Low-Level Mesovortices within Squall Lines and Bow Echoes. Part II: Their Genesis and Implications

1. Introduction

In this second of a two-part paper, we continue our examination of low-level (altitudes below ∼1 km AGL), meso-γ-scale (horizontal scales ∼2–20 km and timescales ∼1 h; Orlanski 1975) vortices, or mesovortices, that form at the leading edge of extensive quasi-linear mesoscale convective systems (QLCSs) such as squall lines and bow echoes. The structure and evolution of low-level mesovortices in QLCSs were characterized in Weisman and Trapp (2003, hereafter Part I), as was the range of unidirectional environmental wind profiles most conducive to their development. Our focus in Part II is on the genesis of these vortices and then, more generally, on their roles in the convective system structure and evolution.

We recall previous observational (e.g., Smull and Houze 1987; Schmidt and Cotton 1989) and theoretical and/or numerical cloud-modeling studies (e.g., Thorpe et al. 1982; Rotunno et al. 1988; Weisman 1992, 1993) of QLCSs that have focused primarily on convective-system-scale characteristics and how these relate to the longevity, severity, and overall dynamics of the system itself. A particularly relevant characteristic is the midlevel (altitudes between ∼3 and 7 km AGL) mesovortex pair that forms at the lateral ends of a finite convective system as well as at the ends of embedded bowing segments. These “book-end” or “line-end” vortices act to focus the rear inflow (hence leading-edge lift, etc.), contributing on the system scale to perhaps as much as 30%–50% of the total rear-inflow strength during the mature phase of the QLCS (Weisman 1993).

The genesis mechanisms of midlevel line-end vortices have been studied recently by Weisman and Davis (1998, hereafter WD98). WD98 showed that subsystem-scale (∼5–10 km diameter) line-end vortices are formed as ambient crosswise horizontal vorticity (i.e., V_H⊥ω_H, where V_H and ω_H are the horizontal velocity and vorticity vectors, respectively) is vertically tilted by downdrafts associated with embedded bowing segments. System-scale (approximately tens of kilometers) line-end vortices, on the other hand, are formed primarily through the vertical tilting, by the system-scale updraft, of crosswise horizontal vorticity generated in horizontal buoyancy gradients along the gust front. The development of a larger-scale (approximately hundreds of kilometers) midlevel cyclonic vortex in the stratiform region of an asymmetric convective system owes largely to the stretching of planetary vorticity by mesoscale updrafts (e.g., Bartels and Maddox 1991; Skamarock et al. 1994; WD98).

It is instructive to compare these mechanisms with those that generate mesocyclones in supercell storms. At midlevels, mesocyclones generally develop through the vertical tilting and stretching by the supercell updraft of ambient horizontal vorticity [e.g., see the review by Davies-Jones et al. (2001)]. According to Rotunno and Klemp (1985) [Davies-Jones and Brooks (1993)], mesocyclogenesis at low levels occurs as streamwise horizontal vorticity (i.e., V_H ‖ ω_H), generated primarily in buoyancy gradients along the forward- (rear) flank gust front, and is vertically tilted in the storm's main updraft (rear-flank downdraft). Alternative explanations have been offered in Davies-Jones (2000a) and Wakimoto et al. (1998), the latter involving the release of a horizontal “shearing” or barotropic instability inherent in a zone of concentrated, preexisting vertical vorticity (effectively, a vertical vortex sheet). In brief, such a zone that exists along, say, a gust front becomes unstable and then “rolls” up into discrete, like-signed vortices of uniform, along-front spacing (see Carbone 1983; Lee and Wilhelmson 1997; Mak 2001). This particular mechanism is often used to explain tornadoes and/or their parent vortices within observed squall lines and bow echoes (e.g., Forbes and Wakimoto 1983; Przybylinski 1995).

As demonstrated in Part I, supercell mesocyclones evolve and are structurally quite different than mesovortices in extensive QLCSs. Accordingly, little discussion is devoted hereafter to supercell mesocyclones and, in particular, lines of supercells. Though environments with large vertical wind shear over deep layers—believed to be most often supportive of supercell storm development—are included for completeness in our experimental matrix (see Table 1 of Part I), we concentrate our study on the products of environments of unidirectional vertical wind shear (U_S) over relatively shallow layers (Fig. 3 of Part I) and convective available potential energy (CAPE) of 2200 J kg⁻¹.

For example, in environments with U_S = 10 to 15 m s⁻¹ over a 2.5- to 5-km depth, an upshear-tilted system results, with relatively weak line-end, system-scale vortices at midlevels (e.g., Figs. 4a,b of Part I). At low levels, only weak, insignificant vortices develop; for our purposes, a “significant” mesovortex is one with a diameter ≥4 km (four horizontal grid intervals; nominally resolved), maximum vertical vorticity ≥0.01 s⁻¹, vertical depth >1 km, and general time and space coherency. Environments with U_S = 20 to 30 m s⁻¹/2.5 to 5 km support the formation of a squall line that develops large bowing segments with significant vortices at mid- and low-levels (Figs. 1, 2). Our objective in Part II is to (i) determine the genesis mechanism of such low-level mesovortices and then (ii) explore their roles in the generation of damaging surface winds and in the evolution and also the structure of the parent QLCS.

2. Experimental methodology

The design of this numerical cloud-modeling experiment is detailed in Part I. Summarizing here, we use the Klemp and Wilhelmson (1978) cloud-resolving numerical model over a domain that is 500 km in the horizontal directions and 17.5 km in the vertical direction. Horizontal gridpoint spacings of 1 km and vertical grid stretching (with 0.3-km gridpoint spacing in the lowest 1 km) are used to represent well the horizontal and vertical structure of the mesovortices. The model is integrated in time to 6 h. All simulations, unless otherwise indicated, include effects of the Coriolis force (assuming a constant f plane, with Coriolis parameter f = 10⁻⁴ s⁻¹), which is applied only to the wind perturbations.

Sensitivity of low-level QLCS structure to unidirectional environmental wind shear over the range 10 ≤ U_S ≤ 30 m s⁻¹ over 2.5-, 5.0-, or 7.5-km depths is discussed extensively in Part I. Part II is devoted primarily to analysis of the U_S = 20 m s⁻¹/2.5 km experiment (hereafter denoted as 20/2.5/f; an analogous convention is followed for other experiments), the results of which we attempt to generalize to other QLCSs.

3. Overview of the simulation with an environmental shear of U_S = 20 m s⁻¹ over 2.5 km

Comparable to observed severe convective systems, the QLCS simulated in an environment with U_S = 20 m s⁻¹/2.5 km has an evolution and structural characteristics described as follows: Storms triggered initially by the thermal perturbations form rainy downdrafts and associated cold pools whose mutual interaction leads to, after 2 h of model integration, an effectively continuous gust front on the 160-km length scale of the line of initial thermals. Midlevel vortex couplets (Fig. 1a) and also nascent low-level cyclonic mesovortices (Fig. 2a) can be found at this early stage of evolution, characterized by a group of individual cells (e.g., Klimowski et al. 2000). Evident within the resultant squall line at t = 3 h are midlevel line-end vortices with diameters of about 15 km and low-level vortices elsewhere along the line with diameters of 5–10 km (Figs. 1b, 2b). In particular, the cyclonic vortex identified as V1 exemplifies the type of low-level mesovortices of most interest here: it persists for at least 2 h, extends through midlevels, resides in a location just behind the leading edge of the cool air (−1-K isotherm), and is associated locally with a hook shape in both the model rainwater field and the midlevel updraft (see also Part I).

By t ≥ 4 h the linear convective system evolves into one with large, outward bowing segments. Attendant with the primary bowing segment are a system-scale midlevel vortex couplet and rear-inflow jet (RIJ; Smull and Houze 1987), the latter extending 40–50 km rearward from the segment's apex (Figs. 1c,e). The RIJ is generally elevated, save for a small branch that descends to low levels just behind the gust front (Figs. 2d,e). The significant low-level cyclonic mesovortices, particularly the one denoted BEV1 (bow-echo vortex 1), are now located exclusively north of the bow apex (Figs. 2c,e). This noteworthy result, consistent at least with tornado observations¹ in bow-shaped convective systems (e.g., Fujita 1979; Przybylinski 1995), elicits two additional findings: 1) a north-of-apex bias in cyclonic vortex location does not exist prior to large bow-segment development and 2) a low-level counterpart to the midlevel anticyclonic vortices is generally absent in the simulated QLCS except at the extreme southern end of the system.

A result that is generally inconsistent with most bow-echo observations is the location of the strongest low-level winds at these later times: tens of kilometers northwest of the apex and in association with low-level mesovortices (see section 5). We regard these as “straight line” winds—in contrast with swirling, tornadic winds that are subgrid scale here—and note that they occur in addition to those found just behind the bow-echo apex, as is typically conceptualized (e.g., Fujita 1978; Przyblinski 1995; Weisman 2001; Wakimoto 2001) (Figs. 2d,e).

The asymmetry of the mature mesoscale convective system (MCS) is also apparent by t ≥ 4 h. As discussed by Weisman (1993), Skamarock et al. (1994), WD98, and others, such system-scale asymmetry is promoted through the Coriolis force. Other, more local effects ascribed to Coriolis force can be revealed by comparing the 20/2.5/f results with those from a counterpart simulation with f set to zero (20/2.5/0) (Figs. 3, 4). Indeed, although at t = 2 h the midlevel vortex structure in both cases is nearly identical, as are many other facets of the motion and precipitation fields (see, e.g., Figs. 1a, 3a), significant low-level mesovortices are conspicuously absent in the f = 0 case (Fig. 4a). The low-level wind field is free of vortices at later times as well (Figs. 4b–e), suggesting a probable link between mesovortexgenesis and f, explored in the next section. Yet another apparent effect of f regards the midlevel updraft. At t > 3 h in the 20/2.5/0 simulation, we find that the midlevel updraft becomes rather uniform horizontally (Figs. 3c–e), lacking the segments and subsystem-scale vortices observed at these times in the 20/2.5/f simulation (Figs. 1c–e). As discussed in section 6, such segmentation is related to the presence of low-level mesovortices and hence can be viewed as a secondary effect of f.

4. Analysis of low-level mesovortexgenesis

The development of a prominent low-level vortex such as V1 is now examined. Vortex V1 is one of at least four leading-edge mesovortices that are well formed by t = 2 h. At this nascent stage of the modeled QLCS, low-level vortexgenesis is disclosed more readily because the convective system is still symmetrical and, in this regard, less complicated structurally than at later stages. Our knowledge of V1's formation, however, is used later in this section to explain vortexgenesis within a mature QLCS with large bowing segments.

a. Early-stage vortexgenesis

The developmental history of V1 (and of the other early-stage vortices) can be traced back to at least t = 1 h 20 min. At this time, V1 is the cyclonic member of a symmetrical cyclonic–anticyclonic vortex couplet that straddles a low-level downdraft and rainwater maximum (Fig. 5a); the downdraft originates at midlevels, in conjunction with a short-lived cell split. Thereafter, the couplet separates owing to outflow expansion and subsequent updraft and downdraft evolution. Vortex V1 continues to intensify, while its anticyclonic counterpart experiences very little growth (Fig. 5b). Figure 5 suggests the need to determine (i) the process(es) responsible for the formation of the low-level vortex couplet and then (ii) the means by which the symmetry in the vortex couplet's development is broken. An obvious clue to (ii) is immediately provided by the 20/2.5/0 simulation: A low-level vortex couplet is generated by t = 1 h 20 min yet, in contrast to the couplet in 20/2.5/f, remains symmetrical and weak through t = 1 h 40 min (Figs. 5c,d).

1) Vertical vorticity equation analysis

Consider the vertical vorticity equation formed from the model equations, which can be written as follows:

View Expanded

where ζ_a = ζ + f is absolute vertical vorticity, D = D_υî + (−D_u)ĵ composes the eddy-mixing terms from the horizontal momentum equations, ∇_H is the horizontal gradient operator, and V_H and ω_H are the horizontal velocity and vorticity vectors, respectively. The rhs terms in Eq. (4.1) govern vertical tilting of horizontal vorticity, stretching of planetary plus relative vertical vorticity, and eddy mixing of absolute vertical vorticity, respectively. We examine these forcing terms in perhaps the most familiar of the two complementary approaches taken herein to reveal the vortexgenesis mechanism.

We begin with a consideration of the 20/2.5/0 simulation, which represents the simplest or most idealized case, since the solution is inherently symmetrical and also mirrors the 20/2.5/f solution through ∼1 h 20 min (Fig. 5). Using plots of horizontal vorticity and vertical velocity, one can deduce that the generating mechanism of the low-level vortex couplet is simply the tilting of initially crosswise horizontal vorticity in a downdraft. Indeed, Fig. 6 depicts a horizontal vortex ring that was baroclinically generated in cold-air outflow from a prior downdraft, then expanded, and now passes in part through the core of a new downdraft. Tilting of the horizontal vorticity generates cyclonic vertical vorticity south of the downdraft core and anticyclonic vertical vorticity north of the core.

The tilting process can be quantified by a time integration of relevant ζ-forcing terms along a backward trajectory, originating at t = 1 h 20 min within the z = 0.4 km ζ_max (Fig. 6); trajectory calculations are performed using 1-min history files. Figure 7 proves that most of the ζ generated by t = 1 h 20 min is through the tilting of horizontal vorticity in descending air (i.e., after t ∼ 1 h 15 min along the trajectories). As substantiated by the buoyancy field in Fig. 6, such horizontal vorticity is primarily baroclinic (i.e., horizontal vorticity vectors are parallel to buoyancy contours), while horizontal vorticity tilted in rising air along the trajectories (i.e., prior to t ∼ 1 h 15 min) is barotropic or due to the environmental wind shear (see Dutton 1986, 389–390). Note that in the descending air parcels, negative (positive) stretching of relative vertical vorticity counteracts the positive (negative) tilting of baroclinic horizontal vorticity.

The mechanism that breaks the symmetry of the vortex couplet and hence leads to a dominant cyclonic vortex involves planetary vorticity, as evidenced by the disparity between the 20/2.5/f and 20/2.5/0 experimental results (Figs. 8a,b). An even greater disparity exists between the 20/2.5/0 solution and one from an experiment with f = 2 × 10⁻⁴ s⁻¹ (20/2.5/2f; Fig. 8c). The 20/2.5/2f equivalent of V1 has developed more rapidly and is larger in scale at 2 h than V1; generally speaking, this holds true at all times for this and other low-level mesovortices in the 20/2.5/2f experiment (not shown). Though admittedly an unrealistic experiment (f actually ranges from 0 at the equator to ±1.46 × 10⁻⁴ s⁻¹ at the two poles), such a clear model response to a doubling in Coriolis parameter value suggests to us a direct effect of f on the mesovortexgenesis, which we now explore.

Recall that f enters Eq. (4.1) through the vertical stretching of planetary vorticity. To estimate the magnitude of this process in the simulated QLCS, we examine a parcel's vertical vorticity growth along a forward trajectory, originating again at 1 h 20 min within the z = 0.4 km ζ_max (see Fig. 6); note that along this trajectory, the parcel exits the downdraft and then enters and rises in the leading-edge updraft. The parcel is initialized with ζ₀ = f = 10⁻⁴ s⁻¹, which is allowed to grow only through vertical stretching along the trajectory, but does not interact with the surrounding flow. As thus governed [see Eq. (4.1)] by

View Expanded

vertical vorticity along the trajectory increases from an initial value of 1 × 10⁻⁴ s⁻¹ at 1 h 20 min (and z = 0.4 km) to 153 × 10⁻⁴ s⁻¹ at 1 h 50 min (and z = 5.8 km) (Fig. 9)! Strictly speaking, this parcel's vertical vorticity at t = 1 h 50 min cannot be qualified as “low level.” However, a local or Eulerian application of Eq. (4.2) at low levels, using representative values of horizontal convergence (∼−1 × 10⁻³ to −5 × 10⁻³ s⁻¹), yields comparable magnitudes of vertical vorticity over the 30-min period. Either way, the implication here is that vertical stretching of initial vertical vorticity equivalent to midlatitude f can significantly enhance the cyclonic vortex and significantly diminish the anticyclonic vortex.

2) Circulation equation analysis

We now turn to the circulation equation for an alternative perspective and, ultimately, for confirmation of the conclusions made thus far on the vortexgenesis mechanism. Herein we consider circulation in an Eulerian framework rather than analyzing circulation about a material curve (e.g., Rotunno and Klemp 1985; Davies-Jones and Brooks 1993; Trapp and Fiedler 1995) that, in the present case, becomes topologically too deformed to afford accurate evaluation of the circulation forcing terms [see, e.g., Eq. (2) of Skamarock et al. (1994)].

We begin with the absolute vertical vorticity equation, now written as

View Expanded

Integrating Eq. (4.3) over horizontal control area A (that is held fixed to the grid) and then applying the divergence theorem gives

View Expanded

where the line integral is about A, assuming outward unit normal n̂. Equation (4.4) describes the absolute² circulation tendency, whose forcing terms hereafter are referred to as ζ flux, f flux, ω flux, and mixing, respectively. An illustration of how these terms (less mixing) contribute to positive circulation tendency is provided in Fig. 10.

We note that one advantage of this analysis approach is that it reveals the macroscopic properties of vortexgenesis without the need to choose a “representative” trajectory, as in the preceding Lagrangian analysis of Eq. (4.1). We now apply Eq. (4.4) to the 20/2.5/0 simulation, as done before. Horizontal control areas at z = 0.4 km (the second grid level above the ground) are used for the line integrations. These 14 km × 14 km areas A and A′ enclose the respective cyclonic and anticyclonic members of the low-level vortex couplet during a 30-min period (1 h 20 min to 1 h 50 min) of the couplet's initial growth (see Fig. 5). Line-integrated forcing terms in Eq. (4.4) are time integrated over this interval as C(t)_{ω−flux,etc.} = ∫^t_t0 (ω flux, etc.) dt′ and then compared with the time series of circulation.

For the purposes of this initial, idealized application, we disregard contributions from mixing and the horizontal flux of relative vorticity and focus solely on circulation generation in the absence of preexisting relative circulation/vertical vorticity. In doing so, the Eulerian circulation perspective shows us first of all that the low-level vortex couplet is generated through a large ω flux (ω′ flux) that contributes positively (negatively) to circulation C (C′) (Fig. 11). Such |ω flux| arises primarily from the depression of southward-oriented horizontal vortex lines along the north (south) boundary of area A (A′) (see Figs. 6, 5c,d), which is consistent with the previously arrived conclusion of couplet formation through horizontal vortex-line tilting.

Also consistent is the symmetry-breaking mechanism, which in the Eulerian circulation analysis is through the f-flux term. The time-integrated effect of this term can be quantified in this f = 0 case by computing a “hypothetical” f flux, using the actual ∮ − V_H · n̂ dl but with f = 10⁻⁴ s⁻¹ instead of f = 0 s⁻¹. Note from Fig. 11 that this hypothetical flux of planetary vorticity into the control areas would act to increase circulation monotonically, owing to consistent inflow through both the eastern and western boundaries of A and A′. Indeed, over a 30-min interval, the time-integrated magnitude of the hypothetical f flux is just slightly less than that of the |ω flux|. This result suggests to us that positive f flux into area A′ (A) should help mitigate negative (enhance positive) circulation gained by the ω′ flux (ω flux) and thereby preclude (allow) the development of an anticyclonic (cyclonic) mesovortex near the ground.

A circulation analysis of the 20/2.5/f simulation, which includes all terms in Eq. (4.4), confirms this basic result of the preceding exercise (Fig. 12). Note that the sizeable contribution to positive and negative circulation, respectively, from the flux of relative vorticity into/out of areas A and A′ is explained in part by relative vorticity generated outside the control areas and in part as a consequence or artifact of fixed control areas and a northeasterly storm-motion vector.³

Some final calculations are offered to emphasize further the direct role of planetary vorticity in the low-level mesovortexgenesis. As developed in Davies-Jones (1986, 216–217), an equation that governs the cross-sectional area a(t) of a vortex tube in an inviscid, barotropic fluid can be derived from Eq. (4.1) and expressed as

View Expanded

Area a of the vortex tube will contract/expand given some constant horizontal divergence δ within a. By virtue of the assumptions above, circulation C about the vortex is constant. Hence, we can initially let a(0) = C/ζ₀. At a later time τ when the vortex core radius has contracted/expanded to r_c, the cross-sectional area is a(τ) = πr²_c. Integrating (4.5) over the interval 0 ≤ t ≤ τ and then solving for τ gives

View Expanded

Applied to our low-level mesovortex problem, Eq. (4.6) yields τ = 65 min given δ = −1 × 10⁻³, r_c = 2.5 km, C = 1 × 10⁵, and ζ₀ = f = 1 × 10⁻⁴. Thus, this simple model shows that planetary vorticity alone can be concentrated into a mesovortex in roughly 1 h. We note that calculations by Lilly (1976) also support this statement, even though his were used to explain the development of supercell mesocyclones and tornadoes. Of course, strong, low-level mesocyclones form routinely in supercells simulated with f = 0 (e.g., Klemp and Rotunno 1983; Wicker and Wilhelmson 1995), as mechanisms internal to supercells are at least sufficient for mesocyclogenesis; as just demonstrated, strong, low-level mesovortices only form in QLCSs simulated with f ≠ 0.

5. Association with damaging, near-ground winds

One implication of the low-level mesovortices simulated herein is their tendency to be associated with strong winds, which we assert would be manifested in hypothetical “straight line” damage patterns (e.g., Fujita 1978; Forbes and Wakimoto 1983), considering the asymmetry and breadth of the vortices. In the following, we investigate mesovortex-associated “damaging” winds and also compare such to damaging, convectively produced winds often found at the apex of the bow echo (Fujita 1978, 1979).

Consistent with the conceptual models of Fujita (1978, 1979), a plot of the magnitude of the ground-relative horizontal winds⁴ (V_GR) at z = 127 m and t = 5 h shows a kilometer-wide strip of V_GR ≥ 30 m s⁻¹ just behind the gust front at the primary bow-echo apex (Fig. 16a); these winds are due to descending rear inflow and its accompanying high perturbation pressure. More prominent in this figure, however, is the broad area of V_GR ≥ 30 m s⁻¹ that encompasses the two 35 m s⁻¹ wind maxima associated with the south-southwest flanks of vortices BEV1 and BEV2.⁵ Such a mesovortex–high-wind association is maintained during the interval 2 ≤ t ≤ 6 h (Fig. 17) and, moreover, explains the increase with time in the areal extent of strong winds. For example, the large area enclosed by the 35 m s⁻¹ isotach at t = 6 h can be related to an amalgamation of BEV1 and BEV2. We can contrast this evolution with that in the 20/2.5/0 simulation, which is a “control” case of sorts, owing to its lack of significant low-level mesovortices. Correspondingly, high wind speeds can be found at low levels only in a narrow zone behind the gust front (Fig. 16b).

One may infer from the preceding paragraph that in the 20/2.5/f simulation, near-ground winds at the bow-echo apex can be less damaging than those with the mesovortices. Quantified in terms of local wind duration, this inference is correct: at a point fixed at the ground and affected by BEV2 (see Fig. 16a), ground-relative winds are greater than or equal to 30 (35) m s⁻¹ for 402 (162) s, during the 40-min period centered at t = 5 h (Fig. 18). In contrast, at a point affected by the bow-echo apex, ground-relative winds are greater than or equal to 30 m s⁻¹ for 78 s (Fig. 18). Additional quantitative confirmation is given in Table 1, which indicates that at t = 5 h the horizontal area encompassing the V_GR = 30 m s⁻¹ isotach associated with BEV1 and BEV2 is an order of magnitude larger than that in the vicinity of the apex (see also Fig. 16a); an even larger difference in this areal extent of damaging winds with respect to the two system-relative locations is found at t = 6 h (and also for V_GR ≥ 35 m s⁻¹; Table 1).

Observational data that corroborate our model results can be found in Miller and Johns (2000). They show, for example, that in the case of the mesoscale convective system of 4 July 1999, a large blowdown of trees “occurred underneath the northern part of the storm complex—not the rapidly bowing southern section,” and add that wind damage “along the path of the very intense bow echo is not nearly as widespread and has only pockets of very severe damage.” The attribution by Miller and Johns of the widespread severe-wind damage to embedded high-precipitation supercell storms and the review by Seimon (1998) of “devastating windstorms” owing to supercell mesocyclones at the surface motivates the following analysis in which we seek to determine the forcing of what have been labeled thus far as mesovortex-associated winds.

Consider the trajectory of a parcel that populates the wind maximum at t = 5 h near BEV2 (e.g., Fig. 16a). The trajectory originates 20 min prior in a location ∼15 km to the northwest and at an altitude generally less than or equal to 1 km (e.g., Fig. 19a). Its rate of descent from this altitude never exceeds 2 m s⁻¹; a similar conclusion can be reached for eight other parcels in the vicinity of BEV2. Hence, we can rule out the possibility that locally intense downdrafts or downbursts are responsible for the large V_GR near the mesovortices. The other, perhaps more apparent possibility based on the pressure field in Fig. 16a is that the damaging winds are driven by the low pressure, hence large horizontal pressure gradients, induced by the mesovortices. The following analysis of the pressure-gradient forcing of horizontal momentum along the trajectory allows an evaluation of this hypothesis.

Perturbation pressure π can be decomposed, as in Rotunno and Klemp (1985), into contributions from “buoyancy” (B) (π_B) and “dynamics” (π_DN), where

View Expanded

where, in tensor notation, ω_i is the 3D vorticity vector, e_ij is the 3D rate of strain tensor,

View Expanded

and all other variables have their traditional meanings. Of particular interest is the contribution to the dynamics pressure from the vertical component of vorticity squared [hereafter referred to as “vorticity squared,” π_ζζ; first term on the rhs of Eq. (5.1b), evaluated for i = 3], through which the effect of the mesovortices on the pressure field is represented. We compute the pressure-gradient force (HPGF) in the horizontal direction locally parallel to a trajectory,

c_pθπs,(5.2)

where ∂s = [(∂x)² + (∂y)²]^1/2, and then time integrate the HPGF owing separately to buoyancy, dynamics, and vorticity squared along all or part of the trajectory,

View Expanded

where V₀ is the magnitude of the horizontal wind at time t₀, and * is the generic subscript for each of the three contributions.

During the interval 4 h 50 min ≤ t ≤ 5 h, the parcel experiences a dramatic horizontal acceleration, at heights generally less than 0.2 km (Fig. 19a). Buoyancy forcing, or that associated directly with the cold pool, is responsible for most of the parcel acceleration until about a minute prior to t = 5 h; over the entire interval, however, the time-integrated buoyancy forcing contributes only 18% to the net gain in horizontal wind. In contrast, the contribution from −c_pθ∂π_ζζ/∂s is initially small, at times well before the parcel is influenced by the vortex-induced low pressure. Over the entire period of integration, however, the integrated contribution amounts to more than three times that due to the cold-pool forcing. Clearly, the strongest low-level winds at this stage of the simulated QLCS are due largely to the low-level mesovortex circulations.

An obvious question at this point regards how well these conclusions can be generalized to QLCSs inhabiting environments with vertical wind profiles other than with U_S = 20 m s⁻¹/2.5 km. As demonstrated in Part I, significant, low-level mesovortices tend not to form within simulated QLCSs when the environment has weak low-level shear. Illustrating this result is the weak, upshear-tilted, effectively vortex-free QLCS produced in the 10/2.5/f experiment (Fig. 20a). Noteworthy, however, is the appearance of low-level winds with V_GR ≥ 30 m s⁻¹in a ∼10 km wide band behind a bowing segment (Fig. 20b). Recalling the study by Weisman (1992), such a comparatively large area of strong surface winds trailing the convective system's leading edge is to be expected with an environmental shear of U_S ∼ 10 to 15 m s⁻¹/2.5 km (and with moderate environmental CAPE), owing to a resultant rear-inflow jet that descends and spreads laterally at the ground, well behind the gust front (Fig. 20b). In contrast, within environments of moderate-to-strong vertical wind shear (i.e., U_S ≥ 20 m s⁻¹/2.5 or 5 km in our model study) the RIJ tends to be elevated ∼2–3 km above the ground; a branch of the rear inflow descends immediately behind the gust front, allowing only for a very thin strip of strong, postfrontal winds (Figs. 20c,d). Such environments also permit the formation of intense low-level mesovortices (see Part I) that, as just shown, can induce especially strong and damaging winds (Figs. 16a, 20d).

6. Effect on system structure and evolution

Intuition followed by close examination of the experimental results suggests that low-level mesovortices can also affect convective system structure and evolution. Case in point, the 20/2.5/f and 20/2.5/0 simulations have largely imperceptible differences at t ∼ 2 h, save for the respective presence and absence of developing low-level mesovortices (cf. Figs. 1a, 2a and Figs. 3a, 4a). At t = 3 h, however, we begin to find—exclusively in the 20/2.5/f simulation—the existence of pronounced horizontal undulations in the leading-edge updraft that by t = 4 h become updraft “fractures” (cf. Figs. 1b,c, 2b,c and Figs. 3b,c, 4b,c). Such fractures span a considerable depth of the model troposphere, as can be visualized in a 3D rendering of vertical velocity (Fig. 21), and tend to be spatially correlated with low-level mesovortices such as BEV1 (see also Figs. 22a,b).

For more insight into this additional mesovortex implication, we again turn to decompositions of pressure, expressed now in terms of −c_pθ∂π_B/∂z + B and −c_pθ∂π_DN/∂z, the buoyancy forcing and dynamics forcing, respectively, of vertical momentum (Rotunno and Klemp 1982). During the mature stage of our modeled QLCS, we notice a dynamics-forcing minimum and maximum on the left and right flanks, respectively, of BEV1 and BEV2 at z = 3 km (Fig. 22c). These dynamics-forcing couplets can be attributed to the vertical tilt toward the south-southwest of the vortices and to the low pressure they induce. Hence, as alluded to in Fig. 21, a low-level mesovortex tends to reduce the midlevel (but also low-level; e.g., Fig. 22b) updraft at the system's leading edge; a mesovortex aloft tends to increase midlevel updraft behind the system's leading edge, although such an increase is offset by the negative buoyancy forcing at midlevels (Fig. 22d) associated with negatively buoyant air within the cold pool. The net effect is an absence of updraft above the low-level vortex position. Over time, this translates into a breakup or segmentation of the previously (nearly) continuous convective line, with new midlevel vortices often forming at the ends of the new segments, through the means described by WD98 and additionally through upward advection of low-level mesovortex vorticity (see also Part I).

7. Summary and conclusions

Using a numerical cloud model, we have simulated long-lived quasi-linear mesoconvective systems (QLCSs) that possess significant, low-level meso-γ-scale vortices. We analyzed in detail an experiment with a model base-state CAPE of 2200 J kg⁻¹ and unidirectional wind shear of 20 m s⁻¹ over a surface-based depth of 2.5 km; this is an environment supportive of a squall line that develops strongly bowed segments. Sensitivity of low-level QLCS structure to environmental wind shear was discussed extensively in Part I (Weisman and Trapp 2003), which otherwise supports the robustness of the general results. The experiments and analyses of the current study have gained us fundamental insight into the genesis and implications of low-level mesovortices in QLCSs.

The mesovortices are generated just behind the leading-edge gust front of the QLCS, initially anywhere in the along-system direction. Once the QLCS becomes predominantly bow shaped, a northern bias in vortex location develops in the along-system direction. At all QLCS stages, most of the prominent low-level vortices rotate cyclonically. At all stages of a QLCS simulated without Coriolis forcing, low-level vortices tend not to be prominent, regardless of rotational sense.

Mesovortexgenesis is initiated at low levels by the tilting, in downdrafts, of initially crosswise baroclinic horizontal vorticity (Fig. 23); such horizontal vorticity may be associated with an RIJ (mature QLCS) or the cool outflow of a rainy downdraft (developing QLCS). Over a period of less than an hour, the symmetrical vortex couplet that results from tilting gives way to a dominant cyclonic vortex as the relative and, more notably, planetary vorticity is stretched vertically: hence, the Coriolis force plays a direct role in the genesis of low-level, cyclonic mesovortices and also in the mitigation of low-level, anticyclonic mesovortexgenesis. This proposed mechanism is different from that of supercellular low-level mesocyclogenesis vis-à-vis (i) the role of planetary vorticity (necessary and direct) and (ii) the velocity-vector relative orientation of the predominant horizontal vorticity (crosswise rather than streamwise) that is vertically tilted. Regarding (ii), the predominance of streamwise horizontal vorticity at low levels in supercells equates to an immediate formation of cyclonic low-level mesocyclones (e.g., see Fig. 9 of Davies-Jones and Brooks 1993), without the need of a symmetry- or vortex-couplet-breaking mechanism like the stretching of planetary vorticity. Note that such symmetry breaking in the real atmosphere would also involve the stretching of synoptic-scale relative vorticity (e.g., along cold fronts), which may be abundant in the environments in which mesoconvective systems form and/or evolve.

We emphasize here as in Part I that many of the mesovortices form first within the lowest several hundred meters above the ground and thereafter grow upward to result in a mesovortex that extends through midlevels. Hence, the low-level mesovortices need not be preceded by and form beneath a midlevel mesovortex. Conversely, the midlevel mesovortices need not precede and otherwise be associated with a low-level mesovortex.

Analyses of forcing terms in the vertical and horizontal momentum equations revealed two implications of the low-level mesovortices. The first is that downward-directed vertical pressure gradients induced by the vortices effectively segment the previously (nearly) continuous convective line (Fig. 24), with new midlevel vortices often forming at the ends of the new segments. The second represents a new paradigm, akin to that proposed for supercells by Seimon (1998), for damaging low-level wind production in bow echoes: quantified in terms of duration and areal extent, the strongest low-level winds are found in association with mesovortices, several tens of kilometers to the northwest of the bow apex. Occurring with QLCSs in moderately to strongly sheared environments, such damaging “straight line” winds are driven by the large horizontal pressure gradients associated with the mesovortices and exist in addition to the less damaging winds due to descending rear inflow at the bow-echo apex (Fig. 24). Weakly sheared environments, in contrast, support QLCSs that lack significant mesovortices but that still can produce damaging surface winds via descending rear inflow.

Observations that can be compared with our model results are currently lacking but will be available following the Bow Echo and Mesoscale Convective Vortex (MCV) Experiment (BAMEX; Davis et al. 2001). Analyses of the high-resolution BAMEX datasets, used in conjunction with real-case simulations (e.g., Atkins and Arnott 2002), will be used to verify, test the generality of, and/or explore further the mesovortexgenesis mechanism and subsequent implications described herein.