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    Schematic of tilting contribution on the boundary of the circulation box. Large arrows at left indicate meridional flow decreasing with height. This is associated with the horizontal vorticity vector pointing out of the box at right. Vertical motion on the boundary of the box is indicated by a dashed arrow. A hypothetically displaced vortex line is indicated by a thin solid line, with the sense of rotation about a vertical axis indicated by arrowed ellipses.

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    (a),(b) Weather Surveillance Radar-1988 Doppler (WSR-88D) composite reflectivity at (a) 0500 and (b) 1800 UTC 11 Jun 2003. (c),(d) Model-derived maximum reflectivity in column using Thompson reflectivity algorithm with winds (ground relative) at 500 hPa superposed for (c) 0500 and (d) 1800 UTC 11 Jun 2003. Black squares in (c) and (d) indicate the locations of the circulation boxes, 324 km on a side. State abbreviations: AL = Alabama; AR = Arkansas; IL = Illinois; KY = Kentucky; MO = Missouri; MS = Mississippi; OK = Oklahoma; TN = Tennessee; TX = Texas. Long wind barbs indicate 5 m s−1.

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    (a),(b) Vertical cross section of meridional wind through the MCV center at 1800 UTC 11 Jun: (a) observed, reproduced from Davis and Trier (2007); (b) simulated, averaged over 120 km in the north–south direction. Plots show ground-relative flow. Contour interval is 5 m s−1, with dashed lines denoting northerly flow.

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    (a) Surface observations from the Automated Surface Observing System (ASOS) at 1800 UTC 11 Jun 2003 and from BAMEX dropsondes (plotted without station symbol) time–space corrected to 1730 UTC as in Davis and Trier (2007), with temperature analysis shown using a 2°C contour interval, superposed on a Geostationary Operational Environmental Satellite (GOES) infrared satellite image valid for 1800 UTC 11 Jun. (b) Model fields corresponding to (a), with cloud-top temperature shown in grayscale shown at bottom of plot. The × symbol denotes the approximate position of the MCV center.

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    (a),(b) WSR-88D composite reflectivity at (a) 0500 UTC and (b) 1800 UTC 6 Jul 2003. (c),(d) Model-derived maximum reflectivity in column using Thompson reflectivity algorithm with winds (ground relative) at 500 hPa superposed for (c) 0500 UTC 6 Jul and (d) 1800 UTC 6 Jul; black squares indicate the locations of the circulation boxes, 320 km on a side. State abbreviations: IA = Iowa; IL = Illinois; MN = Minnesota; MO = Missouri; NE = Nebraska; and WI = Wisconsin. Long wind barbs indicate 5 m s−1.

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    Quad-Doppler wind and reflectivity analysis valid for 0550 UTC 6 Jul. The Naval Research Laboratory (NRL) P-3 and the National Oceanic and Atmospheric Administration (NOAA) P-3 tail Doppler radars were synthesized using the technique described in Wakimoto et al. (2006a): winds and reflectivity at (a) 1.6 and (b) 5.2 km AGL. Vectors are relative to an assumed eastward system motion of 14 m s−1. The V symbol denotes the line-end vortex location.

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    (a) Surface observations at 1800 UTC 6 Jul, with temperature analysis shown using a 2°C contour interval, superposed on GOES infrared satellite image also valid for 1800 UTC 6 Jul; (b) model fields corresponding to (a), with cloud-top temperature shown in grayscale shown at bottom of plot. Observed winds and temperatures were obtained from ASOS stations and BAMEX dropsondes. The × denotes the approximate position of the MCV center.

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    Box-averaged wind profiles from (a) 10–11 Jun and (b) 5–6 Jul. Averaging occurs over an area 324 km × 324 km. Winds are ground relative. System motion is indicated by thin dashed lines. Solid lines indicate the wind profiles at 2100 UTC on (a) 10 Jun and (b) 5 Jul; heavy dashed lines show the profiles at 1800 UTC on (a) 11 Jun and (b) 6 Jul, respectively.

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    (a),(b) Vertical profiles of box-averaged (a) final absolute vorticity (η; gray dashed), total vorticity change over final 27 h of simulation (δζ; black solid), total PV change over final 27 h (δPV; gray solid), and sum of hourly rates of change of vorticity from all rhs terms in (4) except friction (Σ), for (a) 10–11 Jun and (b) 5–6 Jul. (c),(d) Total vorticity changes from eddy flux (dashed), stretching (thick solid), and tilting (thin solid) terms in (4) for (c) 10–11 Jun and (d) 5–6 Jul.

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    (a)–(e) Time–pressure series of hourly changes in box-averaged vorticity representing (a) full simulated changes, (b) the sum of rhs terms in (4) except friction, (c) eddy flux, (d) stretching, and (e) tilting for 10–11 Jun. (f)–(j) As in (a)–(e), respectively, but for 5–6 Jul. The first time depicted is 2200 UTC. Data represent the vorticity change for the hour ending at the times shown.

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    As in Fig. 10, but for vertical mass flux (−ω/g) integrated over the circulation box for (a) 10–11 Jun and (b) 5–6 Jul.

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    Vertical velocity (cm s−1; color) and meridional velocity (contour interval = 2 m s−1) along the eastern boundary of the circulation box at (a) 0100 UTC 11 Jun and (b) 0400 UTC 5 Jul. Heavy contours indicate southerly wind; thin contours indicate northerly wind. Heaviest black curves enclose regions where the contribution to vortex tilting is most strongly negative (anticyclonic tendency within the box).

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    Relative vorticity at 900 hPa and system-relative winds for (a) 0400 and (b) 0900 UTC 11 Jun and for (c) 0400 and (d) 0900 UTC 6 Jul. Units are 10−4 s−1. Red lines denote boundaries of circulation box. Coordinates in schematic at lower right refer to text.

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    (a) Difference of moist static energy, normalized by Cp (see text) between 300 and 900 hPa (positive for conditionally stable conditions) for 10–11 Jun (dashed) and 5–6 Jul (solid). (b) Box-averaged relative humidity for 10–11 Jun (dashed) and 5–6 Jul (solid) cases in the layer from levels 21 to 26 (roughly 600–800 hPa).

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    Skew–T diagrams averaged over 324 km × 324 km box valid for (a) 2100 UTC 10 Jun (red) and 1500 UTC 11 Jun (black) and for (b) 2100 UTC 5 Jul (red) and 1500 UTC 6 Jul (black).

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    Schema depicting the development of cyclonic vorticity at the surface. Gray shading denotes areas of cyclonic vorticity. Thin solid lines depict vertical circulation, dashed for decaying circulation. Heavy gray arrows show system-relative environmental flow. Shown are three stages: (a) mature MCS with the midtropospheric MCV and line-end vortex developed and well separated; (b) MCV and line-end vorticity superposed; (c) erect column of cyclonic vorticity reaching the surface.

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The Vertical Structure of Mesoscale Convective Vortices

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  • 1 Mesoscale and Microscale Division, National Center for Atmospheric Research,* Boulder, Colorado
  • | 2 Department of Earth and Atmospheric Sciences, University at Albany, State University of New York, Albany, New York
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Abstract

Simulations of two cases of developing mesoscale convective vortices (MCVs) are examined to determine the dynamics governing the origin and vertical structure of these features. Although one case evolves in strong vertical wind shear and the other evolves in modest shear, the evolutions are remarkably similar. In addition to the well-known mesoscale convergence that spins up vorticity in the midtroposphere, the generation of vorticity in the lower troposphere occurs along the convergent outflow boundary of the parent mesoscale convective system (MCS). Lateral transport of this vorticity from the convective region back beneath the midtropospheric vorticity center is important for obtaining a deep column of cyclonic vorticity. However, this behavior would be only transient without a secondary phase of vorticity growth in the lower troposphere that results from a radical change in the divergence profile favoring lower-tropospheric convergence. Following the decay of the nocturnal MCS, subsequent convection occurs in a condition of greater relative humidity through the lower troposphere and small conditional instability. Vorticity and potential vorticity are efficiently produced near the top of the boundary layer and a cyclonic circulation appears at the surface.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation

Corresponding author address: Christopher A. Davis, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. Email: cdavis@ucar.edu

Abstract

Simulations of two cases of developing mesoscale convective vortices (MCVs) are examined to determine the dynamics governing the origin and vertical structure of these features. Although one case evolves in strong vertical wind shear and the other evolves in modest shear, the evolutions are remarkably similar. In addition to the well-known mesoscale convergence that spins up vorticity in the midtroposphere, the generation of vorticity in the lower troposphere occurs along the convergent outflow boundary of the parent mesoscale convective system (MCS). Lateral transport of this vorticity from the convective region back beneath the midtropospheric vorticity center is important for obtaining a deep column of cyclonic vorticity. However, this behavior would be only transient without a secondary phase of vorticity growth in the lower troposphere that results from a radical change in the divergence profile favoring lower-tropospheric convergence. Following the decay of the nocturnal MCS, subsequent convection occurs in a condition of greater relative humidity through the lower troposphere and small conditional instability. Vorticity and potential vorticity are efficiently produced near the top of the boundary layer and a cyclonic circulation appears at the surface.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation

Corresponding author address: Christopher A. Davis, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. Email: cdavis@ucar.edu

1. Introduction

Organized deep moist atmospheric convection projects onto many scales of motion. Although individual convection cells are perhaps only 1 km or so in horizontal scale, the propensity for cells to engender larger scales of motion through gravity waves or gravity currents they emit is well known. The rotational component of the flow resulting from convection projects onto many scales of motion as well. Of primary interest to the present study are mesoscale vortices that flank lines of deep moist convection (line-end vortices) and broad circulations often observed to the rear of lines of convection (mesoscale convective vortices or MCVs). The importance of these features is their ability to persist beyond the decay of the convection from which they arise and thus to affect clouds and precipitation far downstream from their origin.

Line-end vortices on scales of 20–50 km occur on the end of narrow, quasi-linear regions of deep convection. Often these vortices initiate from the tilting of horizontal vorticity. Stretching of vorticity follows to further strengthen the circulation (Davis and Weisman 1994; Cram et al. 2002). In addition, the outflow boundary is often a locus of cyclonic vorticity, and the end of such a vorticity filament can simply “roll up” to form a vortex. The line-end vortex is often a relatively shallow feature confined to the lowest 3 km or so (Weisman 1993).

The MCV is the class of largest mesoscale vortex that owes its existence to organized moist convection. Typically 100–300 km in diameter, these vortices are several kilometers deep and sometimes span most of the troposphere (Fritsch et al. 1994; Davis and Trier 2007). From a vorticity dynamics perspective, the MCV is often viewed as resulting from the convergence of synoptic-scale vorticity, with the largest contribution coming from earth’s rotation (Bartels and Maddox 1991; Skamarock et al. 1994) but with substantial modification from mobile, short-wavelength troughs (Zhang 1992). Without the Coriolis force, idealized simulations produce not a single dominant vortex, but rather a counterrotating vortex pair (Skamarock et al. 1994; Davis and Weisman 1994).

The relative contribution of tilting versus stretching of vorticity to the formation of mesoscale vortices has not been made clear in the context of observations or of simulations of observed MCVs. Kirk (2007) presents evidence of two pathways to MCV formation from the perspective of the curl of the momentum transport. One can readily translate this perspective into tilting versus stretching of vorticity, and it appears that either can dominate in a given case (Brandes 1990; Zhang 1992; Kirk 2007). In coarse-grid models that rely on cumulus parameterization or prescribed heating to model moist convection (e.g., Zhang 1992; Jiang and Raymond 1995; Kirk 2007), it is difficult to properly represent the tilting of horizontal vorticity. This misrepresentation of tilting occurs because such models often fail to produce sufficient negative buoyancy and thus err in their generation of horizontal vorticity (Weisman and Davis 1998). Clarification of the role of vortex tilting therefore requires models that can explicitly represent the generation of cold pools and rear-inflow jets, together with their associated horizontal vorticity.

The literature is generally unclear about the difference between a cyclonic line-end vortex and an MCV. Skamarock et al. (1994) showed that a line-end vortex develops within the first 3–4 h of mesoscale convective system (MCS) evolution in idealized simulations. MCSs tend to become more asymmetric with time in a rotating environment, with larger-scale (100-km diameter) vortices resembling MCVs emerging after about 6 h (e.g., Fritsch and Forbes 2001, their Fig. 9.14). However, the origin of these simulated vortices is closely tied to the end of a quasi-linear convective feature, and the altitude of maximum vortex intensity tends to occur from 2–3 km. MCVs usually maximize between 500 and 600 hPa (4–6-km altitude) (Zhang 1992; Fritsch et al. 1994; Bartels et al. 1997; Davis and Trier 2007). Davis and Trier (2002) and Trier and Davis (2002) suggested that deep MCVs may result from the superposition of a midtropospheric vortex and a line-end vortex. The present study will present evidence that supports this concept.

Previous studies have documented that some MCVs penetrate to the surface (Bosart and Sanders 1981; Fritsch et al. 1994; Rogers and Fritsch 2001). In MCVs over land, this penetration may have consequences in forming surface fronts and organizing precipitation (Galarneau et al. 2009). Over tropical oceans, the appearance of a cyclonic circulation at the surface is instrumental for initiating air–sea interaction (Rotunno and Emanuel 1987).

Davis and Trier (2002) demonstrated that such a deep MCV can result from the superposition of a midtropospheric MCV with a lower-tropospheric, line-end vortex. Furthermore, Davis and Trier (2007) observed strong vertical wind shear in the lowest few kilometers in cases of MCVs with little or no signature at the surface. These two studies both suggest that the factor determining the vertical penetration of an MCV to the surface is the formation of an additional cyclonic potential vorticity (PV) anomaly within a kilometer or so of the ground. This idea is consistent with the “bottom up” paradigm of tropical cyclogenesis wherein deep moist convection in a suitably moist environment generates lower tropospheric PV (Tory et al. 2007 and references therein). However, the details of the MCV formation process were not sampled in the Bow Echo and MCV Experiment (BAMEX) cases in which the mature MCV was later well observed. Thus, we are still left with the unresolved issue of how an MCV reaches the surface.

The principal tool used in this study is numerical simulations using the Advanced Research Weather Research and Forecasting Model (ARW; Skamarock et al. 2005). Diagnosis of these simulations will be performed primarily using vorticity budgets, based on the flux form of the vorticity equation as described in section 2. In section 3, observed MCSs and their representation in simulations using the ARW model are described. The vorticity diagnostics are applied in section 4 and results are summarized in section 5.

2. Vorticity dynamics

a. Vorticity equation

The traditional form for the equation representing the local change of relative vorticity is
i1520-0469-66-3-686-e1
where ζ is the relative vorticity, η the absolute vorticity, ω the vertical velocity in pressure coordinates (x, y, p), and F the frictional force. As shown in Haynes and McIntyre (1987), (1) can be rewritten as
i1520-0469-66-3-686-e2
where the divergence is in the horizontal plane; that is, the flux has no vertical component in pressure coordinates. Here, the horizontal vector K will be referred to as the vorticity flux vector. The form (2) has been exploited extensively by Davis and Weisman (1994), Raymond et al. (1998), and others in the analysis of relative vorticity in convective systems and tropical depressions. Its virtue is that one can examine the net mesoscale circulation within a region in which complex convection and vorticity dynamics are taking place without having to explicitly analyze the full complexity. If one integrates (2) over any closed region and applies Gauss’s theorem (also referred to here as the divergence theorem), then
i1520-0469-66-3-686-e3
where C denotes the circulation. Hence, only the component of K normal to the boundary of a closed region need be considered to evaluate the tendency of circulation within the region.

b. Interpretation of the “tilting” term

Kirk (2007) noted that the second term under the divergence operator in (2) has not been interpreted adequately in the literature. Although previous authors refer to this as a tilting term, it actually combines the tilting term with the vertical advection term in (1), and so the interpretation of this term has been obscure. Here we make explicit the relationship of the second term on the right-hand side (rhs) of (2) with vortex tilting.

It is first worth noting that only the horizontal vorticity associated with the vertical shear of the horizontal wind appears. However, this is not an approximation. The full horizontal vorticity may be included in the rhs of (2). Terms involving the horizontal vorticity arising from horizontal gradients of vertical velocity simply cancel out. Thus, we may equate − × ∂v/∂p with the horizontal vorticity from the perspective of tilting vorticity into the vertical.

Consider a closed region on a surface of constant pressure. For simplicity this is assumed to be a square box. The term −ω( × ∂v/∂p) · represents the correlation between vertical velocity and the component of the horizontal vorticity directed normal to the box. If one imagines the vorticity as represented by vortex lines in the horizontal plane, vertical motion will lift or depress the vortex line on the boundary of the box. In the example shown (Fig. 1), lifting of a vortex line directed outward produces a dipole of vorticity, with the cyclonic portion of the dipole inside the box and the anticyclonic portion outside the box.1 In this case, the net circulation within the box will increase because of the tilting of horizontal vortex lines into the vertical. Clearly, if the updraft were entirely within the box, there could be no net change of vorticity and circulation within the box due to tilting.

c. Stretching versus transport: Mean and eddy terms

Returning now to the first term on the rhs of (2), there is some uncertainty about how to interpret this combination of stretching and horizontal vorticity advection. The line-integral form (3) indicates that this term will contribute to vorticity within a region (box) if there is a correlation between the vertical vorticity and flow normal to the box. In general, the full term can be decomposed into mean and eddy contributions. Using overbars to define the average value around the perimeter of the box, primes to denote a perturbation from this value, and tildes to indicate the average over the area of the box, (3) becomes
i1520-0469-66-3-686-e4
where we have used the divergence theorem to relate the average wind component normal to the box to the mean divergence δ̃ over the area A of the box. The eddy flux term represents the correlation between vorticity perturbations on the edge of the box and wind perturbations normal to the box. Inward flow collocated with a positive vorticity perturbation or outward flow collocated with a negative vorticity perturbation will both increase the circulation within the box. Even in a flow that is nondivergent, the eddy flux term can contribute to an accumulation of vorticity within a closed region. In what follows, horizontal vorticity advection is identified uniquely with the eddy flux term, whereas vortex stretching (or simply “stretching”) is synonymous with the mean term.

3. Numerical simulations

The configuration of the ARW for the present forecasts follows that reported by Done et al. (2004) for the real-time simulations during BAMEX (Davis et al. 2004), except that the version of ARW has been upgraded to 2.2 with alternative physical parameterizations chosen for the present study. The model domain was a single 4-km mesh with 500 points in each horizontal direction. There were 35 levels spaced roughly 200 m apart in the lowest kilometer with monotonic stretching to about 1-km spacing near and above 14 km. The model top was at 50 hPa (about 19 km).

The ARW was initialized from output from the then-operational National Centers for Environmental Prediction (NCEP) Eta Model (NCEP-Eta; Black 1994). The NCEP-Eta featured a 12-km grid spacing that was coarsened to 40 km before being obtained from NCEP and covered much of North America. Forecasts were initialized at 0000 UTC on 10 June and 5 July 2003. Little structure was present in the initial conditions on the scale of MCSs (roughly 100–200 km). Lateral boundary conditions were specified from 3-h output from the corresponding NCEP-Eta forecast for both ARW forecasts.

The physical parameterizations used in both ARW forecasts include the Mellor–Yamada–Janjic boundary layer scheme (Mellor and Yamada 1982; Janjic 2002), which predicts turbulent kinetic energy, and the Thompson microphysics scheme (Thompson et al. 2004). The Thompson scheme predicts five classes of condensate (cloud water, cloud ice, rain, snow, and graupel), but it is designed to produce a larger quantity of small hydrometeors and typically results in a more extensive stratiform region than does the Lin et al. (1983) scheme used in the earlier BAMEX simulations (Done et al. 2004). Although condensate variables were initialized to be zero, they appeared to spin up during the first 2–3 h of the simulations.

4. Overview of two BAMEX MCVs

a. 11 June 2003

The primary MCS, within which the MCV formed, initiated near 2100 UTC 10 June 2003 over western Oklahoma and matured into an asymmetric squall line by 0500 UTC 11 June over central Oklahoma (Fig. 2a). The corresponding radar reflectivity derived from the ARW simulation (Fig. 2c) represents the maximum in a vertical column and was obtained using an algorithm written explicitly for the Thompson microphysical scheme (G. Thompson 2008, personal communication). The simulated reflectivity attains somewhat larger peak values in the convective cores than observed but overall is able to produce a realistic evolution of the primary MCS, including an extensive stratiform precipitation region (Figs. 2a,c). The primary MCS was generally 100–200 km farther south, and convection ahead of the primary MCS was more widespread and farther south in the model than in observations. Widespread convection north and east of the primary MCS did occur in reality, but several hours later than in the simulation. Remnants of this convection were still evident at 1800 UTC 11 June over central Kentucky (Fig. 2b).

The simulated MCV in its formative stages could be seen from the cyclonic shift of winds at 500 hPa to the west of the deep convection in Fig. 2c. As the convection decayed, the vortex became relatively more prominent during the daytime on 11 June, with the center over northwestern Arkansas by 1800 UTC 11 June (Fig. 2d). This location was about 200 km southwest of the observed MCV location at that time (Davis and Trier 2007). The precipitation shield poleward of the vortex had a different configuration than observed, namely a southwest–northeast band of moderate intensity in the model versus a more north–south band in nature (Figs. 2b,d). However, an extensive east–west-oriented precipitation band did develop poleward of the observed MCV by about 0000 UTC 12 June (Trier and Davis 2007; Galarneau et al. 2009, their Fig. 11b).

The vertical structure, scale, and intensity of the mature MCV were well simulated, as summarized in Fig. 3. The maximum meridional winds were southerlies of about 17 m s−1 in the model and observations. The horizontal scale, judged by the zonal distance between positive and negative wind maxima, was just over 300 km, and the level of the maximum meridional wind was slightly below 600 hPa in both the simulation and observations. A slight westward tilt with height in the winds was suggested, and there was a surface cyclonic circulation present in both.

Detailed surface analyses (Fig. 4) offer a better depiction of the surface signature of the vortex. The cyclonic circulation appeared elongated from southwest to northeast in both the simulation and observations, with the coolest air mostly in phase with the axis of cyclonic circulation. The cool air occurred primarily because of reduced insolation beneath an extensive cloud shield that remained with the vortex in addition to the effects of evaporatively cooled air from earlier precipitation. Temperature minima in the cool air over northern Arkansas were a few degrees lower in the model than in the observations (note the area below 20°C in Fig. 4b). The warmest air was found over southeast Arkansas and the Mississippi Valley in the southwesterly flow. Secondary convection initiated in the warm air by 1800 UTC 11 June (Fig. 2b; see also Trier and Davis 2007), and broadly similar convection occurred in the simulation (Fig. 2d).

b. 6 July 2003

The bow echo of 6 July 2003, studied in detail in two recent papers (Wakimoto et al. 2006a,b), exhibited an intense MCS that formed over north central Nebraska (Fig. 5a), and rapidly developed into a severe wind–producing system with maximum surface winds in the Omaha, Nebraska area of around 40 m s−1. Following peak intensity around 0500–0600 UTC, the time when extensive airborne Doppler radar measurements were being made, the system rapidly dissipated in Iowa (not shown). The simulation developed an analogous MCS about 100 km farther south than observed. The simulated MCS briefly displayed a bowing convection line (Fig. 5c) but weakened earlier than the observed system (not shown).

The overall depiction of convection at 1800 UTC 6 July shows an arc-shaped region of moderate intensity in the observations (Fig. 5b), with a similar pattern in the model nearly collocated with the midtropospheric circulation center (Fig. 5d). Widespread deep moist convection initiated just prior to 1800 UTC 6 July over southwestern and eastern Wisconsin in the simulation but initiated about 2 h later in the observations (latter not shown). The simulated convection may have occurred earlier than observed because the model failed to produce an earlier band of convection in the same region. The remnants of this convection are visible over Lake Michigan at 1800 UTC 6 July (Fig. 5b).

Evidence for a strong, line-end vortex confined to the lower troposphere was present in airborne quad-Doppler radar observations, obtained as described in Wakimoto et al. (2006a), at 0550 UTC 6 July (Fig. 6a). This vortex, depicted at 1.6 km AGL, was confined to the lowest 2.5 km and was elongated from northwest to southeast along the northern end of a line of intense convection. Its shallow vertical structure and location relative to deep convection suggest that this feature was a line-end vortex. That this feature was not directly connected to the developing midtropospheric MCV is shown by the primarily southerly and southwesterly analyzed flow at 5.2 km (Fig. 6b). The numerical simulation results discussed in section 5 support this interpretation of a shallow, line-end vortex initially distinct from a midtropospheric cyclonic circulation.

A comparison of surface conditions at 1800 UTC 6 July (Fig. 7) shows that there was a well-defined cyclonic circulation located over southwestern Wisconsin in both the simulation and observations. In the model, this location is approximately beneath the midtropospheric vorticity center (Fig. 5d). The surface cyclonic circulation was perhaps slightly weaker in the observations owing to the absence of northerly flow over southwest Wisconsin and northeast Iowa. The minimum surface temperature in the model was at least 2°C lower than observed in this region, as was noted for the 10–11 June case (Fig. 4), although cloud cover in the model was not notably greater than observed. The simulated cyclonic circulation appears embedded in the baroclinicity on the southern edge of the cold pool in the model, and there is a suggestion of a similar but weaker structure in the observations. The poleward surge of warm moist air to the west of Lake Michigan helped to destabilize the atmosphere and initiate widespread deep convection in both the model and atmosphere during the afternoon of 6 July (not shown).

The observed vertical wind shear in the 6 July case was markedly stronger and deeper than in the 11 June case, as evidenced by comparing the results from Wakimoto et al. (2006a) with Davis and Trier (2007). Comparison of the shear profiles from these observational studies with the simulated shear profiles (Fig. 8) indicates good agreement. The environment just prior to the initiation of the parent MCS in the 11 June case exhibited about 7 m s−1 wind shear concentrated in the 2.5–5.5-km layer (Fig. 8a). Meanwhile, the incipient environment for the 6 July case revealed about 20 m s−1 wind shear in the same layer (Fig. 8b). A reduction of wind shear in the lower-to-middle troposphere occurred in both the 10–11 June and 5–6 July cases by 1800 UTC on the day following MCV formation. The question of whether this wind shear reduction represented a synoptic-scale variation independent of the MCS or was induced by the MCS itself is not examined here.

5. Results of vorticity diagnostics

The terms in (4) were computed from the ARW output files, extracted at hourly intervals. The equation was scaled by a time increment of 1 h to express the vorticity tendency as an hourly change of vorticity. The scale of the box within which diagnostics were computed (henceforth, the “circulation box”) was chosen as 81 × 81 grid points (324 km × 324 km). This scale represents the approximate distance between meridional velocity extrema in Fig. 4 for the 10–11 June case (and for the 5–6 July case; not shown). Because each vortex was nearly circular in its mature state, this distance can also be thought of as twice the radius of maximum wind. Placement of the box was somewhat subjective but was chosen to maximize the circulation within the box at 500 hPa at each time. To avoid a center that moved irregularly, a piecewise constant translation velocity was specified (Table 1). The translation velocity vector has been subtracted from model winds for all diagnostics shown.

The edge of the box often intercepted active convection and associated cell-scale vorticity structures. These structures created some sensitivity in the balance of the budget to the precise placement of the box. To improve the balance of the vorticity budget, an ensemble approach was adopted, wherein a distribution of budgets was computed at each output time. At each hourly diagnostic time, the box was perturbed from its central location (centered on the MCV) ±40 km in 8-km increments in both the x and y directions. Thus, 121 “samples” of the budget (11 × 11) were computed for the left-hand side (lhs) of (4) and separately for each term on the right-hand side of (4) except for the friction term. The average of the distribution was the statistic used to compare budget terms. Therefore, when viewing the results it must be recalled that contributions to the vorticity budget represent ensemble averages.

To compare the total vorticity change with the sum of the budget terms (ignoring friction) and thus verify that the budget balances, the difference in circulation (lhs) between two time levels t and t + Δt was compared with the average of the rhs terms at t and t + Δt. The value of Δt was 1 h, the output frequency of the model fields. The vorticity budget over the final 27 h of each simulation was also examined by summing the 1-h vorticity changes on both sides of (4) over this time interval.

In Fig. 9 are displayed vertical profiles of the different terms in (4), averaged over the system-following 81 × 81 point box and accumulated from 21 to 48 h of each simulation. Results are expressed in terms of box-average vorticity changes. The vertical profiles of vorticity change over 27 h show increases that are similar in magnitude for both cases (Figs. 9a,b). Increases in the 600–700-hPa layer were about 10−4 s−1. There were relatively larger vorticity increases at 900 hPa and above 500 hPa in the 6 July case. The budget was not extended down to 950 hPa because that layer was below ground within the circulation box during the early portions of both simulations. Furthermore, the neglect of friction in the vorticity budget would be unwarranted so close to the ground. At the levels shown, the neglect of friction (and other dissipation) does not seem detrimental to obtaining a nearly balanced budget. The overall balance of the budget is generally good, with some discrepancies noted at 900 and 400 hPa. As will be seen in the time–pressure series of budget terms (Fig. 10), the temporal fluctuations of the sum of the budget terms mimic the actual change of vorticity even at 900 and 400 hPa.

The stretching term in (4) dominated the budget in the midtroposphere in both cases (Figs. 9c,d). This is an anticipated result and echoes numerous previous modeling studies (e.g., Zhang 1992). Vortex compression (negative stretching) in the lower troposphere was also apparent, but this was more than compensated for by the eddy flux term. Hence, the key to increasing the circulation beneath the midtropospheric vortex must have been the transport of vorticity from outside the box. The box was roughly centered on the stratiform region of precipitation during the mature stage of the MCS (Figs. 2a,b and 5a,b). It will be shown that vorticity was transported from the convective region rearward to beneath the midlevel center.

The tilting term was generally negative, more notably so in the 11 June case (Figs. 9c,d). This result contrasts with previous studies (Brandes 1990; Kirk 2003; Weisman and Davis 1998; Cram et al. 2002) that show tilting having a positive influence on the development of cyclonic vorticity in the lower troposphere. This discrepancy will be explored further below.

The change in potential vorticity over the 27-h period was broadly similar to the change in vorticity (Figs. 9a,b). In particular, the PV increased notably at 900 hPa during the period. This implies that the appearance of a cyclonic circulation at the surface was not merely the downward penetration of the circulation about a midtropospheric PV anomaly; rather, it resulted from a deep column of cyclonic PV that contained a substantial anomaly near the surface. This result argues against the vertical penetration mechanism described by Rogers and Fritsch (2001), at least in these two cases.

Time–pressure diagrams of the terms in (4) indicate when the different processes attained importance during the evolution of each MCV (Fig. 10). In the 11 June case, the hourly rate of change of vorticity peaked between 0200 and 0600 UTC 11 June as the main downdraft developed (cf. Figs. 10a and 11a). In the 5 July case, an analogous increase of cyclonic vorticity occurred prior to the development of the strong downdraft (cf. Figs. 10f and 11b). By 0600–0800 UTC (about 0200 local time), the midtropospheric cyclonic vorticity anomaly had attained its greatest magnitude. By 1000 UTC both the stretching and tilting terms contributed to a decrease of vorticity in the middle troposphere (Figs. 10d,e,i,j). This trend continued through 1800 UTC in both cases. Thus, the simulated midtropospheric vortex attained its greatest intensity during the mature stage of the nocturnal MCS and weakened toward and after sunrise.

In the lower troposphere, the tilting and stretching terms were both negative until around 0600 UTC (Figs. 10d,e,i,j). The vortex compression was confined to below 800 hPa as a result of cold downdrafts and lower-tropospheric divergence. However, the eddy flux term was generally positive throughout this period, especially at 900 hPa (Figs. 10c,h). The tilting term was negative until around the time of maximum downward mass flux in both cases, when it became weakly positive (Figs. 10e,j and 11a,b).

In both observed cases there was significant convection ahead of the nocturnal MCS that formed an outflow boundary that intersected the eastern edge of the box. A cross section (Fig. 12) of parallel (meridional) and vertical wind components reveals that much of the negative effect of tilting came from the negative correlation of vertical motion with meridional shear above the southward advancing cold pool associated with convection to the east of the primary MCS. Recall from Fig. 1 that the horizontal vorticity normal to the east side of the box is dominated by −∂υ/∂p, such that a positive meridional shear results in an inward-pointing vortex line. Ascent on the boundary will make the vortex line point downward inside the box; hence, it will produce negative relative vorticity and a negative circulation change. The regions contributing most notably to the negative circulation change are highlighted in Fig. 12 (see also Figs. 10e,j). Note that the effect described here is generally absent from previous idealized simulations (e.g., Weisman and Davis 1998).

To better understand the phenomenology connected with the eddy flux term, it is instructive to examine plots of relative vorticity at 900 hPa (Fig. 13). These plots indicate that a significant positive correlation existed between vorticity and inward-directed wind perturbations along the southern and eastern boundaries of the box. To the extent that the flow mainly varies in the east–west direction (parallel to the southern side of the box), the eddy flux term is
i1520-0469-66-3-686-e5
where the subscript ES refers to the contribution of the eddy flux across the southern boundary (y = 0) to the circulation change in the box. Here, υ̃ = (υL + υ0)/2 and L is the length of the side of the box. The final form of (5) expresses the circulation tendency as the average of the normal velocity components at the end points of the side multiplied by the net variation of normal wind along the side of the box. In particular, the resulting expression is not dependent on the detailed vorticity and wind along the side of the box. On the eastern side of the box, an analogous expression will obtain:
i1520-0469-66-3-686-e6

As the MCS matured, the convective line typically propagated faster than the stratiform region progressed. As noted by Pandya and Durran (1996), the difference in speed can be interpreted as the effect of rearward-propagating gravity waves emanating from the strong diabatic heating near and just rearward of the convective line. The eddy flux contribution along the southern boundary eventually ceased as the upshear tilt of the system increased and the leading convective line propagated away from the developing midtropospheric vorticity maximum. However, the flux was maintained on the eastern boundary as the vorticity along the line was advected rearward (following the midtropospheric vortex). This “plume” of vorticity is clearly exhibited in Figs. 13b,d. In this sense, the mean shear favored the vertical alignment of cyclonic vorticity by transporting the lower-tropospheric cyclonic vorticity rearward beneath the midtropospheric vortex. This effect follows from (6), where the easterly relative inflow makes ũ negative and the cyclonic vorticity on the edge of the box is associated with uL < u0.

However, unless vorticity can be “trapped” in the box, the shear will eventually result in vorticity leaking out the rearward (upshear) side of the box. While the vorticity “source” from the convective line decays late at night, relative rearward flow will expel vorticity from beneath the midlevel center. A negative circulation change in the lower troposphere due to the eddy flux (i.e., transport) term was apparent in both cases during the morning following MCV formation (Figs. 10c,h). This effect was mitigated by two factors. One factor was the overall reduction in the lower-tropospheric vertical wind shear during the morning following MCS occurrence (Fig. 8). This reduction in shear presumably made the negative eddy flux contribution smaller than it would otherwise have been. Reduction in shear can occur from either a variation of ambient atmospheric properties along the MCS track or from convective-induced reduction of the shear. Trier et al. (2006) showed clearly that environmental variation, driven in part by the systematic differences in diurnal forcing from the Great Plains to the Mississippi Valley, was a significant contributor toward the weakening of vertical shear eastward. Shear reduction from convective momentum transport is also possible, but quantification of this effect will not be attempted here.

The other factor mitigating the loss of vorticity due to transport out of the box is the direct contribution to strengthening the low-level vortex from condensation heating, perhaps even at the expense of the midlevel circulation. Note that the divergence profile changed radically around 1000 UTC (near sunrise) to a pattern with lower tropospheric convergence and midtropospheric divergence (Figs. 10d,i and 11). To examine whether this change might have had a thermodynamic origin, the moist static energy (MSE) was used:
i1520-0469-66-3-686-e7
where Cp is the heat capacity, T the temperature, Φ the geopotential, Lυ the latent heat of vaporization, and q the mixing ratio of water vapor. To obtain units of temperature, MSE is divided by Cp (assumed constant) in what follows. A decrease of MSE with height signals conditional instability. In both cases, the early evening organized convection with its cold downdrafts reduced the area-mean moist static energy of lower-tropospheric air parcels while increasing MSE in the upper troposphere through convectively induced warming. These processes changed the sign of the vertical variation of MSE (Fig. 14a). The relative humidity of the lower and middle troposphere increased notably as the MCV/MCS system progressed eastward (Fig. 14b), especially in the 5–6 July case.

The net effect on the difference in MSE between the upper and lower troposphere was to create a moist, nearly neutral condition (Fig. 15) during the morning following MCV formation. Parcels lifted from the surface at 1500 UTC following the decay of the nocturnal MCS became buoyant by at most 1–2°C on average and typically reached their level of neutral buoyancy between 400 and 500 hPa. Hence, detrainment well below the tropopause would be expected. This is consistent with the divergence inferred in this layer (Fig. 11). The cyclonic vorticity beneath the midtropospheric vortex strengthened during this time because of convergence (Figs. 10a,d,f,i) as the midtropospheric cyclonic circulation weakened. The result was a deep vortex with a near-surface signature in cyclonic circulation.

6. Summary and conclusions

The vorticity dynamics governing the formation, evolution, and vertical structure of two MCVs from BAMEX has been presented. Analysis was based on Eulerian, flux-form vorticity diagnostics derived from fully explicit simulations using the ARW model. The 10–11 June 2003 primary MCS developed in modest vertical wind shear and produced an MCV that lasted for several days (Davis and Trier 2007; Galarneau et al. 2009). The 5–6 July 2003 MCS developed in a strongly sheared environment and was noted for damaging winds (Wakimoto et al. 2006a,b) while also producing a long-lived MCV. In both cases, the MCV was important for initiating widespread deep convection during the subsequent diurnal heating cycle.

In both cases, the cyclonic circulation of the MCV became apparent at the surface as summarized by the schema in Fig. 16. The vertical extension of the vortex was enhanced by (i) vorticity generation along the outflow boundary that congealed into a line-end vortex distinct from the midtropospheric vortex center (Fig. 16a); (ii) vertical shear that transported the vorticity rearward from the leading convective line to beneath the midlevel center, thus aligning the vorticity in a vertical column (Fig. 16b); (iii) reduction of vertical shear following maturation of the MCS (Fig. 16b); and (iv) a change in the divergence profile that favored vorticity generation near the surface (Fig. 16d). The change in the divergence profile resulted from moistening and reducing conditional instability within the atmosphere around the MCV as the parent MCS matured. In this more stable moist state, the vorticity and PV at low altitudes grew at the expense of the cyclonic vorticity and PV in the midtroposphere. The favorability of such a state for the generation of lower-tropospheric cyclonic vorticity was noted by Raymond and Sessions (2007) in the context of tropical cyclone formation.

From the above point of view, the longevity of an MCV with a surface cyclonic signature appears to be not well connected to the existence of widespread, strong conditional instability near the vortex. It appears that moistening in a stabilized environment is of primary importance. This concept also explains the tendency of vortices to appear at the surface during the morning after the formation of a midtropospheric vortex center. Although the removal of surface cool air may play some role in promoting a surface vortex, the change in the divergence profile to converging flow at low altitudes is more important. Of relevance here is the dynamical paradigm of the diabatic Rossby vortex, described by Conzemius et al. (2007) as a primarily vortical disturbance that sustains itself in the presence of vertical shear by organizing latent heat release in an environment that is moist with small (or zero) conditional instability.

As part of the compromise for performing detailed examinations of two cases, we have left open the issue of generality of results. The examination here of both weakly sheared and strongly sheared environments helps bolster the generality of these results and thus dispel the idea that long-lived MCVs can only form in weakly sheared environments. The overarching future objective is to understand the systematic relationship between organized convection and vorticity in the middle and lower troposphere. This includes quantifying the diurnal and propagating signatures of vorticity that accompany such convection and investigating the systematic role of such vorticity in generating new convection downstream of its origin. A large sample of cases is needed for this task. A similar priority exists in understanding tropical convection and tropical cyclogenesis, wherein the wave–vortex duality of disturbances such as easterly waves has been established (Berry and Thorncroft 2005), but the governing mesoscale dynamics controlling the transition of such disturbances into tropical cyclones remains unconfirmed.

Acknowledgments

The authors thank Dr. Stan Trier of NCAR for his valuable comments on the manuscript; Dr. Hanne V. Murphey (University of Washington and University of Califormia, Los Angeles), Dr. Roger Wakimoto (NCAR), and Dr. David P. Jorgensen (NSSL) for providing quad-Doppler analyses from the 6 July event during BAMEX; and Dave Vollaro (University at Albany, SUNY) for processing the satellite imagery shown in Figs. 4a and 7a. The authors also thank Dr. Morris Weisman of NCAR for collaborations on the BAMEX field phase and insights about WRF simulations of MCSs. The authors are grateful to Professor Dave Raymond (New Mexico Institute of Mining and Technology) and an anonymous reviewer for many helpful suggestions. The second author was supported by National Science Foundation Grant ATM-0553017.

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  • Wakimoto, R. M., , H. V. Murphey, , C. A. Davis, , and N. T. Atkins, 2006b: High winds generated by bow echoes. Part II: The relationship between the mesovortices and damaging straight-line winds. Mon. Wea. Rev., 134 , 28132829.

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  • Weisman, M. L., 1993: The genesis of severe, long-lived bow echoes. J. Atmos. Sci., 50 , 645670.

  • Weisman, M. L., , and C. A. Davis, 1998: Mechanisms for the generation of mesoscale vortices within quasi-linear convective systems. J. Atmos. Sci., 55 , 26032622.

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  • Zhang, D-L., 1992: The formation of a cooling-induced mesovortex in the trailing stratiform region of a midlatitude squall line. Mon. Wea. Rev., 120 , 27632785.

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Fig. 1.
Fig. 1.

Schematic of tilting contribution on the boundary of the circulation box. Large arrows at left indicate meridional flow decreasing with height. This is associated with the horizontal vorticity vector pointing out of the box at right. Vertical motion on the boundary of the box is indicated by a dashed arrow. A hypothetically displaced vortex line is indicated by a thin solid line, with the sense of rotation about a vertical axis indicated by arrowed ellipses.

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 2.
Fig. 2.

(a),(b) Weather Surveillance Radar-1988 Doppler (WSR-88D) composite reflectivity at (a) 0500 and (b) 1800 UTC 11 Jun 2003. (c),(d) Model-derived maximum reflectivity in column using Thompson reflectivity algorithm with winds (ground relative) at 500 hPa superposed for (c) 0500 and (d) 1800 UTC 11 Jun 2003. Black squares in (c) and (d) indicate the locations of the circulation boxes, 324 km on a side. State abbreviations: AL = Alabama; AR = Arkansas; IL = Illinois; KY = Kentucky; MO = Missouri; MS = Mississippi; OK = Oklahoma; TN = Tennessee; TX = Texas. Long wind barbs indicate 5 m s−1.

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 3.
Fig. 3.

(a),(b) Vertical cross section of meridional wind through the MCV center at 1800 UTC 11 Jun: (a) observed, reproduced from Davis and Trier (2007); (b) simulated, averaged over 120 km in the north–south direction. Plots show ground-relative flow. Contour interval is 5 m s−1, with dashed lines denoting northerly flow.

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 4.
Fig. 4.

(a) Surface observations from the Automated Surface Observing System (ASOS) at 1800 UTC 11 Jun 2003 and from BAMEX dropsondes (plotted without station symbol) time–space corrected to 1730 UTC as in Davis and Trier (2007), with temperature analysis shown using a 2°C contour interval, superposed on a Geostationary Operational Environmental Satellite (GOES) infrared satellite image valid for 1800 UTC 11 Jun. (b) Model fields corresponding to (a), with cloud-top temperature shown in grayscale shown at bottom of plot. The × symbol denotes the approximate position of the MCV center.

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 5.
Fig. 5.

(a),(b) WSR-88D composite reflectivity at (a) 0500 UTC and (b) 1800 UTC 6 Jul 2003. (c),(d) Model-derived maximum reflectivity in column using Thompson reflectivity algorithm with winds (ground relative) at 500 hPa superposed for (c) 0500 UTC 6 Jul and (d) 1800 UTC 6 Jul; black squares indicate the locations of the circulation boxes, 320 km on a side. State abbreviations: IA = Iowa; IL = Illinois; MN = Minnesota; MO = Missouri; NE = Nebraska; and WI = Wisconsin. Long wind barbs indicate 5 m s−1.

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 6.
Fig. 6.

Quad-Doppler wind and reflectivity analysis valid for 0550 UTC 6 Jul. The Naval Research Laboratory (NRL) P-3 and the National Oceanic and Atmospheric Administration (NOAA) P-3 tail Doppler radars were synthesized using the technique described in Wakimoto et al. (2006a): winds and reflectivity at (a) 1.6 and (b) 5.2 km AGL. Vectors are relative to an assumed eastward system motion of 14 m s−1. The V symbol denotes the line-end vortex location.

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 7.
Fig. 7.

(a) Surface observations at 1800 UTC 6 Jul, with temperature analysis shown using a 2°C contour interval, superposed on GOES infrared satellite image also valid for 1800 UTC 6 Jul; (b) model fields corresponding to (a), with cloud-top temperature shown in grayscale shown at bottom of plot. Observed winds and temperatures were obtained from ASOS stations and BAMEX dropsondes. The × denotes the approximate position of the MCV center.

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 8.
Fig. 8.

Box-averaged wind profiles from (a) 10–11 Jun and (b) 5–6 Jul. Averaging occurs over an area 324 km × 324 km. Winds are ground relative. System motion is indicated by thin dashed lines. Solid lines indicate the wind profiles at 2100 UTC on (a) 10 Jun and (b) 5 Jul; heavy dashed lines show the profiles at 1800 UTC on (a) 11 Jun and (b) 6 Jul, respectively.

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 9.
Fig. 9.

(a),(b) Vertical profiles of box-averaged (a) final absolute vorticity (η; gray dashed), total vorticity change over final 27 h of simulation (δζ; black solid), total PV change over final 27 h (δPV; gray solid), and sum of hourly rates of change of vorticity from all rhs terms in (4) except friction (Σ), for (a) 10–11 Jun and (b) 5–6 Jul. (c),(d) Total vorticity changes from eddy flux (dashed), stretching (thick solid), and tilting (thin solid) terms in (4) for (c) 10–11 Jun and (d) 5–6 Jul.

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 10.
Fig. 10.

(a)–(e) Time–pressure series of hourly changes in box-averaged vorticity representing (a) full simulated changes, (b) the sum of rhs terms in (4) except friction, (c) eddy flux, (d) stretching, and (e) tilting for 10–11 Jun. (f)–(j) As in (a)–(e), respectively, but for 5–6 Jul. The first time depicted is 2200 UTC. Data represent the vorticity change for the hour ending at the times shown.

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 11.
Fig. 11.

As in Fig. 10, but for vertical mass flux (−ω/g) integrated over the circulation box for (a) 10–11 Jun and (b) 5–6 Jul.

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 12.
Fig. 12.

Vertical velocity (cm s−1; color) and meridional velocity (contour interval = 2 m s−1) along the eastern boundary of the circulation box at (a) 0100 UTC 11 Jun and (b) 0400 UTC 5 Jul. Heavy contours indicate southerly wind; thin contours indicate northerly wind. Heaviest black curves enclose regions where the contribution to vortex tilting is most strongly negative (anticyclonic tendency within the box).

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 13.
Fig. 13.

Relative vorticity at 900 hPa and system-relative winds for (a) 0400 and (b) 0900 UTC 11 Jun and for (c) 0400 and (d) 0900 UTC 6 Jul. Units are 10−4 s−1. Red lines denote boundaries of circulation box. Coordinates in schematic at lower right refer to text.

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 14.
Fig. 14.

(a) Difference of moist static energy, normalized by Cp (see text) between 300 and 900 hPa (positive for conditionally stable conditions) for 10–11 Jun (dashed) and 5–6 Jul (solid). (b) Box-averaged relative humidity for 10–11 Jun (dashed) and 5–6 Jul (solid) cases in the layer from levels 21 to 26 (roughly 600–800 hPa).

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 15.
Fig. 15.

Skew–T diagrams averaged over 324 km × 324 km box valid for (a) 2100 UTC 10 Jun (red) and 1500 UTC 11 Jun (black) and for (b) 2100 UTC 5 Jul (red) and 1500 UTC 6 Jul (black).

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Fig. 16.
Fig. 16.

Schema depicting the development of cyclonic vorticity at the surface. Gray shading denotes areas of cyclonic vorticity. Thin solid lines depict vertical circulation, dashed for decaying circulation. Heavy gray arrows show system-relative environmental flow. Shown are three stages: (a) mature MCS with the midtropospheric MCV and line-end vortex developed and well separated; (b) MCV and line-end vorticity superposed; (c) erect column of cyclonic vorticity reaching the surface.

Citation: Journal of the Atmospheric Sciences 66, 3; 10.1175/2008JAS2819.1

Table 1.

Assumed system motion vectors: U = eastward movement, V = northward movement (both in m s−1).

Table 1.

1

As noted by a reviewer (Dave Raymond), the effect depicted in Fig. 1 can also be interpreted as a Reynolds-like stress divergence due to the vertical advection of horizontal momentum. The relevant term is the normal derivative of the vertical advection of the horizontal momentum component parallel to the edge of the box, −∂/∂n(ωυ/∂p), where υ = v · dl and the normal direction points outward.

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