1. Introduction
The collocation of positive vertical velocity (w) and vertical vorticity (ζ) in a supercell is known as a “mesocyclone,” and has been a primary focus of supercell research for several decades (Browning 1964; Davies-Jones 1984, 2002; Rotunno and Klemp 1982, 1985; Markowski and Richardson 2014; Dahl 2017). The low-level mesocyclone is of significant interest, due to its connection with tornadoes (Adlerman et al. 1999; Coffer et al. 2017; Murdzek et al. 2020; Flournoy et al. 2020; Peters et al. 2023), and the strength of low-level mesocyclone rotation has an established connection to low-level preexisting environmental and baroclinic horizontal vorticity (ωh; Klemp and Rotunno 1983; Davies-Jones 1984, 2022; Rotunno and Klemp 1985; Dahl et al. 2014; Dahl 2015; Coffer and Parker 2015; Peters et al. 2020b; Goldacker and Parker 2021; hereafter, “preexisting environmental horizontal vorticity” is referred to as simply “environmental vorticity”). While the tilting of low-level (i.e., 0–3 km AGL) environmental vorticity associated with the background vertical wind shear is understood to result in the development and maintenance of the midlevel mesocyclone (Rotunno 1981; Rotunno and Klemp 1982; Davies-Jones 1984), the influence of environmental vorticity at midlevels (e.g., 3–6 km AGL) on the midlevel mesocyclone is less understood.
The potential importance of vertical wind shear at midlevels (hereafter “midlevel shear”) is heightened by the fact that vorticity within the midlevel mesocyclone plays a role in determining vertical pressure gradient accelerations, which are known to influence the strength of the updraft (Rotunno and Klemp 1982; Brandes 1984; McCaul and Weisman 1996; Weisman and Rotunno 2000; Goldacker and Parker 2021). Several studies have found that alignment of the midlevel mesocyclone with the low-level mesocyclone is necessary for low-level updraft intensification (Dowell and Bluestein 2002; Skinner et al. 2014; Marquis et al. 2016; Guarriello et al. 2018; Brown and Nowotarski 2019). Peters et al. (2020b) noted that most air participating in updraft vertical vorticity maxima at 4–8 km AGL originated from above 2 km AGL, suggesting that tilted environmental vorticity originating from levels higher than often studied plays a nonnegligible role in the midlevel mesocyclone and associated low pressure. Motivated by these issues, in this study we examine the influences of midlevel environmental vorticity on supercell updrafts and characteristics.
Unlike at low levels, midlevel environmental vorticity exists in a layer that typically has no convective available potential energy (CAPE). Thompson et al. (2007) defined the conditionally unstable layer that provides the vast majority of parcels participating in the updraft core (Nowotarski et al. 2020) as the “effective inflow layer” (EIL), which is typically contained below 3 km. To evaluate the effect of midlevel environmental vorticity on a supercell’s updraft, we must consider the entrainment of above-EIL air, which, by definition, has less CAPE than EIL air.
The effects of entrainment have been a focal point of studies on cumulus parameterization and tropical convection for decades (Emanuel 1991; Lin and Arakawa 1997a,b; Zipser 2003; Romps and Kuang 2010; de Rooy et al. 2013; Morrison 2016a,b, 2017). In the severe storms community, the effects of entrainment on precipitation intensity, appearance, and hazards of severe thunderstorms have been examined in many previous studies (Bluestein and Parks 1983; Bluestein and Woodall 1990; Gilmore and Wicker 1998; James and Markowski 2010; Grant and van den Heever 2014), but have only been rigorously applied to severe thunderstorm updraft thermodynamics in recent years (Peters et al. 2019, 2020b,c, 2022a,b,c; Lasher-Trapp et al. 2021; Jo and Lasher-Trapp 2022, 2023; Mulholland et al. 2021). These previous studies have primarily focused on the thermodynamic effect of entrainment, which entails a reduction of buoyancy and precipitation efficiency. While increased shear results in greater wake entrainment at early stages (LeBel and Markowski 2023), supercell updrafts usually become wide enough to resist any deleterious effects. Any kinematic influence of entrained vorticity-rich air during the mature stage remains ambiguous, and observed supercell proximity soundings often show large shear and associated environmental vorticity in the middle troposphere (Maddox 1976; Parker 2014; Coniglio and Parker 2020). While the entrainment of midlevel air is locally detrimental to the buoyancy of an updraft, tilted midlevel environmental vorticity could enhance the pressure perturbation associated with the midlevel mesocyclone, ultimately increasing updraft strength. Therefore, we will examine the following hypothesis: Increasing midlevel shear enhances the midlevel mesocyclone.
To examine this hypothesis, an intuitive first step would be to consider the relationship between updraft vertical vorticity and midlevel shear (MLS; for simplicity, we treat MLS as a time-independent, fixed environmental parameter herein). However, compared to an environment with small MLS, an environment with large MLS (and midlevel environmental vorticity) requires faster mid- and upper-level winds, resulting in a faster storm motion relative to the low-level hodograph. Therefore, any influence of MLS and tilted environmental vorticity on a mesocyclone could be conflated with influences from altered storm-relative variables. The effect of increasing MLS on storm-relative variables becomes apparent when considering a vertical shear profile representative of observed Northern Hemisphere supercell events, where shear is predominantly southerly below 1 km and veers to attain a larger westerly component above 1 km (Maddox 1976; Davies-Jones 1984; Parker 2014; Coniglio and Parker 2020). In such a vertical shear profile, increasing westerly shear above 1 km results in a storm motion that is more removed from the low-level hodograph (i.e., lowest 0–1 km AGL), meaning that low-level storm-relative flow (LL SR flow) has increased. This relationship is visible in Fig. 1, discussed in detail in section 2, and is borne out in the idealized simulations of Brooks et al. (1994), Warren et al. (2017), and Peters et al. (2019), where increasing deep-layer shear results in larger LL SR flow, which has an established relationship with supercell updrafts.
Hodograph and skew T. The H1–H5 labels demarcate the 6-km wind for each respective hodograph. The first fuchsia dot on the hodograph indicates the 250-m wind, where clockwise curvature with height begins. All storm-relative calculations use the Bunkers RM motion. The dashed red line indicates virtual temperature. NCAPE is the CAPE divided by the depth between the LFC and EL. Hodograph rings are every 10 m s−1.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
Davies-Jones (1984) and Droegemeier et al. (1993) noted that LL SR flow must exceed a threshold for supercell maintenance, often around 10 m s−1. Warren et al. (2017) found that simulated supercell updrafts grew wider as LL SR flow increased, resulting in larger vertical mass flux and hydrometeor production. Peters et al. (2019) affirmed this relationship, demonstrating that increased updraft width (a product of increased mass flux via increased LL SR flow and inflow) leads to updraft cores that are more sheltered from entrained air, and these less-diluted updraft cores have larger buoyancy (Morrison 2017; Morrison et al. 2020; Peters et al. 2020c). The decreased interaction of entrained midlevel air with the cores of wider updrafts is a focal point of our analysis, since this implies that the cores of wider updrafts have little interaction with midlevel environmental vorticity. Furthermore, updraft width has been connected to downdraft size and buoyancy perturbations in cold pools (Marion and Trapp 2019) and off-hodograph propagation (Davies-Jones 2002).
Given the structure of a typical supercell-supportive hodograph, an increase in MLS results in an increase in both midlevel environmental vorticity and LL SR flow (Fig. 1). These two variables are physically connected, and holding LL SR flow constant while MLS increases would require changing shear over other layers (and unrealistic hodographs). Therefore, we intentionally do not perform an experiment where the effect of MLS is isolated. Assuming that the effect of tilted midlevel environmental vorticity is generally similar to that of low-level environmental vorticity (i.e., locally large vertical vorticity), increasing MLS, by virtue of its connection with LL SR flow, will lead to multiple distinct influences on supercell characteristics. LL SR flow exerts a large control on updraft width, while midlevel shear likely influences updraft rotation. To thoroughly evaluate the influence of MLS on supercells, the unique influences of each variable must be examined. Therefore, in this study we address two questions:
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How does tilted midlevel environmental vorticity influence a supercell mesocyclone?
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How does low-level storm-relative flow modulate the updraft and influence of tilted midlevel environmental vorticity?
Output from a matrix of simulated supercells is used to address these questions. In addition to differences between simulated supercells caused by variations in MLS and LL SR flow, we find regions of large storm-generated horizontal vorticity at midlevels that play a role in updraft dynamics. These findings are discussed in detail.
2. Methods
a. Model details
To answer our questions, we ran and investigated a matrix of 10 simulated supercells in environments with varied MLS and relative humidity (RH). All simulations were performed using Cloud Model 1 (CM1; Bryan and Fritsch 2002) version 21.0. Storms were simulated within a 120 km × 120 km × 18.5 km storm-following domain, with 250-m horizontal grid spacing and constant 100-m vertical grid spacing, a grid capable of sufficiently resolving finescale, turbulent convective processes (Lebo and Morrison 2015). The lowest model level was 50 m. The upper and lower boundary conditions were free slip, and lateral boundary conditions were open radiative. Rayleigh damping was applied above 15 km. Morrison double-moment microphysics (Morrison et al. 2009) were used, simulations were run for three hours, and data files were saved every five minutes. A warm bubble (Klemp and Wilhelmson 1978) was used to initiate convection, with a +5-K temperature perturbation and depth of 1400 m, similar to Parker (2017), but with a width of 10 km. The namelist.input file and model soundings can be accessed through the repository linked in the data availability statement.
b. Choosing the thermodynamic profile and hodograph
We used two modified versions of the VORTEX-2 composite, tornadic near-field thermodynamic profile (Parker 2014) for our simulations (Fig. 1). One profile contains high 3–6-km RH (81%, layer averaged), and the other contains low 3–6-km RH (26%, layer averaged). Several test runs proved warm bubble convection initiation (CI) to be exceedingly difficult in the unmodified VORTEX-2 thermodynamic profile due to dry air. To facilitate CI, the 0–1-km mixing ratio was increased by 1 g kg−1 relative to the original sounding, and we nonuniformly increased the mixing ratio in the 1–3-km layer through a process of trial and error. These two modifications facilitated warm bubble CI and storm maintenance, even in the presence of the added midlevel dry layer. Low free-tropospheric RH is known to be detrimental to updraft buoyancy, particularly when updrafts are narrow (Morrison 2017). In contrast, high free-tropospheric RH can support updrafts at even very narrow widths (Morrison et al. 2020, 2022; Peters et al. 2020c, 2022b,c). For our purposes, midlevel RH was varied as an experimental parameter to influence the dilution of the updraft core by entrained midlevel air and characterize how this impacts its interaction with the associated vorticity.
The vertical wind profile is based on the Rotunno and Klemp (1982) quarter-circle hodograph but is modified to better represent observed hodographs in supercell events, primarily those in the Great Plains during spring (Fig. 1; e.g., Coniglio and Parker 2020; Parker 2014; Maddox 1976). All curvature is concentrated below 1 km, but above a layer of unidirectional, southerly shear from 0 to 250 m, as in the composite supercell sounding of Coniglio and Parker (2020). The 0–3-km segments of each hodograph are identical for each ensemble member, with shear and ground-relative wind speeds roughly consistent with the values of the dataset in Coniglio and Parker (2020). There is no shear above 6 km in any simulation as the wind is held constant at its 6-km value.
MLS (henceforth referring to bulk wind difference the 3–6-km layer) is westerly and unidirectional in all simulations, and increases from 0 to 30 m s−1 driving an increase in 3–6-km environmental vorticity from 0 to 0.01 s−1 across five unique hodographs (H1–H5). As MLS increases, the storm motion increases relative to the low-level hodograph, increasing LL SR flow, akin to Brooks et al. (1994) and Warren et al. (2017). Using the storm motion predicted by the method in Bunkers et al. (2000, 2014), the 0–0.5- and 0–1-km streamwise vorticity magnitude is held nearly constant; the largest difference between any two hodographs is less than 5%. Low-level storm-relative helicity (SRH; Lilly 1986a,b; Davies-Jones et al. 1990) increases incrementally between H1 and H5, but is driven only by an increase in LL SR flow, not streamwise vorticity. The only layer where environmental vorticity changes across simulations is the midlevels, lending confidence that any rotational differences between simulated updrafts are the result of variations in MLS, LL SR flow, or stochastic internal storm processes (Coffer et al. 2017; Flournoy et al. 2020; Markowski 2020; Lyza et al. 2022). Two different thermodynamic profiles and five different hodographs resulted in a suite of 10 simulations driven from unique initial model profiles, the output of which is analyzed in the following section. Individual members are referred to by their hodograph (e.g., H2) and midlevel RH value (e.g., “dry” or “moist”).
Many previous supercell modeling studies have focused on tornadogenesis in environments characterized by high-end values of shear and SRH (Klemp and Rotunno 1983; Wicker and Wilhelmson 1995; Schenkman et al. 2014; Orf et al. 2017; Coffer and Parker 2017; Flournoy et al. 2020). To better represent environments associated with the majority of supercells, which tend to be nontornadic (Trapp et al. 2005), our hodographs contain values of low-level shear and SRH that fall within the middle 50% of nontornadic or weakly tornadic supercell environments in large datasets of modeled and observed proximity soundings (Rasmussen and Blanchard 1998; Thompson et al. 2007; Nixon and Allen 2022), and are similar to the two most common hodographs from Warren et al. (2021, see their Figs. 4 and 6).
c. Diagnosing dynamical contributions to vertical velocity
From Eq. (1),
d. Updraft tracking, time averages, and tracers
To assess general updraft characteristics, we analyze several time-averaged variables. We define the center of the updraft as the centroid of all locations where vertical velocity exceeds the 75th-percentile value of all 3–6-km layer-averaged vertical velocity values larger than 5 m s−1 within the right-moving storm, similar to the method used by Warren et al. (2017). Several other methods for tracking the updraft center were tested, but this method produced time-averaged data that best reflected trends and features across manually inspected individual time steps. All time-averaged plots consist of data from each time step centered on this updraft center point and averaged over the corresponding length of time, but most plan views and cross sections display data at a single time step so that the clarity of finescale, often brief processes is preserved. General updraft metrics (e.g., rotational velocity) are computed for each time step and then divided by the corresponding length of time.
At t = 0 min, passive tracers were initialized from 0 to 2.5 km (∼90% of EIL depth) and 3–6 km AGL (midlevels), allowing us to isolate regions where midlevel air has mixed with CAPE-rich air originating from the EIL, and where EIL air has ascended through the midlevels without dilution. This allows us to separate the updraft into regions that have and have not been influenced by entrained midlevel air and the associated environmental vorticity.
3. Results
a. How does tilted midlevel environmental vorticity influence the midlevel mesocyclone?
Each of the 10 simulations contain discrete, right-moving supercells exhibiting continuous regions of mesocyclone-strength vertical vorticity [>0.005 s−1; the threshold used by Davies-Jones (1984) to define a mesocyclone] extending throughout several kilometers of the updraft (a view of the midlevel mesocyclones is provided in Fig. 2). Our mentions of “midlevel mesocyclone” primarily refer to the region of generally positive vertical vorticity contained within undiluted EIL air at midlevels, where the tilting of low-level environmental vorticity is commonly understood to result in rotation (e.g., Rotunno and Klemp 1982; Davies-Jones 1984). These supercells persist through at least t = 120 min, after which the simulated storms in the H1 and H2 environments weaken considerably. Therefore, our analysis focuses primarily on the t = 1–2-h period.
16 × 16 km2 plan views for each storm at 6 km AGL, displayed at the time of maximum 6-km rotational velocity for each storm within the t = 1–2-h period, showing vertical vorticity (red to blue fill), where vertical velocity equals 10 m s−1 (gray contour), the outline of where EIL tracer concentration exceeds 99% (dashed black contour), and storm-relative winds (vectors, plotted every 1 km with darker vectors indicating larger vertical velocity). (a),(c),(e),(g),(i) Simulations where midlevel RH is low are denoted by brown text, and (b),(d),(f),(h),(j) simulations where midlevel RH is high are denoted by green text.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
At 6 km AGL, vertical vorticity maxima in each storm occur where EIL air has mixed with entrained above-EIL air (i.e., outside of the >99% EIL tracer concentration contour, Fig. 2), suggesting that the tilting of midlevel environmental vorticity may contribute to local maxima in vertical vorticity. This is corroborated by the simulations of Peters et al. (2020b, their Figs. 17c,d) and the radar observations of Cai and Wakimoto (2001, their Fig. 11a), who found large vertical vorticity at the edge of the midlevel updraft in environments with large MLS. However, the largest values of vertical vorticity actually occur within the diluted midlevel updraft in the H2-moist case (Fig. 2d), even though MLS is small (as well as in the other H2 and H1 cases, but the extent of undiluted EIL air at 6 km is very small in those updrafts). Furthermore, pronounced vertical vorticity minima often occur near the maxima, and in some cases are larger in magnitude than any nearby positive vertical vorticity.
These results warrant a more objective analysis of mesocyclone strength within the 10 simulations. To do this, we analyze trends in rotational velocity [calculated as
Midlevel shear vs 6-km rotational velocity, averaged over the t = 1–2-h period, (a) within the entire updraft (where w exceeds 10 m s−1), (b) within the part of the updraft where EIL tracer concentration exceeds 99%, and (c) within the part of the updraft where midlevel tracer concentration exceeds 1%. The Pearson and Spearman rank correlation coefficients and p values are displayed on the right side of each plot, with boldface text atop an unhatched background indicating statistical significance. Warm colors behind the values indicate positive correlation coefficients, with values closer to 1 appearing atop red backgrounds, and cool colors behind the values indicate negative correlation coefficients, with values closer to −1 appearing atop dark blue backgrounds.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
Within the region of the 6-km updraft that has mixed with midlevel air, and therefore is directly influenced by MLS, there is a weak negative correlation between MLS and rotational velocity (Fig. 3c). This continues to indicate that increasing MLS does not lead to an increase in cohesive updraft rotation. Even without considering the particularly weak rotational velocities of the diluted H5 updraft regions, there is no trend in rotational velocity across the simulations, despite a 20 m s−1 difference in MLS. When averaging variables over the 3–6-km layer, each of the results presented in Fig. 3 hold true.
While Fig. 3 suggests that increasing midlevel environmental vorticity does not lead to increased updraft rotation, the presence of vertical vorticity maxima outside of the undiluted EIL air in Fig. 2 suggests perhaps a more localized influence of MLS. To investigate this, we analyze vertical cross sections passing south to north through the midlevel updraft (Fig. 4) along the paths plotted in Fig. 2. The tilting of midlevel environmental vorticity is indicated by hatched regions within the dashed black contour on the south (left) side of the midlevel updraft. In each of the H4 and H5 simulations (Figs. 4g–j), local vertical vorticity maxima of 0.02–0.05 s−1 can be found where midlevel tracer concentration exceeds 25% in the vicinity of positive tilting, indicating that the tilting of midlevel environmental vorticity is at least partially contributing to a local increase in vertical vorticity on the southern edge of the updraft. This signal is less evident in the H1 and H2 simulations (Figs. 4a–d); the largest values of vertical vorticity tend to reside outside of the midlevel air. The vertical vorticity pattern in those updrafts, however, tends to be more complicated and difficult to interpret, perhaps indicative of a thermal chain-like structure characteristic of narrower updrafts (e.g., Peters et al. 2020c).
South-to-north (left to right in each panel) vertical cross sections through each updraft at its time of maximum 6-km rotational velocity during the t = 1–2-h period along the paths in Fig. 2. The cross sections extend 18 km in the y direction and 9 km in the z direction (z-axis labels in km). Shown is vertical vorticity as in Fig. 2, tilting (black hatching), cloud (qi + qc > 0.0001 g kg−1; gray fill), the outline of where 3–6-km tracer concentration exceeds 25% (dashed black contours), and storm-relative wind vectors plotted every 1500 m in the horizontal and 600 m in the vertical, with darker vectors indicating larger vertical velocity.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
Tilted midlevel environmental vorticity contributes to local maxima in vertical vorticity at the southern edge of the midlevel updraft (Fig. 4). However, horizontal vorticity maxima in this same part of the updraft tend to be 2–4 times larger than any nearby vertical vorticity (Fig. 5). As a result,
As in Fig. 4, but showing positive x-direction horizontal vorticity (orange fill) and nonlinear dynamic pressure perturbation (blue to red contours). The tracer concentration contour is omitted in this figure.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
Figure 6 shows
As in Fig. 2, but showing horizontal vorticity (orange fill), nonlinear dynamic pressure perturbation (blue to red contours), and outlines of where vertical vorticity exceeds 0.04 s−1 (dashed pink contours) and is less than −0.04 s−1 (dashed blue contours).
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
b. The formation and characteristics of horizontal rotors
Horizontal, toroidal circulations have long been observed and known to influence the dynamics of real and idealized cumulus clouds (Hill 1894; Damiani and Vali 2007; Morrison and Peters 2018). However, the shear in supercell environments substantially modifies updrafts from their initial cumuliform stages. After Rotunno and Klemp (1982, 147–148, 1985) suggested that baroclinically generated horizontal vortex rings around the updraft could substantially contribute to storm splitting, Cai and Wakimoto (2001) observed and described these regions of large horizontal vorticity (as depicted in Fig. 5) in terms of their relationship to a supercell updraft. In their radar analysis, they noted that large horizontal vorticity developed at the edge of the midlevel updraft due to a horizontal gradient in buoyancy (see their Fig. 11f). This baroclinically generated horizontal vorticity is also discussed by Lasher-Trapp et al. (2021) and Jo and Lasher-Trapp (2022, 2023). In their analyses of entrainment in a simulated supercell thunderstorm, they described persistent “ribbon-like features” of horizontal vorticity that formed along the horizontal buoyancy gradient at the updraft edge and gradually ascended along the southern edge of the updraft. Our analysis affirms these findings, with large horizontal vorticity occurring almost exclusively along horizontal gradients in buoyancy (Fig. 7). We colloquially refer to these features as “horizontal rotors.” Regions of large horizontal vorticity can exist away from buoyancy gradients in the turbulent wake of the updraft (e.g., Fig. 7g), but this is to be expected given downstream advection via the midlevel storm-relative winds, which also explains the slight downstream displacement of the largest values of horizontal vorticity from the sharpest buoyancy gradients. Note that modifications to the local wind field due to the rotors themselves could alter the buoyancy distribution and associated gradients. Given our findings and those of the studies cited above, we are confident that horizontal rotors form primarily through baroclinic generation of vorticity, and we often refer to these features as “baroclinic vorticity.” As shown in Fig. 5, multiple horizontal rotors can exist simultaneously at different vertical levels on the updraft edge.
As in Fig. 6, but plan views are 11.5 × 11.5 km2 and shown is the horizontal gradient in buoyancy (cool fill), and horizontal vorticity contoured in orange at three values. Cross-sectional paths are omitted in this figure.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
As seen in Fig. 6, localized regions of large vertical vorticity occur in conjunction with large horizontal vorticity. We attribute this, in addition to the tilting of midlevel environmental vorticity demonstrated in Fig. 4, to the tilting of baroclinic horizontal vorticity into the vertical. This process was analyzed by Damiani and Vali (2007), who observed that tilted toroidal circulations around cumulus clouds resulted in vertical vorticity of 0.04–0.1 s−1. This tilting of baroclinic horizontal vorticity into the vertical is also shown by Lasher-Trapp et al. (2021, their Fig. 12), who found that horizontal rotors often contained a vertical component. Since baroclinic horizontal vorticity in horizontal rotors is very large in our simulations (often exceeding 0.1 s−1 per Figs. 5–7), even a slightly tilted horizontal rotor can result in large vertical vorticity.
A west–east vertical cross section through the southern edge of the H4-dry updraft (Fig. 8) affirms that horizontal rotors can indeed have substantial vertical tilt. As in the south–north cross sections (Fig. 5), negative
West-to-east (left to right side of the figure) vertical cross section along the path through the H4-dry storm shown in Fig. 6g. Shown is cloud (qi + qc > 0.0001 g kg−1; gray fill), horizontal vorticity (orange fill), outlines of where vertical vorticity exceeds (is less than) 0.04 s−1 (−0.04 s−1; pink and blue dashed contours, respectively), where nonlinear dynamic pressure perturbation equals −4 hPa (blue contour), and storm-relative wind vectors (shaded green to purple by the speed and direction of the storm-relative υ wind) every 400 m in the vertical and 1000 m in the horizontal. The cross section extends 8 km in the z direction and 8 km in the x direction. The z-axis labels are in kilometers.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
Horizontal rotors are most common on the southern side of the updraft (e.g., Fig. 6). This is because the prevailing southwesterly to westerly midlevel SR flow is more aligned with flow in the southern part the updraft and less aligned with flow in the northern part, which, per Lasher-Trapp et al. (2021), maximizes stretching of horizontal vorticity. While horizontal wind vectors within the midlevel updraft are certainly not indicative of solid-body rotation (Fig. 2; as in Dahl 2017), general cyclonic curvature of flow within the updraft clearly contributes to this result as described in Lasher-Trapp et al. (2021). Given that the tilting of midlevel environmental vorticity and horizontal rotors both occur at the southern edge of the updraft (Figs. 4 and 8), these two processes are both partially responsible for the local maxima in vertical vorticity in this region, providing more reasoning for why vertical vorticity within the diluted updraft is often larger than that within the undiluted updraft (Fig. 2).
c. Trends in horizontal rotor characteristics as low-level storm-relative flow and midlevel shear increase
As LL SR flow increases (a result of altered storm motion associated with increased MLS), the minimum
The 0–1-km storm-relative flow calculated using the average simulated storm motion over t = 1–2 h vs (a) the minimum nonlinear dynamic pressure perturbation (hPa) in the 4–7-km layer where horizontal vorticity exceeds 0.04 s−1, (b) horizontal area where 5–7-km layer-averaged vertical velocity exceeds 5 m s−1, and (c) the standard deviation of the center of the horizontal rotor relative to the maximum 3–6-km layer-averaged vertical velocity. Brown (green) text indicates simulations with low (high) midlevel RH. All values are averaged over t = 1–2 h. The Pearson and Spearman rank correlation coefficients and p values are displayed as in Fig. 3.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
Another element leading to, on average, stronger horizontal rotors (as measured by their associated
Over the t = 1–2-h period, the H1-dry, H1-moist, and H2-dry storms (the storms with the weakest horizontal rotors) have much lower consistency in the updraft-relative location of the horizontal rotor (Fig. 9c). The maximum 5–7-km layer-averaged x component of horizontal vorticity along the updraft edge was used as the location of the horizontal rotor, and each time step was manually inspected to ensure this point was representative of the center of the rotor. The few times the maximum was not associated with a horizontal rotor (due to horizontal vorticity maxima that had been advected well downstream of the updraft), the maximum in horizontal vorticity at the updraft edge was manually assigned as the center location.
Excluding the H1-dry, H1-moist, and H2-dry cases, differences in the consistency of the location of the horizontal rotor show no trend as LL SR flow increases, possibly because each updraft now has a more plume-like, steady-state structure. This suggests that differences in updraft steadiness cannot explain the increase in horizontal rotor strength outside of the weakest storms.
As MLS increases, midlevel storm-relative winds become stronger and attain an increasing westerly component (Fig. 1). This is visible near the bottom of the plan views in Fig. 7; 6-km storm-relative winds become stronger and more westerly from H1–H5. In general, the storm-relative wind vectors in Fig. 7 become more orthogonal to the horizontal buoyancy gradient at the southern edge of the updraft from H1–H5, which likely contributes to the increasing trend in rotor strength through increased generation of baroclinic vorticity owing to longer residence times within the gradient (e.g., Klemp and Rotunno 1983; Shabbott and Markowski 2006). There are still locations in the H1 and H2 simulations where midlevel SR flow is well aligned with the axis of a horizontal buoyancy gradient, but given the less steady-state nature of these updrafts, this alignment is likely rather transient.
The increase in horizontal rotor strength as shear increases is consistent with the findings of Jo and Lasher-Trapp (2022, 2023). Lasher-Trapp et al. (2021) and Jo and Lasher-Trapp (2022, 2023) argued that increased horizontal stretching along the southern edge of the midlevel updraft in environments with stronger midlevel storm-relative flow contributed to this trend, but horizontal stretching of vorticity does not systematically increase as midlevel SR flow increases in our simulations (not shown, likely due to similar midlevel mesocyclone strengths), meaning that it cannot explain the increase in rotor strength. We find the same result as Lasher-Trapp et al. (2021) and Jo and Lasher-Trapp (2022, 2023), but believe that it is explained by mechanisms that differ somewhat from their findings.
In summary, we suspect that the robust decrease in
d. The dynamical impact of horizontal rotors
A consequence of large vorticity at the midlevel updraft edge, primarily associated with horizontal rotors (Figs. 5, 6, and 8) but also with tilted midlevel environmental vorticity (Fig. 4), is locally low nonlinear dynamic pressure. If the vertical gradient of this perturbation pressure is negative, an upward-directed acceleration occurs beneath the pressure minimum [Eq. (2)]. To assess changes in vertical accelerations related to different vorticity patterns and wind shear, we analyze the NLDPA and LDPA terms of Eq. (2).
In Fig. 10, LDPA (Figs. 10a–j) and NLDPA (Figs. 10k–t) averaged over the 0–6-km layer are shaded, with positive values in red (i.e., an upward-directed acceleration induced by locally low dynamic pressure aloft). As would be expected, LDPA exhibits a steady increasing trend in magnitude and spatial extent as MLS and LL SR flow increase (Figs. 10a–j). This is consistent with a stronger updraft-in-shear effect (Rotunno and Klemp 1982) as updraft width (Davies-Jones 2002) and shear increase, and suggests an increasing preference for upward vertical motion on the downshear flank of the updraft as shear increases. NLDPA also exhibits a steady increasing trend in magnitude and spatial extent as MLS and LL SR flow increase, with the greatest increase in magnitude focused on the southern and southeastern flanks of the midlevel updraft (Figs. 10k–t). NLDPA averaged over the 0–6-km layer is often more than an order of magnitude larger than that of LDPA [Fig. 10; Weisman and Rotunno (2000) also found LDPA to be much smaller than NLDPA in and around supercell updrafts]. Given the larger magnitude of NLDPA and its association with the horizontal rotor, the remainder of this section primarily focuses on the impacts of NLDPA on the updraft. It should be noted that the effective buoyancy pressure acceleration [EBPA, first term in Eq. (2)] also increases as MLS and LL SR flow increase (not shown), which is to be expected given the larger buoyancy in wider, less-diluted updrafts (Peters et al. 2019, 2020b; but theoretically only until a width allowing for an undiluted core is achieved; Jeevanjee and Romps 2016). This does lead to stronger updrafts via stronger vertical accelerations within the undiluted updraft core of EIL air (not shown), but has been well documented by recent studies, so we defer the reader to the previous citations for more information.
20 × 20 km2 plan views of each storm, averaged over t = 1–2 h, showing 0–6-km layer-averaged (a)–(j) LDPA (blue to red fill) and (k)–(t) NLDPA (red fill), where 3–6-km layer-averaged vertical velocity equals 10 m s−1 [first gray contour, every additional 5 m s−1 in gray in (a)–(j)] where the vertical gradient in storm-modified horizontal vorticity is larger than the vertical gradient in vertical vorticity over the 0–6-km layer [in (k)–(t); black hatching] Note that the NLDPA magnitudes shaded are greater than one order of magnitude larger than that of LDPA.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
We believe that the increase in magnitude and spatial extent of NLDPA from H1–H5 (Figs. 10k–t) is primarily a result of decreasing
In addition to the collocation of NLDPA maxima where horizontal vorticity is driving low
In addition to increasing in magnitude, the location of maximum 0–6-km layer-averaged NLDPA shifts from the eastern flank of the midlevel updraft in the H1 storms to the southern flank in the H4 and H5 storms (Figs. 10k–t). Warren et al. (2017) found this same trend in their simulations as upper-level shear and LL SR flow increased (see their Fig. 13). They noted that the maximum NLDPA was “associated with a peak in midlevel vorticity” (Warren et al. 2017, p. 2672). Given our results, it seems likely that horizontal vorticity associated with horizontal rotors accounted for most of the peak in midlevel vorticity and was responsible for larger 0–6-km NLDPA in their simulations with larger LL SR flow. Again, the increase in vertical vorticity resulting from tilted midlevel environmental vorticity may partly explain this finding, but the trends described above are primarily the result of larger and stronger horizontal rotors when LL SR flow is larger (as shown in Figs. 9a and 10k–t). Similarly, Peters et al. (2020b) found a positive correlation between LL SR flow and NLDPA, particularly at midlevels (see their Fig. 14b), and speculated that this result could be partially explained by the tilting of larger above-EIL environmental vorticity typically present in large LL SR flow environments (since large LL SR flow often requires large shear above ∼1 km). While tilted above-EIL environmental vorticity does slightly contribute to larger NLDPA when MLS is greater, the stronger horizontal rotors likely account for most of this result from Peters et al. (2020b).
The primarily nonlinear (Fig. 10) dynamic pressure accelerations associated with horizontal rotors have a pronounced influence on parcels that pass beneath them (Fig. 11). At t = 90 min during the H5-dry simulation, 4790 parcels were initialized every 500 m in the vertical and 1000 m in the horizontal within a box extending 20 km in the x direction, 17 km in the y direction, and 7 km in the z direction encompassing the southern half of the updraft, surrounding air, and much of the air to the west of the updraft. Parcels were integrated forward in time for 15 min using the model time step, and parcel data were output every 6 s.
Plan views of the H5-dry storm at t = 99 min showing 6-km horizontal vorticity (orange fill), where 6-km vertical velocity equals 10 m s−1 (gray contours), 6-km pressure perturbation (blue to red contours), and parcel trajectories over the 15-min integration period for (a) those that participate in the EIL-driven updraft and (d) those that participate in the rotor-induced updraft extension. Parcel trajectories appear on top of all fields if they exceed z = 6 km. Parcels were considered to participate in the EIL-driven updraft if they attained an EIL tracer concentration of more than 20% at any time or originated within the EIL. All parcels were required to pass through region extending from x = 3.75–6.75 km, y = 3.25–5.5 km, and z = 4–5.5 km, which is beneath the most intense portion of the horizontal rotor. The circles indicate parcel locations at t = 105 min and are colored by height [as in (b) and (e)]. (b),(e) Parcel vertical velocity along each trajectory, with lines colored by parcel height. Average vertical velocity is outlined in black. (c),(f) Average parcel vertical acceleration (black line; the region between the maximum and minimum is shaded gray), average parcel dynamic pressure acceleration (blue line), average parcel buoyancy (orange line), and average parcel acceleration due to anything but dynamic pressure acceleration and buoyancy (green line). Average parcel heights are indicated atop colored dots for each kilometer.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
Within a 36 s period centered on t = 99 min (9 min after parcel initialization), we identified 27 parcels that passed beneath the rotor (see the caption of Fig. 11). Parcels that participate in the EIL-driven updraft (Figs. 11a–c) during this period are analyzed separately from those that participate in an eastward extension of the updraft (Figs. 11d–f). A few parcels pass through the low-level updraft, are detrained, then enter the updraft again before passing beneath the rotor (Fig. 11a), resulting in a highly variable vertical velocity pattern for the first 8 min (Fig. 11b). Other parcels participating in the EIL-driven updraft when they pass beneath the horizontal rotor experience gradual ascent below 4 km AGL as buoyancy increases, until the “boost” from DPA beneath the horizontal rotor aids in greatly increasing the vertical velocity (by an average of 15 m s−1 from t = 98–100 min, Figs. 11b,c). After this, parcels are either detrained or continue to ascend through the upper levels of the updraft, and their vertical velocities decrease owing to strong downward-directed DPA, a result of downward-directed NLDPA above the
Midlevel parcels that do not experience significant mixing with EIL-air (on average, the parcels analyzed in Figs. 11d–f attain a maximum EIL tracer concentration of less than 6%, not shown) within the updraft also experience a significant increase in vertical velocity as a result of DPA beneath the horizontal rotor. These parcels generally approach the southern edge of the updraft from the west with weak vertical velocity, but again experience a large positive vertical acceleration beginning just before t = 98 min. Rather than enhance preexisting positive vertical velocity, as is the case for parcels already residing in the updraft, DPA associated with the horizontal rotor generates a new region of vertical velocity. Most of these parcels achieve vertical velocities of 10–20 m s−1 and contribute to a region of large vertical velocity extending eastward from the southern side of the updraft (Fig. 11d). These regions of enhanced midlevel vertical velocity immediately downstream of the horizontal rotor are also visible in the H3-dry, H3-moist, and H4-dry simulations (Figs. 6e–g). After passing beneath the rotor, parcels continue to experience positive DPA (consistent with positive LDPA on the downshear flank of the updraft in Fig. 10i), but its influence is outweighed by the development of strong negative buoyancy associated with adiabatic cooling, which leads to negative vertical velocity by t = 105 min.
For parcels that have substantially mixed with updraft air when passing beneath the rotor, DPA from t = 97.7–99.7 min contributes to an average increase in vertical velocity of 11.3 m s−1, which is 62% of the total increase in vertical velocity over the same time period. For those that have not, DPA from t = 98–100 min contributes to an average increase in vertical velocity of 5.9 m s−1, 52% of the total increase in vertical velocity over the same time period. Buoyancy accounts for 36% of the total increase in vertical velocity for the updraft parcels, and 39% for the nonupdraft parcels. This indicates that the rotor-induced acceleration works in tandem with, but is substantially larger than, the background state of positive buoyancy within and near the updraft.
e. A comparison of nonlinear dynamics in time
We now present an analysis of the H5-moist storm at two individual time steps. Throughout the t = 1–2-h period, differences in mesocyclone strength are rather small across the simulations (Figs. 2 and 3), and differences in midlevel vorticity-driven dynamics between storms are primarily caused by differences in the strength of horizontal rotors (Fig. 10). In the t = 2–3-h period, however, the H5-moist mesocyclone undergoes a period of pronounced strengthening, where an increase in vertical vorticity in the low-level mesocyclone leads to a groundward extension of the updraft and further intensification of low-level rotation (i.e., a “dynamical response”; Goldacker and Parker 2021), resulting in the most intense mesocyclone out of any simulation at any time.
In the H5-moist storm, the largest values of 0–6-km NLDPA are aligned with the horizontal rotor through at least t = 2 h (Fig. 10t). A vertical cross section at t = 105 min (Fig. 12) provides additional context on why this occurs. At this time,
South-to-north (left to right in each panel) vertical cross section through the center of the mesocyclone at t = 105 min for the H5-moist storm. (a) Cloud outline (qi + qc > 0.0001 g kg−1; gray fill), vertical vorticity (red to blue fill), where 3–6-km tracer concentration exceeds 25% (dashed yellow contour), nonlinear dynamic pressure perturbation (blue and red contours), SR wind vectors plotted every 1 km in the vertical and 2.5 km in the horizontal, shaded by vertical velocity (darker arrows indicating larger vertical velocity), and the region of negative nonlinear dynamic pressure perturbation induced by the mesocyclone is indicated by the dashed black line near y = 15. (b) The ratio of vertical vorticity to total vorticity (orange to red fill), total storm-modified vorticity (gray contours), and nonlinear dynamic pressure perturbation contoured at −4 hPa (blue contours). Axes labels are in kilometers.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
This shows that there are different mechanisms for dynamic vertical forcing at different levels in the updraft. Even though the mesocyclone contains weaker vorticity than the horizontal rotor, it extends closer to the ground, inducing larger NLDPA in the 0–1-km layer (Fig. 13a, note that the southwestward extension of large NLDPA is partially facilitated by deformation-driven positive
20 × 20 km2 plan views for the H5-moist storm at t = 105 min. (a) The 0–1-km layer-averaged NLDPA (blue to red fill). Regions where the maximum horizontal vorticity in the 4–8-km layer exceeds 0.08 s−1 are outlined in orange. Areas where 1-km vertical vorticity exceeds 0.01 s−1 are outlined in purple. (b) The 1–6-km layer-averaged NLDPA [blue to red fill; note the change in magnitude from (a)]. Minimum nonlinear dynamic pressure in the 4–8-km layer is contoured in blue. Areas where vertical vorticity is larger than horizontal vorticity at the location of minimum 4–8-km nonlinear dynamic pressure perturbation are hatched in black. The gray contour indicates where 6-km vertical velocity equals 10 m s−1 in both plots, and the gray dashed line in both plots indicates the path of the cross section in Fig. 12.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
Regions where vertical vorticity is larger than horizontal vorticity at the minimum value of
By t = 170 min, the mesocyclone has strengthened considerably (Fig. 14a), with vertical vorticity exceeding 0.1 s−1, several times larger than at t = 105 min. Accordingly, the minimum
As in Fig. 12, but for t = 170 min.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
At t = 170 min, the 1–6-km NLDPA field on the southern edge of the updraft is again dominated by the influence of the horizontal rotor (Fig. 15). At this time, however, the minimum 4–8-km
As in Fig. 13, but at t = 170 min, and 1-km vertical vorticity in (a) is outlined at 0.05 s−1. Note that the scale for 0–1-km layer-averaged NLDPA is an order of magnitude larger than in Fig. 13. The gray dashed line in both plots indicates the path of the cross section in Fig. 14.
Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0082.1
At both t = 105 min and t = 170 min, despite drastic differences in low-level mesocyclone strength, the largest 0–1-km NLDPA is associated with the low-level mesocyclone (Figs. 13a and 15a). Furthermore, 0–1-km NLDPA shows no connection to the horizontal rotor, and is generally much larger (1+ orders of magnitude) than 1–6-km NLDPA. This discrepancy in magnitude is partially a result of the larger depth (5 km) over which horizontal rotor-induced NLDPA was calculated, which can “wash out” the most intense regions of NLDPA associated with the relatively shallow, elevated horizontal rotor. In fact, the kilometer-deep layer below the center of the horizontal rotor for the H5-moist case at t = 105 min (Fig. 12a) experiences NLDPA on the order of that experienced in the kilometer-deep layer beneath the strong low-level mesocyclone at t = 170 min. This is implied by the sharp vertical gradient in
This analysis of the H5-moist storm in time supports our impression that, in the 0–1-km layer, the acceleration induced by the horizontal rotor is negligible compared to the acceleration induced by the low-level mesocyclone, especially if the mesocyclone undergoes a pronounced increase in strength. While the first part of the preceding statement is intuitive, disentangling the location and magnitude of dynamical impacts from each of these large-vorticity features allows us to more confidently draw conclusions about the specific role that MLS and horizontal rotors play in supercell dynamics.
4. Discussion
We stress that the primary changes in updraft dynamics simulated herein as midlevel shear increases are not the result of increased environmental vorticity. The largest dynamical differences between storms simulated in environments with varied midlevel shear are related to horizontal rotors. Horizontal rotors appear to be connected to LL SR flow, a quantity indirectly related to midlevel shear. Changes in vertically oriented updraft rotation at midlevels, a quantity directly associated with the tilting of midlevel environmental vorticity inherent in midlevel shear, are small. Therefore, we argue that the most important effect of midlevel shear on a supercell is its control over LL SR flow. Midlevel shear influences the magnitude of vertical vorticity that results from the tilting of midlevel environmental vorticity at the updraft edge, which certainly plays a small role in generating low nonlinear dynamic pressure at midlevels, but is ultimately overshadowed by the dynamical influence of much larger horizontal vorticity within the horizontal rotor, a feature tied to updraft properties that are more connected to LL SR flow than midlevel environmental vorticity.
Operational forecasters have noted that a lack of midlevel shear is often associated with a lack of supercell “organization.” The results herein suggest that the perceived lack of organization is not a result of small midlevel environmental vorticity, and is likely connected to other factors, such as small low-level SR flow that often accompanies weak midlevel shear.
There is likely a connection between horizontal rotors and storm motion. Though their calculations were not shown, Rotunno and Klemp (1982, 147–148, 1985) noted that horizontal vorticity associated with the horizontal buoyancy gradient at the updraft edge could induce a pressure perturbation exerting a comparable influence on storm splitting as that resulting from vertical vorticity. Cai and Wakimoto (2001) presented observational evidence that horizontal rotors play as large a role as vertical vorticity in the “rightward bias” of a supercell updraft, and the high resolution of our simulations and those of Lasher-Trapp et al. (2021) may mean that we are resolving these relatively small-scale horizontal rotors more clearly than previous simulations or radar observations.
It is possible that larger NLDPA associated with horizontal rotors on the updraft’s southern flank leads to increased rightward, off-hodograph propagation, which is associated with increased tornado potential (Coniglio and Parker 2020; Flournoy et al. 2021). This could partially explain the results of Coniglio and Parker (2020) and Coniglio and Jewell (2022), who found LL SR flow to be significantly larger for tornadic compared to nontornadic supercells. Indeed, the H4 and H5 storms, relative to the predicted right-moving motion, move more to the right than the H1 and H2 storms (not shown). However, Davies-Jones (2002) showed that wider updrafts exhibit larger off-hodograph linear propagation. Therefore, it is unclear if this enhanced off-hodograph propagation is related solely to updraft width or dynamical effects of horizontal rotors in conjunction with updraft width. Additionally, the bulk of the acceleration induced by the rotor resides above the conditionally unstable EIL, subjecting its influence to further question. At the very least, lifting in association with the horizontal rotor could lead to near-field environmental modifications. Coniglio and Parker (2020, their Figs. 19d,e) showed that 1–3-km RH increased on approach to the southern flank of observed supercell updrafts, which may be at least partially attributable to ascent induced by horizontal rotors and resultant cooling. The influence of horizontal rotors on storm motion is currently being investigated.
The formation and controls on intensity of horizontal rotors is an open area of research. While increased low-level storm-relative flow leads to wider updrafts that are more buoyant and steady state at midlevels, typically resulting in stronger horizontal rotors, the influence of storm-relative flow at midlevels could be further investigated, given that it is known to impact storm evolution, structure [primarily upper-level storm-relative flow as in Rasmussen and Straka (1998)], and tornado production (Brooks et al. 1994; Gray and Frame 2021). In addition, storms in environments with low midlevel RH tended to have narrower midlevel updrafts (Fig. 9a). Given that LL SR flow and RH influence updraft width, which is well correlated with hydrometeor production (Grant and van den Heever 2014; Warren et al. 2017) and downdraft area (Marion and Trapp 2019), these results indicate that LL SR flow and free-tropospheric RH may be particularly relevant in determining where a supercell falls on the low-precipitation–classic-high-precipitation spectrum (e.g., large LL SR flow and high free-tropospheric RH may generally be more supportive of “high-precipitation” storms). Our simulated storms tended to have larger LL SR flow when midlevel RH was higher (Fig. 9; also seen in Bunkers et al. 2014), suggesting that free-tropospheric RH may influence low-level SR flow by impacting storm motion.
Pounds et al. (2024) observed that hailstones grow larger in the northeastern part of the midlevel updraft where cross-updraft flow is weaker owing to the diversion of southwesterly storm-relative flow around the updraft. Rotor-induced vertical accelerations may be relevant to hail production via alterations to updraft width and/or shape, since a change in updraft shape could modulate the size and location of the region favorable for hail growth. In other words, specific characteristics of horizontal rotors may represent a pathway by which increasing LL SR flow promotes larger hailstone growth. Future work should investigate how updraft shape is modulated by shear and horizontal rotors, and how this relates to hail production, as in Dennis and Kumjian (2017).
Doppler radar datasets (e.g., Van Den Broeke et al. 2023) may be particularly important in detecting horizontal rotors. Snyder et al. (2020) found evidence of an intense “quasi-horizontal vortex” as low as 1 km AGL in a supercell thunderstorm. Pressure retrieval as performed in Cai and Wakimoto (2001) would provide insight into the dynamics and influences of real-world horizontal rotors.
5. Conclusions
In this study, we provided an analysis of the influence of midlevel environmental vorticity associated with midlevel shear on supercell updrafts based on idealized numerical simulations. We also spent a considerable portion of our analysis evaluating the impact of regions of large storm-generated horizontal vorticity at midlevels, which we call horizontal rotors. Given our findings valid for the 10 simulations herein, we can answer our two questions about midlevel shear.
a. How does tilted midlevel environmental vorticity influence a supercell mesocyclone?
Cohesive updraft rotation does not exhibit a statistically significant trend with midlevel shear. However, the tilting of midlevel environmental vorticity does often lead to an area of large vertical vorticity on the southern edge of the midlevel updraft. The magnitude of this vertical vorticity can exceed that within EIL air in the center of the updraft (i.e., what we refer to as the “midlevel mesocyclone”) when midlevel shear is large, but does not lead to an increase in cohesive updraft rotation.
b. How does low-level storm-relative flow modulate the updraft and influence of tilted midlevel environmental vorticity?
Low-level storm-relative flow is related to updraft width. When midlevel shear is large, storm motions are faster relative to the low-level hodograph, low-level storm-relative flow is larger, and updrafts are wider. Midlevel air is kept from entering the cores of the wider updrafts, meaning that the only region where tilted midlevel environmental vorticity enhances vertical vorticity is the updraft edge.
The remaining conclusions relate to the horizontal rotor.
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Updrafts in environments with larger midlevel shear and low-level storm-relative flow have a larger nonlinear dynamic pressure acceleration on their southern flank. This is primarily the result of stronger horizontal rotors at midlevels when updrafts are wider and midlevel storm-relative flow is more parallel to the southern edge of the updraft.
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Horizontal vorticity associated with horizontal rotors is generally larger than that of vertical vorticity resulting from tilted low-level or midlevel environmental vorticity, and therefore plays a larger role in generating low pressure.
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For most of a storm’s life cycle, the largest negative pressure perturbation at midlevels occurs in conjunction with the largest horizontal vorticity in the horizontal rotors, not vertical vorticity within the midlevel mesocyclone. This statement is reversed if the mesocyclone has undergone a pronounced increase in strength.
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The vertical tilt of horizontal rotors leads to large vertical vorticity along the updraft edge, often larger than that within the mesocyclone.
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The dynamic pressure acceleration resulting from low pressure within the horizontal rotor substantially enhances vertical velocity near the southern edge of the updraft and leads to a new region of rising air downstream of the rotor.
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Regardless of the strength of the horizontal rotors and the mesocyclone, the strongest dynamic forcing in the lowest kilometer is driven by low pressure associated with vertical vorticity in the low-level mesocyclone, but the strongest dynamic forcing at the southern edge of the midlevel updraft is driven by horizontal rotors.
We emphasize that our conclusions are based on simulated, idealized supercells, and real-world results would likely be influenced by external forcing mechanisms not considered by the model such as storm mergers (Flournoy et al. 2022), terrain (Satrio et al. 2020; Katona and Markowski 2021), environmental inhomogeneities (Richardson et al. 2007; Nowotarski et al. 2014; Gray and Frame 2019; Brown et al. 2021), as well as more realistic microphysics (Murdzek et al. 2022), representation of Coriolis force, pressure gradient force, and convection initiation (Roberts et al. 2016; Markowski and Bryan 2016; Davies-Jones 2021), and different thermodynamic environments (McCaul and Weisman 2001; Kirkpatrick et al. 2009; Brown and Nowotarski 2019). Future modeling work should perform more realistic simulations and/or test the sensitivity of these results to different numerical designs. Continued storm-scale analyses of hundreds or thousands of observed supercell evolutionary traits (e.g., Gropp and Davenport 2018; Coniglio and Parker 2020; Davenport 2021; Flournoy et al. 2022; Lyza et al. 2022) will shed light on the relevance of these findings to real supercells and their hazards.
Acknowledgments.
Funding was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement NA21OAR4320204, U.S. Department of Commerce. The statements, findings, conclusions, and recommendations are those of the authors and do not necessarily reflect the views of NOAA or the U.S. Department of Commerce. J. Peters’s efforts were supported by National Science Foundation (NSF) Grants AGS-1928666, AGS-1841674, and the Department of Energy Atmospheric System Research (DOE ASR) Grant DE-SC0000246356. We thank three anonymous reviewers for thorough and thoughtful reviews of previous versions of this manuscript that greatly streamlined the revision process and led to this much improved version. We thank Drs. Mike Coniglio and Israel Jirak for internal reviews of this manuscript, and Dr. George Bryan for his continual support of CM1. All simulations were performed on NCAR’s Cheyenne supercomputer (Computational and Information Systems Laboratory 2019).
Data availability statement.
The namelist.input file, text files of the model soundings, and analysis code can be found at https://github.com/andrewtornado11/MLSResearch. CM1 can be downloaded from https://www2.mmm.ucar.edu/people/bryan/cm1/.
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