curved hodographs (i.e., when is small, e.g., when the wind is approximately normal to the vertical shear vector, approximately along the horizontal vorticity vector). From numerical-simulation experiments evidence has been found, however, that the Lamb term is at least as large as the Bernoulli term. Thus, nonlinear processes are responsible mainly for propagation away from the shear vector for both straight and curved hodographs. The nonlinear perturbation-pressure term, which does not depend on hodograph curvature, is of the greatest fundamental importance in supercell behavior. The linear analysis demonstrating the correlation between vertical velocity and vorticity neglects nonlinear processes, which can be significant.

Originally, the helicity paradigm was developed because it had been found that helical flows (rotating updrafts) are longer-lasting, owing to a reduced cascade of turbulent kinetic energy down to smaller scales (Lilly, 1986). This aspect of helicity as applied to supercells remains incompletely explored.

The Origin of the Low-Level Mesocyclone

Figure 10. Idealized depiction of how cyclonic vorticity may be generated as a combination of tilting and baroclinic generation and causes the vorticity of parcels to change from anticyclonic to cyclonic while descending in a downdraft. (top) Consider a vertical plane indicated by the dashed line. The red streamline represents streamwise vorticity in the forward flank, not as it approaches the downdraft but where it represents the trajectory. (bottom) Suppose that just inside the cold side of a rear-flank downdraft that is wrapping around a mesocyclone, the temperature gradient vector points into the page, to the left of the flow, so that the baroclinic generation of vorticity is in the direction of the arrow at the right. As the parcel sinks, baroclinic vorticity continues to be generated, while the vorticity vector, which was tilted downward by downdraft (accompanied by anticyclonic vorticity), becomes tilted upward (accompanied by a cyclonic vorticity) as it is advected faster southward below than it is aloft, as at the “foot” of a density current (where the flow of the density current is toward the ambient air to the south but much weaker above the density current) or in the presence of strong low-level environmental vertical shear in the southerly direction, and finally enters the base of updraft where it is stretched. Trajectories (TRAJ) in the vertical plane are denoted by solid curved lines with arrows; the three-dimensional vorticity vector is indicated by the vectors. This figure effectively shows how an air parcel coming from the forward flank may wrap around the mesocyclone and then enter the downdraft but become tilted upward by vertical shear and then pass underneath the updraft.

Adapted from Davies-Jones and Brooks (1993).

The mechanism by which a low-level mesocyclone is produced in a supercell is different from that which produces a midlevel mesocyclone. In the former case, horizontal vorticity is produced baroclinically along the edge of and within the forward flank of the supercell (Figure 10). This vorticity is approximately streamwise; that is, its vector is approximately along the storm-relative wind flow. Thus, the baroclinically generated vorticity at low levels is tilted upward by the updraft and cyclonic vorticity is produced (Markowski et al., 2012; Rotunno & Klemp, 1985). Efforts to find cases in which there is a significant contribution from the low-level horizontal vorticity associated with vertical shear in the environment (a barotropic source) have not been successful, even though highly streamwise vorticity can often be found entering the updraft. Why this is so is not entirely understood. The midlevel and low-level mesocyclones may coexist separately or be connected in the vertical.

It is thought that convergence under an updraft acting to increase vertical vorticity that was generated baroclinically is not sufficient for tornadogenesis because the vortex that is formed is rapidly advected upward away from the ground (Davies-Jones & Brooks, 1993). This thinking has led to hypotheses for how a downdraft might act to bring vorticity aloft down to the ground. One such paradigm, supported by idealized numerical simulations (Markowski & Richardson, 2014), has air with streamwise vorticity generated in the FFD flowing upward and wrapping around the mesocyclone and then downward in the RFD, where horizontal vorticity is generated baroclinically such that the three-dimensional vorticity vector does not point downward, in the same direction as air motion, but is maintained more in the horizontal direction (Figure 10). The air parcel then enters the updraft and is tilted, and vorticity is enhanced through stretching closer to the ground. The RFD is driven in part by a downward-directed perturbation pressure gradient above the region of maximum low-level vorticity and in part thermodynamically by evaporation of water substance. In ordinary cells, however, tornadoes are observed even before precipitation has been observed, that is, in the absence of any significant downdraft. This observation suggests that frictional convergence must be an important contributor to tornado formation (Rotunno, 2013) at least in some cases, though numerical simulations of supercells without friction can produce realistic-looking intense vortices near the surface (Orf et al., 2014).

Cool air must be present at low levels in order that horizontal vorticity be generated baroclinically: If the air is too cool, then the rear-flank gust front, driven horizontally like a density current (Benjamin, 1968), will outrun its parent storm. If the air is not cool enough, then vorticity is not generated rapidly enough (Markowski & Richardson, 2014). The current thinking is that to produce the strongest possible low-level mesocyclone, the rate of generation of baroclinic vorticity must be rapid enough and air parcels must reside long enough in the zone where it is being generated. Strong low-level shear normal to the shear aloft (Grams et al., 2012; Wicker, 1996) and low lifting condensation levels (Grams et al. 2012) are thought to encourage low-level mesocyclogenesis (and tornadogenesis) in ways that are not entirely understood yet.

It is thought that tornadogenesis occurs when a low-level vortex becomes very strong near the ground. Underneath the low-level mesocyclone or parent vortex there is an upward-directed perturbation pressure-gradient force, which sustains an updraft and convergence underneath it (Wicker & Wilhelmson, 1995), which acts to increase the vorticity below, thus propagating the vortex to the ground. This process has been referred to as the dynamic pipe effect (Smith & Leslie, 1978). Numerical models even with no explicit boundary layer are able to simulate very strong vortices near the ground (Orf et al., 2014). The dynamic pipe effect, however, has not been observed with rapid-scan radars for midlevel mesocyclones (French et al., 2013; Houser et al., 2015).

Figure 11. The four characteristic regions of a tornado and their properties. (a) Idealized model. (b) Contours of constant angular momentum (solid lines) based on a large-eddy simulation of a low–swirl ratio tornado.

Adapted from Lewellen et al. (2000) and Bluestein (2013).

Figure 12. Photograph from a helicopter of the southern portion of damage from a large, violent tornado in Newcastle and Moore, Oklahoma, on May 20, 2013. Note how the trees are all knocked down to the north, while the tornado traveled from west or west southwest to east or east northeast.

When the vortex gets near enough to the ground so that surface friction acts on it (Lewellen, 1976; Rotunno, 1980, 2013; Wilson & Rotunno, 1986) to reduce the speed of the wind, the approximate balance between the inward direction pressure-gradient force and the centrifugal force that exists above, where the effects of the surface are not felt, is disrupted because the latter is decreased. The result is that an inertial layer (Figure 11) is produced in which air accelerates inward toward the center, creating convergence and a further increase in vorticity. The inertial layer is characterized by both swirl (having an azimuthal wind component) and radial wind. In the inertial layer, the actual friction force is negligible. Near the surface, however, in the (surface) friction layer (Figure 11), the friction force and the pressure-gradient force act approximately to negate each other, and most of the airflow is radially inward with little, if any, swirl. There is recent evidence from the direction of fallen trees in tornadoes that the radial wind component near the ground is in fact greater than the azimuthal component (Karstens, Gallus, Lee, & Finley, 2013) (Figure 12).

Figure 13. Vertical cross section of equivalent radar reflectivity factor through a tornado in Attica, Kansas, on May 12, 2004, from a mobile, 3-mm wavelength, Doppler radar. Range markers are shown every 0.5 km.

Precipitation particles and debris caught in the vortex are centrifuged radially outward, leaving what appears on radar as a weak-echo hole (Bluestein et al., 2007a; Bluestein, Weiss, French, Holthaus, & Tanamachi, 2007b; Bluestein, Weiss, & Pazmany, 2003; Fujita, 1981; Snow, 1984; Wakimoto, Atkins, & Wurman, 2011; Wakimoto & Martner, 1992; Wurman & Gill, 2000) (Figure 1). The weak-echo hole closes up near the ground (Figure 13), probably as a result of the strong radial convergence in the friction layer. When a tornado creates airborne debris, a debris ball is detected at low radar elevation angles (Bluestein, 2013; Houser et al., 2015). Sometimes the weak-echo hole extends all the way up to the top of the parent storm as a weak-echo column (Tanamachi, Bluestein, Houser, Frasier, & Hardwick, 2012), where vorticity is much weaker than it is at the surface. It is therefore likely that vertical advection sustains the weak-echo column where centrifuging is not significant. The relative contributions of centrifuging and vertical advection (through updrafts or downdrafts) remain to be explained.

The depth of the friction layer for a vortex that is characterized by constant circulation increases with distance from the center (Burrgraf, Stewartson, & Belcher, 1971; Wilson & Rotunno, 1986). The depth of the inertial layer is much greater than that of the friction layer and does not vary much with distance from the center (Lewellen et al., 1997) (Figure 11). In real tornadoes, the depths of the friction layer and inertial layer have not been accurately measured.

For a vortex characterized by solid-body rotation, the analytical solutions (Bödewadt, 1940) are similar to those based on Ekman theory for synoptic-scale motions (Bluestein, 1992); the depth of the friction layer is , where $2Ω$ is the vorticity and ν is the kinematic coefficient of viscosity. In this case, there is a vertical circulation, inward flow below, upward flow at the center, and outward flow above, and there is “overshooting” of momentum surfaces radially inward (Figure 11b) (Rotunno, 2014).

Figure 14. Vertical cross section through a large-eddy simulation of a low–swirl ratio tornado. Vectors denote the wind. The vertical (z) and horizontal (x) axes are scaled by the core radius rc; x = 0 is at the origin (r = 0). The shaded gray scale is the magnitude of the wind scaled by the Doppler velocity at the core radius Vc.

Figure 15. Idealized vertical cross sections of flow in a tornado as a function of swirl ratio. The advectives “low,” moderate,” “high,” etc. are relative descriptors, not absolute. Based on Bluestein (2013), Davies-Jones (1986), Davies-Jones et al. (2001), and Wakimoto and Liu (1998).

As the radially inward flowing air accelerates toward the center of the axis of rotation, it must decelerate before reaching the center so that there is an adverse (opposite to the flow) dynamic radial pressure-gradient force near the axis of rotation. Air parcels must then turn upward in the corner flow region (Figures 11, 14, 15,). Such vortices are called one-cell vortices, describing the radial inward flow at low levels, upward flow at the center, radial outward flow aloft, and sinking motion at some distance from the center. For very low swirl ratios, boundary layer separation occurs (Figure 15) so that the air near the surface flows up and over the boundary layer (Davies-Jones, 1986).

As the swirl ratio is increased, an upward jet just above the ground is produced (Figure 14). A vortex column making contact with the ground induces an upward-directed, rotating jet called an endwall vortex (Rotunno, 2013). In a vortex for which there is cyclostrophic balance (a balance between the inward-directed pressure-gradient force and the outward-directed centrifugal force) and solid-body rotation, any axisymmetric contraction/expansion of the vortex through convergence/divergence excites vertically propagating centrifugal waves because, according to the Rayleigh criterion for azimuthal, inviscid flow

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the vortex is stable with respect to radial displacements.

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Figure 16. Photograph of a multivortex tornado near Verden, Oklahoma, during a tornado outbreak on May 3, 1999.

which is typically satisfied for both one- and two-celled vortices.

While the swirl ratio can be rigorously defined in a vortex chamber or the numerical model of a vortex chamber, in the real atmosphere it is more difficult to define. It probably depends on the buoyancy in the cloud above, the dynamic vertical perturbation pressure-gradient force, the depth and width of the boundary layer, and the surface roughness. The swirl ratio, however, is not the only parameter on which the flow pattern in a tornado depends (Lewellen, Lewellen, & Xia, 2000), which presents additional difficulty in understanding tornadoes based simply on the variation of parameters in controlled experiments.

Maximum Possible Wind Speeds

Figure 17. Radial profiles of azimuthally averaged azimuthal velocity (m s–1), radial velocity (m s–1), vertical vorticity (× 10 s–1), divergence (× 100 s–1), circulation (× 10–3 m2 s-1), and radar reflectivity factor (dBZe), from analyses of data collected at a low elevation angle in a tornado in northern Kansas on May 15, 1999, by a mobile, 3-mm wavelength Doppler radar. The circulation (proportional to angular momentum) increases radially outward until a bit beyond 100 m, after which it levels off at about 35,000 m2 s–1.

The maximum wind speeds possible in a single-cell, axisymmetric tornado occur when a material circuit containing circulation is contracted as far as possible. The circulation, as estimated from mobile Doppler radars, is approximately constant beyond some radius, the core radius (Tanamachi, Bluestein, Lee, Bell, & Pazmany, 2007) (Figure 17). For constant circulation, the azimuthal wind drops off as 1/r since $v(r)r=Γ∞/r$, where $Γ∞$ is the circulation of the “background” at $r=∞$. Outside the core, there is no vorticity since curvature vorticity cancels out the shear vorticity.

Since at the center of the tornado there must be no azimuthal wind and r = 0, the circulation/angular momentum must vanish. The azimuthal wind then increases from zero to $Γ∞/rc$, where rc is the core radius. The simplest solution is for the azimuthal wind in a steady state, axisymmetric vortex, is to vary linearly from 0 to vc, the azimuthal wind component at the core radius. A vortex in which the azimuthal wind varies linearly from zero to its core value and then drops off as 1/r beyond the core radius is known as a Rankine combined vortex (Rankine, 1882): Within the core, , where Ω is the solid-body rotation rate; outside of the core, . Observations from mobile Doppler radars indeed show that the azimuthal wind profile in tornadoes looks like that of a Rankine combined vortex (Figure 17). However, the peak in azimuthal wind is not as sharp, probably owing to radial diffusion (by sub-grid-scale eddies) of momentum. The Burgers-Rott vortex analytical solution (Burgers, 1948; Rott, 1958), which allows for diffusion of azimuthal momentum, is similar to what is observed; but vertical motion is upward and unbounded. The more complicated Sullivan vortex allows for both upward and downward motions (Sullivan, 1959).

Since the Rayleigh criterion for stability is satisfied in a Rankine combined vortex, it takes work to contract a ring of material radial inward. The work it takes to contract a ring at the core radius inward to radius r¢ (Bluestein, 2013) is

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As r¢ → 0, the work required →∞. The work that drives the inward displacement of fluid is the work realized by buoyancy above in the parent cloud. A crude measure of how high the winds can be in a tornado is given by the thermodynamic speed limit. While tornadoes are not hydrostatic, a rough estimate of the lowest wind speeds possible is obtained by assuming that atmosphere is hydrostatic, the tornado vortex is in cyclostrophic balance, and the vortex is in solid-body rotation (Lilly, 1969; Snow & Pauley, 1984). It is found that the highest wind speed is

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In such a tornado vortex, the pressure drop at the center (with respect to the pressure “outside” the tornado), at the surface, is

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For vmax ~ 100 m s–1, the pressure drop is ~100 hPa, which has been measured using portable instruments placed in the path of tornadoes (Karstens et al., 2010; Winn et al., 1999).

From mobile Doppler radar measurements of wind speeds in tornadoes and nearby soundings, it has been found that the thermodynamic speed limit is usually exceeded (Bluestein, Unruh, LaDue, Stein, & Speheger, 1993). The simple reason it is exceeded is that a tornado is far from being hydrostatic and for a low-swirl ratio vortex air is drawn radially inward to a smaller radius than would otherwise happen owing to the upward jet, which is driven by an upward-directed dynamic perturbation pressure-gradient force. It has been demonstrated by numerical experiments that the highest possible azimuthal wind speeds occur in an endwall vortex when there is vortex breakdown just above the ground (Fiedler, 1994; Fiedler & Rotunno, 1986). In this case the depth of the tornado boundary layer is “matched” dynamically to the core radius of the vortex aloft, and maximum azimuthal wind speeds of approximately twice the thermodynamic speed limit can be realized.

It therefore appears as if the characteristics of the boundary layer flow affect whether or not a parent storm–produced mesocyclone (or preexisting vortex) can be intensified to tornado strength. When the inflow of angular momentum at large radius is impeded, the inward acceleration of air is increased so that air penetrates to a smaller radius and the vortex intensifies through a process called corner flow collapse (Lewellen & Lewellen, 2007a, 2007b). It has been hypothesized that this process may be triggered when the RFD wraps completely around a low-level mesocyclone or when the surface roughness changes. The tornado’s ultimate maximum intensity is limited because as the surface vorticity becomes substantially greater than that aloft, a downward-directed perturbation pressure-gradient force (exceeding the upward force of buoyancy aloft) shuts off the upward jet (Wicker & Wilhelmson, 1995). It is noteworthy that as the RFD wraps around the low-level mesocyclone, corner flow collapse may occur, while at the same time the vortex is cut off from warm, moist environmental air, needed for buoyancy aloft. It is not known to what extent the end of development (or dissipation) is from dynamic rather than thermodynamic factors.

Figure 18. (a) Photograph of the beginning of a tornado near Cordell, Oklahoma, on May 22, 1981. (b) Mature stage of the Cordell tornado. (c) Decaying stage of the Cordell tornado.

(All photographs © Howard B. Bluestein)

Tornadoes in supercells often progress through an evolution with well-defined stages (Figure 18). The first evidence of a tornado may be a rotating debris cloud at the ground (Figure 18a), followed by a funnel aloft that eventually becomes continuous down to the ground (Figure 18b). The funnel cloud widens as the tornado reaches maturity. As the tornado begins to decay, the funnel cloud narrows and leans with height (Figure 18c), owing to its movement near the ground as it is pushed outward from the parent storm by a rear-flank gust front, which wraps completely around the tornado.

Figure 19. Multiple surges behind the rear-flank gust front in a tornadic supercell, as documented by two mobile Doppler radars in northwest Texas on April 30, 2000. The storm-relative wind field is depicted by vectors. Convergence is coded by gray shading. Solid lines represent the primary forward-flank and rear-flank gust fronts, though only a gradual wind shift is evident in the forward flank. The secondary, rear-flank gust front is shown as a dashed line. Equivalent radar reflectivity factor is contoured every 5 dBZe, beginning at 20 dBZe.

The rear-flank gust front is sometimes accompanied by a descending reflectivity core (Byko, Markowski, & Richardson, 2009; Kosiba et al., 2013; Markowski et al., 2012; Rasmussen, Straka, Gilmore, & Davies-Jones, 2006), which may act to intensify convergence along the rear-flank gust front; the intensification may be a result of an enhancement of negative buoyancy associated with precipitation loading and evaporative cooling as the precipitation falls into unsaturated air below. The “straight-line” flow of air that wraps around the edge of the tornado and low-level mesocyclone may be very strong and inflict damage, making it difficult to ascertain from damage surveys conducted after a tornado has struck whether the damage had been done by the tornado or straight-line winds (Karstens et al., 2013; Mahale et al., 2012). Sometimes there are multiple internal momemtum surges behind the leading edge of the rear-flank gust front (Houser et al., 2015; Kosiba et al., 2013; Skinner et al., 2014) (Figure 19), which may play a role in tornadogenesis, which is not well understood.

A series of vortices often appears along the rear-flank gust front (Bluestein et al., 2003), which sometimes has the character of a vortex sheet (Markowski, Richardson, & Bryan, 2014) and may play some role in tornadogenesis by providing the “seed” vorticity that is amplified to tornado intensity or may just simply accompany the rear-flank gust front independently of whether or not tornadoes form. These vortices are thought to occur as a result of barotropic instability associated with the shear across the gust front or a combination of shear and lobe and clefts created at the leading edge of the cooler air (Lee & Wilhelmson, 1997). The mechanism for the formation of these vortices may be the same as that for the formation of tornadoes in ordinary cell convective storms. Short-lived, relatively weak vortices along the gust front that do not have any connection to the clouds above are called gustnadoes (Bluestein, 1999b).

Figure 20. Idealized models of cyclic mesocyclogenesis (top and middle panels) and effects of hodograph shapes and lengths (bottom panel). The cold pool boundary is indicated by a cold front symbol. Red area indicates vorticity maxima. Light blue indicates updraft areas; dark blue indicates downdraft areas. Yellow contour marks the rain boundary. (top) Occluding cyclic mesocyclogenesis. (middle) Nonoccluding cyclic mesocyclogenesis.

While in many instances a supercell produces one tornado that progresses through its life cycle, in other instances a series of tornadoes, one after another, form, each one progressing through its own life cycle (Dowell & Bluestein, 2002a, 2002b). Cyclic tornadogenesis (and mesocyclogenesis) can result in very long damage paths, which are actually caused by a succession of tornadoes rather than one long-track tornado. There are two main types of cyclic tornadogenesis associated with cyclic mesocyclogenesis (Figure 20) (Adlerman & Droegemeier, 2005; Adlerman, Droegemeier, & Davies-Jones, 1999; French et al., 2008): (1) occluding cyclic mesocyclogenesis (OCM) and (2) nonoccluding mesocyclogenesis (NOCM). Each is affected by the behavior of the rear-flank gust front.

In the case of commonly observed OCM, a new mesocyclone forms along the tip of the surge of the gust front and a new updraft forms, leading to a new tornado, as the previous tornado migrates rearward with respect to new mesocyclone and dissipates. In the case of NOCM, the mesocyclone propagates forward along the forward flank of the supercell and weakens, while a new mesocyclone forms to the rear. There is numerical evidence that OCM tends to occur in environments in which the hodograph is highly curved, while NOCM tends to occur in environments for which the hodograph is relatively straight or is curved only at low levels. As overall vertical shear increases, OCM becomes less likely, NOCM occurs for the less curved hodographs, and more steady mesocyclones occur for the more curved hodographs.

Figure 21. Idealized illustration of vortex lines in a supercell, showing the arched vortex line along the leading edge of the rear-flank gust front with the production of an anticyclonic vortex at the far end of the gust front and a cyclonic vortex at the other end, near the wall cloud. Initially, a circular vortex ring is produced around the rear-flank downdraft (RFD), which drops downward and spreads out (the numbers refer to a sequence in time), but the leading edge is tilted upward by the updrafts associated with the flanking line. FFD, forward-flank downdraft.

In supercells, horizontal vorticity is generated baroclinically along the leading edge of the rear-flank gust front when the air from the RFD is relatively cool (Markowski et al., 2008; Straka, Rasmussen, Davies-Jones, & Markowski, 2007) (Figure 21). Anticyclonic vorticity is generated through tilting at the farthest (from the supercell main updraft) end of the flanking line (Moller, 1978) of cumulus towers. Where the flanking line merges with the main updraft, at the other end, cyclonic vorticity is generated through tilting. It is also possible that anticyclonic vorticity is generated through tilting at the farthest end of the flanking line at the edge of a downdraft acting on environmental vorticity that is of the opposite sign to that generated baroclinically. An anticyclonic-vortex couplet is frequently observed at low levels, and a jet associated with the RFD separates the two vortices. On some rare occasions, for reasons not well understood, the anticyclonic vortex attains tornado intensity after a cyclonic tornado has been observed near the main updraft (Bluestein, 2013; Bluestein et al., 2015; Brown & Knupp, 1980; Fujita, 1981; Wurman, Kosiba, Robinson, & Marshall, 2014). The motion of each of the two tornadoes is usually different as the anticyclonic tornado propagates to the right of the motion of the cyclonic tornado. The differential motion presents a difficulty when weather forecasters issue tornado warnings for the parent storm: the cyclonic tornado tends to move along with the parent storm, while the anticyclonic tornado does not. How to forecast anticyclonic tornadoes is not known.

Avenues of Future Research and Instrument Development

There are a number of emerging areas of research and opportunities for new instrumentation development to further our understanding of severe convective storms and tornadoes. The following are some topics for future consideration:

Expanded Use of Polarimetric Data from Radars: Identification of Hydrometeors and Assimilation into Storm-Scale Numerical Models

Fuzzy logic identification of hydrometeor type (Snyder et al., 2010) and the subsequent correlation between hydrometeor type around the hook echo region (Kumjian, 2011) and tornado occurrence would provide evidence as to whether or not tornadogenesis is more likely when there are larger raindrops, which are not as prone to evaporative cooling as smaller raindrops (French et al., 2014b).

In addition to assimilating radar reflectivity and Doppler velocity into numerical cloud models, the assimilation of polarimetric variables could have an effect on the three-dimensional distribution of meteorological variables (Jung, Xue, Zhang, & Straka, 2008). Thus, the use of independent polarimetric data as an additional constraint might prove to be helpful in studies using Doppler radar data.

Finer-Scale Numerical Simulations of Supercells and Tornadoes: Examination of Boundary-Layer Processes and Coupling between the Tornado and Its Parent Storm

Currently, numerical models simulate supercells and barely have fine enough resolution to produce tornadoes. LES models of tornadoes, which do resolve tornadoes, are not coupled to their parent supercell, so there is no feedback allowed between the tornado and its parent storm. As computer storage capacity and speed increase, it will be possible to simulate an entire storm and its smaller-scale tornado on a fine enough spatial scale to resolve both. It may also be possible to simulate the effects of surface friction more realistically (Nowotarski, Markowski, Richardson, & Bryan, 2014, 2015) and see how the structure of the boundary layer and surface friction affect tornadogenesis (Schenkman, Xue, & Hu, 2014) and tornado structure (Fiedler & Garfield, 2010), while the tornado is coupled to the parent storm. Future studies of storm-scale vortices in supercells and tornadoes must also account for asymmetries in the flow, something for which little has been done, even though most tornadoes appear to be embedded in inhomogeneous environments.

Improved Representation of Cloud and Precipitation Microphysics in Numerical Models: Spectral Bin Models

Most simulations of supercells use parameterizations of microphysics (Kessler, 1969) that suffer from various inaccuracies resulting from an assumed (limited) drop-size distribution (Milbrandt & Yau, 2005). While microphysics models that incorporate separate “bins” for a wide range of particle sizes (and types) exist (Kumjian et al., 2014; Li, Tao, Khain, Simpson, & Johnson, 2009), coupling the microphysical models with three-dimensional dynamic models is not currently done very much, owing to the large amount of computer storage capacity and storage needed. As computers become larger and faster, it will become possible to simulate supercells with much more realistic microphysics and therefore more accurately reproduce the variety of precipitation distributions found in supercells (Rasmussen & Straka, 1998).

Use of Airborne Platforms to Make In Situ Measurements and Radar Measurements in Severe Storms

Making thermodynamic measurements at low level in the cold pool in the forward and rear flanks of supercells is important for verifying the role of the intensity of the cold pools in supercells in fostering or inhibiting tornadogenesis. Ground-based mobile mesonets sometimes have difficulty making measurements in the needed locations because the road network is inadequate. Low-flying unmanned aerial vehicles (UAVs) should be able to make in situ measurements without having any road network problems. However, getting permission to fly UAVs in advance is a challenge in some areas (Houston et al., 2012), and avoiding areas where large hail and very strong winds will be necessary to avoid crashes.

Helicopters have been used to fly near tornadoes and provide stunning video while maintaining a nearly stationary position. It might be possible to develop small, low-power, pulse compression radars to probe tornadoes at low levels from relatively close range without having to contend with difficult road networks and storm-chaser traffic. The biggest challenges will be to keep the system small and lightweight and to be immune to contamination from the rotor blades.

Although airborne radars must fly by storms, rapid-scan radars should be mounted on aircraft to allow for as many looks at the storm flow as possible while near a storm.

Expanded Use of Ground-Based Mobile Platforms to Make In Situ Measurements in Severe Storm Environments

Since supercells change their characteristics when their environment changes, it is necessary to probe the thermodynamic and wind shear profiles near and around them. Mobile, ground-based wind and thermodynamic profiling systems are needed to make these measurements. In addition, they can provide data on the presence of and possible role of gravity waves in supercell behavior (Coleman & Knupp, 2008; Lehmiller, Bluestein, Neiman, Ralph, & Feltz, 2001).

Instrumented kites have been around for a century or more, but now they can be made out of modern materials and equipped with modern instrumentation. Balsley, Jensen, and Frehlich (1998) have described the use of kites for fine-scale measurements in the atmospheric boundary layer. It would be a challenge to develop deployable kites that can withstand high winds and that do not pose a hazard from utility lines, trees, and lightning.

Extremely small, instrumented, airborne probes each equipped with accurate Global Positioning System–determined locations could be used to swarm areas of severe storms to make in situ thermodynamic measurements. It would again be a challenge to release the sensors and integrate all the data, if it becomes possible to implement the devices.

Warn-on-Forecast Improvements: Expanded Use of Ensemble Storm-Scale Numerical Modeling

Numerical models are not capable of predicting the exact location of the formation of storms or their evolution (Bluestein 2009; Brooks, Doswell, & Maddox, 1992). Forecasts of the possibility of supercell tornadoes in the Plains of the United States are made if the large-scale conditions for supercell formation (high shear, at least moderate CAPE, adequate boundary layer moisture, and a means of initiating storms) are present or forecast by models. Watches are issued for broad areas by the National Oceanic and Atmospheric Administration’s Storm Prediction Center if the possibility is considered high enough. Warnings are issued for localized areas when tornadoes are reported or likely if a TVS (and TDS) is observed on surveillance radar.

Simulating the uncertainty of numerical forecasts that result from uncertainty in initial conditions and microphysical and boundary layer parameterizations will aid us in assigning probabilities to the occurrence of tornadoes and other severe weather phenomena as forecast by cloud-allowing numerical forecast models. With an increase in computer storage capacity and speed, we will be able to increase the number of members of the ensemble to get more accurate estimates of probabilities and reduce the grid spacing to 100 m so that the supercells are more accurately represented and warnings may be issued further in advance based on model forecasts rather than with shorter lead times based on actual observations (Stensrud et al., 2009).

Experiments with Infrasound Detection and Signatures in Severe Convective Storms and Tornadoes

There is some evidence that supercells and tornadoes emit infrasound and that infrasound signatures may harbor information about the presence of or likelihood of severe weather (Bedard, 2005). The theoretical basis for signatures and experimental procedures could be developed further to test hypotheses that the signatures have predictive value.

Cloud Electrification Measurements and Modeling

There is no evidence that electrical effects are directly important for tornadogenesis (Davies-Jones, 1986). However, measurements have been made in supercells using electrical field meters carried aloft by balloons (MacGorman et al., 2005). More work should be done to add to our knowledge on how lightning activity is related to storm processes. In addition, lightning data have been assimilated into cloud models in attempts to improve numerical forecasts (Kuhlman, Ziegler, Mansell, MacGorman, & Straka, 2006; Mansell, Ziegler, & MacGorman, 2007). It is possible that changes in lightning characteristics may be related to tornadogenesis as a byproduct.

The Relationship between Updrafts, Downdrafts, and Tornadogenesis as Detected from Above by Satellites

Geostationary satellites that can sense the infrared cloud-top temperature with high temporal resolution can provide information on storm updrafts and downdrafts near storm top and how they are related to tornadogenesis. While tornadogenesis is inherently a low-level process, there is some evidence that downdrafts and collapsing updrafts play a role (Fujita, Forbes, & Umenhofer, 1976). Such satellites may become available in the coming years. Aircraft, both manned and UAVs, could fly over storms with downward-looking radars to provide information on updrafts and downdrafts.

Use of a Pulsed Doppler Lidar to Probe Tornadoes Near the Ground

It is difficult to measure the vertical variation of the wind in the surface friction layer and in the lower portion of the inertial layer in tornadoes using radars, owing to ground-clutter contamination from sidelobes. In some instances in situ measurements at the surface have complemented Doppler radar observations higher up (Kosiba & Wurman, 2013), but the natures of in situ and radar measurements are different (Snyder & Bluestein, 2014). It would be advantageous to use lidars, whose beams are narrow (~20 cm) and collimated so that data can be collected with ultrahigh vertical resolution in the boundary layer (Bluestein et al., 2014). While lidars are not subject to ground-clutter contamination, they cannot penetrate far into regions of precipitation, cloud particles, and probably debris.

The above list is not exhaustive but does contain projects that are most likely possible in the next decade.

Acknowledgments

The author’s research on severe convective storms and tornadoes has been supported, for over three decades, by the National Science Foundation and by the University of Oklahoma in Norman. The author is indebted to his current and former graduate students and to his colleagues at the National Center for Atmospheric Research in Boulder, Colorado, and the National Severe Storms Laboratory in Norman, Oklahoma, for their collaboration and support for many years.

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