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Johannes M. L. Dahl

Abstract

This study addresses the robustness of the baroclinic mechanism that facilitates the onset of surface rotation in supercells by using two idealized simulations with different microphysics parameterizations and by considering previous results. In particular, the importance of ambient crosswise vorticity relative to baroclinically generated vorticity in the development of near-ground cyclonic vorticity is analyzed. The storms were simulated using the CM1 model in a kinematic base state characterized by a straight-line hodograph. A trajectory analysis spanning about 30 min was performed for a large number of parcels that contribute to near-surface vertical-vorticity maxima. The vorticity along these trajectories was decomposed into barotropic and nonbarotropic parts, where the barotropic vorticity represents the effects of the preexisting, substantially crosswise horizontal storm-relative vorticity. The nonbarotropic part represents the vorticity produced baroclinically within the storm. It was found that the imported barotropic vorticity attains a downward component near the surface, while the baroclinic vorticity points upward and dominates. This dominance of the baroclinic vorticity is independent of whether a single-moment or double-moment microphysics parameterization is used. A scaling argument is offered as explanation, predicting that the baroclinic vertical vorticity becomes increasingly dominant as downdraft strength increases.

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Jannick Fischer
and
Johannes M. L. Dahl

Abstract

In the recent literature, the conception has emerged that supercell tornado potential may mostly depend on the strength of the low-level updraft, with more than sufficient subtornadic vertical vorticity being assumed to be present in the outflow. In this study, we use highly idealized simulations with heat sinks and sources to conduct controlled experiments, changing the cold pool or low-level updraft character independently. Multiple, time-dependent heat sinks are employed to produce a realistic near-ground cold pool structure. It is shown that both the cold pool and updraft strength actively contribute to the tornado potential. Furthermore, there is a sharp transition between tornadic and nontornadic cases, indicating a bifurcation between these two regimes triggered by small changes in the heat source or sink magnitude. Moreover, larger updraft strength, updraft width, and cold pool deficit do not necessarily result in a stronger maximum near-ground vertical vorticity. However, a stronger updraft or cold pool can both drastically reduce the time it takes for the first vortex to form.

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Jannick Fischer
and
Johannes M. L. Dahl

Abstract

Although much is known about the environmental conditions necessary for supercell tornadogenesis, the near-ground vorticity dynamics during the tornadogenesis process itself are still somewhat poorly understood. For instance, seemingly contradicting mechanisms responsible for large near-ground vertical vorticity can be found in the literature. Broadly, these mechanisms can be sorted into two classes, one being based on upward tilting of mainly baroclinically produced horizontal vorticity in descending air (here called the downdraft mechanism), while in the other the horizontal vorticity vector is abruptly tilted upward practically at the surface by a strong updraft gradient (referred to as the in-and-up mechanism). In this study, full-physics supercell simulations and highly idealized simulations show that both mechanisms play important roles during tornadogenesis. Pretornadic vertical vorticity maxima are generated via the downdraft mechanism, while the dynamics of a fully developed vortex are dominated by the in-and-up mechanism. Consequently, a transition between the two mechanisms occurs during tornadogenesis. This transition is a result of axisymmetrization of the pretornadic vortex patch and intensification via vertical stretching. These processes facilitate the development of the corner flow, which enables production of vertical vorticity by upward tilting of horizontal vorticity practically at the surface, i.e., the in-and-up mechanism. The transition of mechanisms found here suggests that early stages of tornado formation rely on the downdraft mechanism, which is often limited to a small vertical component of baroclinically generated vorticity. Subsequently, a larger supply of horizontal vorticity (produced baroclinically or via surface drag, or even imported from the environment) may be utilized, which marks a considerable change in the vortex dynamics.

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Johannes M. L. Dahl
and
Jannick Fischer

Abstract

The authors explore the dynamical origins of rotation of a mature tornado-like vortex (TLV) using an idealized numerical simulation of a supercell thunderstorm. Using 30-min forward parcel trajectories that terminate at the base of the TLV, the vorticity dynamics are analyzed for n = 7 parcels. Aside from the integration of the individual terms of the traditional vorticity equation, an alternative formulation of the vorticity equation and its integral, here referred to as vorticity source decomposition, is employed. This formulation is derived on the basis of Truesdell’s “basic vorticity formula,” which is obtained by first formulating the vorticity in material (Lagrangian) coordinates, and then obtaining the components relative to the fixed spatial (Eulerian) basis by applying the vector transformation rule. The analysis highlights surface drag as the most reliable vorticity source for the rotation at the base of the vortex for the analyzed parcels. Moreover, the vorticity source decomposition exposes the importance of small amounts of vorticity produced baroclinically, which may become significant after sufficient stretching occurs. Further, it is shown that ambient vorticity, upon being rearranged as the trajectories pass through the storm, may for some parcels directly contribute to the rotation of the TLV. Finally, the role of diffusion is addressed using analytical solutions of the steady Burgers–Rott vortex, suggesting that diffusion cannot aid in maintaining the vortex core.

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Johannes M. L. Dahl

Abstract

About 140 years ago, Lord Kelvin derived the equations describing waves that travel along the axis of concentrated vortices such as tornadoes. Although Kelvin’s vortex waves, also known as centrifugal waves, feature prominently in the engineering and fluid dynamics literature, they have not attracted as much attention in the field of atmospheric science. To remedy this circumstance, Kelvin’s elegant derivation is retraced, and slightly generalized, to obtain solutions for a hierarchy of vortex flows that model basic features of tornado-like vortices. This treatment seeks to draw attention to the important work that Lord Kelvin did in this field, and reveal the remarkably rich structure and dynamics of these waves. Kelvin’s solutions help explain the vortex breakdown phenomenon routinely observed in modeled tornadoes, and it is shown that his work is compatible with the widely used criticality condition put forth by Benjamin in 1962. Moreover, it is demonstrated that Kelvin’s treatment, with the slight generalization, includes unstable wave solutions that have been invoked to explain some aspects of the formation of multiple-vortex tornadoes. The analysis of the unstable solutions also forms the basis for determining whether, for example, an axisymmetric or a spiral vortex breakdown occurs. Kelvin’s work thus helps explain some of the visible features of tornado-like vortices.

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Johannes M. L. Dahl

Abstract

In many supercell simulations, near-ground vortex formation results from the collapse of an elongated region of enhanced vertical vorticity. In this study, this “roll-up” mechanism is analyzed by investigating the behavior of several 2D elliptic vortex patches. The problem is treated as a nonlinear initial value problem, which is better suited to describe the roll-up mechanism than the more commonly employed normal-mode analysis. Using the Bryan Cloud Model 1, it is demonstrated that the condition for vortex formation is an initial finite-amplitude nonuniformity within the vortex patch. Vortex formation results from differential self-advection due to the flow induced by the patch itself. Background straining motion may either aid or suppress vortex-patch axisymmetrization depending on the initial orientation of the patch relative to the deformation axis. It is also found that in some cases numerical dispersion may lead to nonuniformities that serve as seed for axisymmetrization, thus resulting in unphysical vortex development.

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Johannes M. L. Dahl
and
Christian Boyer
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Jannick Fischer
and
Johannes M. L. Dahl

Abstract

It has long been observed that interactions of a supercell with other storms or storm-scale boundaries sometimes seem to directly instigate tornadogenesis. First, the authors explore the frequency of such constructive interactions. Radar data from WSR-88D are used to categorize 136 tornadic supercells into isolated supercells and supercells that interacted with external factors within 20 min before tornadogenesis. Most cases (80%) showed some form of external influence prior to tornadogenesis. Common patterns of interactions, the typical supercell quadrant that is affected, and changes in azimuthal shear are also identified. To further study these interactions, two sets of idealized Cloud Model 1 (CM1) simulations are performed. The first set demonstrates that the speed of the near-ground horizontal flow relative to the updraft can control whether a vortex patch develops into a tornado. A weaker updraft-relative flow is favorable because the developing vortex stays in the updraft region longer and becomes less tilted. Building on these results, it is shown that external outflow can lead to tornado formation by a deceleration of the updraft-relative flow. The deceleration is caused by the pressure gradient force associated with the external outflow, which is already noticeable several kilometers ahead of the outflow boundary. This offers one possible mechanism by which external outflow can act as a catalyst for supercell tornadogenesis.

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Johannes M. L. Dahl

Abstract

The question of how rotation arises in sheared updrafts is analyzed using the shear and curvature vorticity framework. Local rotation exists where the shear and curvature vorticity have a similar magnitude and the same sign, such that parcels are in near-solid-body rotation. It is shown that the tilting terms of the vertical vorticity equation cannot explain the development of local rotation in the canonical cases where the horizontal vorticity is either purely streamwise or purely crosswise. Rather, vertical shear vorticity develops if crosswise vorticity is tilted, and vertical curvature vorticity develops if streamwise vorticity is tilted. To analyze how local rotation develops, two simulations of updrafts in an environment with crosswise and mostly streamwise vorticity, respectively, are discussed. A trajectory analysis is performed and shear and curvature vorticity budgets are analyzed. It is found that much of the horizontal vorticity near the updraft becomes streamwise, which results from pressure gradient accelerations in the vicinity of the updraft. Consequently, in the analyzed scenarios, the tilting mechanism results primarily in vertical curvature vorticity. Local rotation is achieved via an interchange process that facilitates a partial conversion of vertical curvature vorticity to vertical shear vorticity. Updraft rotation in supercells thus does not result from tilting of horizontal vorticity alone, but partial conversion of curvature to shear vorticity is also required.

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Matthew D. Parker
and
Johannes M. L. Dahl

Abstract

This study uses an idealized heat sink to examine the possible roles of the wind profile in modulating the production of surface vertical vorticity by a downdraft. The basic vorticity evolution in these idealized simulations is consistent with previous work: the process is primarily baroclinic and produces near-ground vertical vorticity within the outflow. Sensitivity experiments affirm that the only fundamental requirement for downdrafts to produce surface vertical vorticity is the existence of ambient downdraft-relative flow. Vertical vorticity production increases monotonically as the low-level downdraft-relative flow increases from zero up through intermediate values (in these experiments, 10–15 m s−1), followed by a monotonic decrease for greater values. This sensitivity has to do with the degree of cooling acquired by parcels as they pass through the idealized heat sink as well as the degree to which horizontal vorticity vectors subsequently attain an orientation that is normal to isosurfaces of vertical velocity. Although the addition of vertical wind shear is not directly helpful to surface vertical vorticity production in these simulations, increased realism of outflow structure is attained in hodographs with ambient streamwise vorticity. Furthermore, the necessary condition of flow through a region of downdraft forcing would in nature probably require the existence of ambient vertical shear. Therefore, shear in the lower troposphere has a possibly important indirect role in modulating the initial production of near-ground rotation.

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