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Paul M. Markowski

Abstract

Idealized simulations are used to investigate the contributions of frictionally generated horizontal vorticity to the development of near-surface vertical vorticity in supercell storms. Of interest is the relative importance of barotropic vorticity (vorticity present in the prestorm environment), baroclinic vorticity (vorticity that is principally generated by horizontal buoyancy gradients), and viscous vorticity (vorticity that originates from the subgrid-scale turbulence parameterization, wherein the effects of surface drag reside), all of which can be advected, tilted, and stretched. Equations for the three partial vorticities are integrated in parallel with the model. The partial vorticity calculations are complemented by analyses of circulation following material circuits, which are often able to be carried out further in time because they are less susceptible to explosive error growth.

Near-surface mesocyclones that develop prior to cold-pool formation (this only happens when the environmental vorticity is crosswise near the surface) are dominated by only barotropic vertical vorticity when the lower boundary is free slip, but both barotropic and viscous vertical vorticity when surface drag is included. Baroclinic vertical vorticity grows large once a cold pool is established, regardless of the lower boundary condition and, in fact, dominates at the time the vortices are most intense in all but one simulation (a simulation dominated early by a barotropic mode of vortex genesis that may not be relevant to real convective storms).

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Paul M. Markowski

Abstract

A simulation of a supercell storm produced for a prior study on tornado predictability is reanalyzed for the purpose of examining the fine-scale details of tornadogenesis. It is found that the formation of a tornado-like vortex in the simulation differs from how such vortices have been understood to form in previous numerical simulations. The main difference between the present simulation and past ones is the inclusion of a turbulent boundary layer in the storm’s environment in the present case, whereas prior simulations have used a laminar boundary layer. The turbulent environment contains significant near-surface vertical vorticity (ζ > 0.03 s−1 at z = 7.5 m), organized in the form of longitudinal streaks aligned with the southerly ground-relative winds. The ζ streaks are associated with corrugations in the vertical plane in the predominantly horizontal, westward-pointing environmental vortex lines; the vortex-line corrugations are produced by the vertical drafts associated with coherent turbulent structures aligned with the aforementioned southerly ground-relative winds (longitudinal coherent structures in the surface layer such as these are well known to the boundary layer and turbulence communities). The ζ streaks serve as focal points for tornadogenesis, and may actually facilitate tornadogenesis, given how near-surface ζ in the environment can rapidly amplify when subjected to the strong, persistent convergence beneath a supercell updraft.

Significance Statement

In high-resolution computer simulations of supercell storms that include a more realistic, turbulent environment, the means by which tornado-like vortices form differs from the mechanism identified in prior simulations using a less realistic, laminar environment. One possibility is that prior simulations develop intense vortices for the wrong reasons. Another possibility could be that tornadoes form in a wide range of ways in the real atmosphere, even within supercell storms that appear to be similar, and increasingly realistic computer simulations are finally now capturing that diversity.

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Paul M. Markowski
and
Yvette P. Richardson

Abstract

Idealized, dry simulations are used to investigate the roles of environmental vertical wind shear and baroclinic vorticity generation in the development of near-surface vortices in supercell-like “pseudostorms.” A cyclonically rotating updraft is produced by a stationary, cylindrical heat source imposed within a horizontally homogeneous environment containing streamwise vorticity. Once a nearly steady state is achieved, a heat sink, which emulates the effects of latent cooling associated with precipitation, is activated on the northeastern flank of the updraft at low levels. Cool outflow emanating from the heat sink spreads beneath the updraft and leads to the development of near-surface vertical vorticity via the “baroclinic mechanism,” as has been diagnosed or inferred in actual supercells that have been simulated and observed.

An intense cyclonic vortex forms in the simulations in which the environmental low-level wind shear is strong and the heat sink is of intermediate strength relative to the other heat sinks tested. Intermediate heat sinks result in the development (baroclinically) of substantial near-surface circulation, yet the cold pools are not excessively strong. Moreover, the strong environmental low-level shear lowers the base of the midlevel mesocyclone, which promotes strong dynamic lifting of near-surface air that previously resided in the heat sink. The superpositioning of the dynamic lifting and circulation-rich, near-surface air having only weak negative buoyancy facilitates near-surface vorticity stretching and vortex genesis. An intense cyclonic vortex fails to form in simulations in which the heat sink is excessively strong or weak or if the low-level environmental shear is weak.

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Andrew J. Oberthaler
and
Paul M. Markowski

Abstract

Numerical simulations are used to investigate how the attenuation of solar radiation by the intervening cumulonimbus cloud, particularly its large anvil, affects the structure, intensity, and evolution of quasi-linear convective systems and the sensitivity of the effects of this “anvil shading” to the ambient wind profile. Shading of the pre-gust-front inflow environment (as opposed to shading of the cold pool) has the most important impact on the convective systems. The magnitude of the low-level cooling, associated baroclinicity, and stabilization of the pre-gust-front environment due to anvil shading generally increases as the duration of the shading increases. Thus, for a given leading anvil length, a slow-moving convective system tends to be affected more by anvil shading than does a fast-moving convective system. Differences in the forward speeds of the convective systems simulated in this study are largely attributable to differences in the mean environmental wind speed over the depth of the troposphere.

Anvil shading reduces the buoyancy realized by the air parcels that ascend through the updrafts. As a result, anvil shading contributes to weaker updrafts relative to control simulations in which clouds are transparent to solar radiation. Anvil shading also affects the convective systems by modifying the low-level (nominally 0–2.5 km AGL) vertical wind shear in the pre-gust-front environment. The shear modifications affect the slope of the updraft region and system-relative rear-to-front flow, and the sign of the modifications is sensitive to the ground-relative vertical wind profile in the far-field environment. The vertical wind shear changes are brought about by baroclinic vorticity generation associated with the horizontal buoyancy gradient that develops in the shaded boundary layer (which makes the pre-gust-front, low-level vertical wind shear less westerly) and by a reduction of the vertical mixing of momentum due to the near-surface (nominally 0–300 m AGL) stabilization that accompanies the shading-induced cooling. The reduced mixing makes the pre-gust-front, low-level vertical shear more (less) westerly if the ambient, near-surface wind and wind shear are westerly (easterly).

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Paul M. Markowski
and
Yvette P. Richardson

Abstract

In idealized numerical simulations of supercell-like “pseudostorms” generated by a heat source and sink in a vertically sheared environment, a tornado-like vortex develops if air possessing large circulation about a vertical axis at the lowest model levels can be converged. This is most likely to happen if the circulation-rich air possesses only weak negative buoyancy (the circulation-rich air has a history of descent, so typically possesses at least some negative buoyancy) and is subjected to an upward-directed vertical perturbation pressure gradient force. This paper further explores the sensitivity of the development of near-surface vertical vorticity to the horizontal position of the heat sink. Shifting the position of the heat sink by only 2–3 km can significantly influence vortex intensity by altering both the baroclinic generation of circulation and the buoyancy of circulation-rich air. Many of the changes in the pseudostorms that arise from shifting the position of the heat sink would be difficult to anticipate. The sensitivity of the pseudostorms to heat sink position probably at least partly explains the well-known sensitivity of near-surface vertical vorticity development to the microphysics parameterizations in more realistic supercell storm simulations, as well as some of the failures of actual supercells to produce tornadoes in seemingly favorable environments.

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Robert Davies-Jones
and
Paul M. Markowski

Abstract

Fine-resolution computer models of supercell storms generate realistic tornadic vortices. Like real tornadoes, the origins of these virtual vortices are mysterious. To diagnose the origin of a tornado, typically a near-ground material circuit is drawn around it. This circuit is then traced back in time using backward trajectories. The rate of change of the circulation around the circuit is equal to the total force circulation. This circulation theorem is used to deduce the origins of the tornado’s large vorticity. However, there is a well-known problem with this approach; with staggered grids, parcel trajectories become uncertain as they dip into the layer next to the ground where horizontal wind cannot be interpolated. To circumvent this dilemma, we obtain a generalized circulation theorem that pertains to any circuit. We apply this theorem either to moving circuits that are constrained to simple surfaces or to a “hybrid” circuit defined next. Let A be the horizontal surface at one grid spacing off the ground. Above A the circuit moves as a material circuit. Horizontal curve segments that move in A with the horizontal wind replace segments of the material circuit that dip below A. The circulation equation for the modified circuit includes the force circulation of the inertial force that is required to keep the curve segments horizontal. This term is easily evaluated on A. Use of planar or circular circuits facilitates explanation of some simple flows. The hybrid-circuit method significantly improves the accuracy of the circulation budget in an idealized supercell simulation.

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Aaron Wang
,
Ying Pan
, and
Paul M. Markowski

Abstract

This work explores the influence of weighted essentially nonoscillatory (WENO) schemes on Cloud Model 1 (CM1) large-eddy simulations (LES) of a quasi-steady, horizontally homogeneous, fully developed, neutral atmospheric boundary layer (ABL). An advantage of applying WENO schemes to scalar advection in compressible models is the elimination of acoustic waves and associated oscillations of domain-total vertical velocity. Applying WENO schemes to momentum advection in addition to scalar advection yields no further advantage but has an adverse effect on resolved turbulence within LES. As a tool designed to reduce numerically generated spurious oscillations, WENO schemes also suppress physically realistic instability development in turbulence-resolving simulations. Thus, applying WENO schemes to momentum advection reduces vortex stretching, suppresses the energy cascade, reduces shear-production of resolved Reynolds stress, and eventually amplifies the differences between the surface-layer mean wind profiles in the LES and the mean wind profiles expected in accordance with the filtered law of the wall (LOTW). The role of WENO schemes in adversely influencing surface-layer turbulence has inspired a concept of anti-WENO (AWENO) schemes to enhance instability development in regions where energy-containing turbulent motions are inadequately resolved by LES grids. The success in reproducing the filtered LOTW via AWENO schemes suggests that improving advection schemes is a critical component toward faithfully simulating near-surface turbulence and dealing with other “terra incognita” problems.

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Paul M. Markowski
,
Jerry M. Straka
, and
Erik N. Rasmussen

Abstract

Idealized numerical simulations are conducted in which an axisymmetric, moist, rotating updraft free of rain is initiated, after which a downdraft is imposed by precipitation loading. The experiments are designed to emulate a supercell updraft that has rotation aloft initially, followed by the formation of a downdraft and descent of a rain curtain on the rear flank. In the idealized simulations, the rain curtain and downdraft are annular, rather than hook-shaped, as is typically observed. The downdraft transports angular momentum, which is initially a maximum aloft and zero at the surface, toward the ground. Once reaching the ground, the circulation-rich air is converged beneath the updraft and a tornado develops. The intensity and longevity of the tornado depend on the thermodynamic characteristics of the angular momentum-transporting downdraft, which are sensitive to the ambient low-level relative humidity and precipitation character of the rain curtain. For large low-level relative humidity and a rain curtain having a relatively small precipitation concentration, the imposed downdraft is warmer than when the low-level relative humidity is small and the precipitation concentration of the rain curtain is large. The simulated tornadoes are stronger and longer-lived when the imposed downdrafts are relatively warm compared to when the downdrafts are relatively cold, owing to a larger amount of convergence of circulation-rich downdraft air. The results may explain some recent observations of the tendency for supercells to be tornadic when their rear-flank downdrafts are associated with relatively small temperature deficits.

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Richard Rotunno
,
Paul M. Markowski
, and
George H. Bryan

Abstract

Numerical models of supercell thunderstorms produce near-ground rotation about a vertical axis (i.e., vertical vorticity) after the development of rain-cooled outflows and downdrafts. The physical processes involved in the production of near-ground vertical vorticity in simulated supercells have been a subject of discussion in the literature for over 30 years. One cause for this lengthy discussion is the difficulty in applying the principles of inviscid vorticity dynamics in a continuous fluid to the viscous evolution of discrete Eulerian simulations. The present paper reports on a Lagrangian analysis of near-ground vorticity from an idealized-supercell simulation with enhanced vertical resolution near the lower surface. The parcel that enters the low-level maximum of vertical vorticity has a history of descent during which its horizontal vorticity is considerably enhanced. In its final approach to this region, the parcel’s enhanced horizontal vorticity is tilted to produce vertical vorticity, which is then amplified through vertical stretching as the parcel rises. A simplified theoretical model is developed that exhibits these same features. The principal conclusion is that vertical vorticity at the parcel’s nadir (its lowest point), although helpful, does not need to be positive for rapid near-surface amplification of vertical vorticity.

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Shawn S. Murdzek
,
Paul M. Markowski
,
Yvette P. Richardson
, and
Matthew R. Kumjian

Abstract

Convective inhibition (CIN) is one of the parameters used by forecasters to determine the inflow layer of a convective storm, but little work has examined the best way to compute CIN. One decision that must be made is whether to lift parcels following a pseudoadiabat (removing hydrometeors as the parcel ascends) or reversible moist adiabat (retaining hydrometeors). To determine which option is best, idealized simulations of ordinary convection are examined using a variety of base states with different reversible CIN values for parcels originating in the lowest 500 m. Parcel trajectories suggest that ascent over the lowest few kilometers, where CIN is typically accumulated, is best conceptualized as a reversible moist adiabatic process instead of a pseudoadiabatic process. Most inflow layers do not contain parcels with substantial reversible CIN, despite these parcels possessing ample convective available potential energy and minimal pseudoadiabatic CIN. If a stronger initiation method is used, or hydrometeor loading is ignored, simulations can ingest more parcels with large amounts of reversible CIN. These results suggest that reversible CIN, not pseudoadiabatic CIN, is the physically relevant way to compute CIN and that forecasters may benefit from examining reversible CIN instead of pseudoadiabatic CIN when determining the inflow layer.

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