Studies of the relationship between environmental forcing and the structure and dynamics of tornado-like vortices

Abstract

Axisymmetric numerical simulations continue to provide insight into how the structure, dynamics, and maximum windspeeds of tornadoes, and other convectively-maintained vortices, are influenced by the surrounding environment. This work is continued with a new numerical model of axisymmetric incompresible flow that incorporates adaptive mesh refinement. The model dynamically increases or decreases the resolution in regions of interest as determined by a specified refinement criterion. Here, the criterion used is based on the cell Reynolds number , so that the flow is guaranteed to be laminar on the scale of the local grid spacing.The model is used to investigate how the altitude and shape of the convective forcing, the size of the domain, and the effective Reynolds number (based on the choice of the eddy viscosity ν) influence the structure and dynamics of the vortex. Over a wide variety of domain and forcing geometries, the vortex Reynolds number Γ/ν (the ratio of the far-field circulation to the eddy viscosity) is shown to be the most important parameter for determining vortex structure and behavior. Furthermore, it is found that the vertical scale of the convective forcing only affects the vortex inasmuch as this vertical scale contributes to the total strength of the convective forcing. The horizontal scale of the convective forcing, however, is found to be the fundamental length scale in the problem, in that it can determine both the circulation of the fluid that is drawn into the vortex core, and also influences the depth of the swirling boundary layer. Higher mean windspeeds are sustained as the eddy viscosity is decreased; however, it is observed that the highest windspeeds are found in the high-swirl, two-celled vortex regime rather than in the low-swirl, one-celled regime, which is contrast with some previous results.

A New Scaling for Tornado-Like Vortices

“…23, 24, and 25). Additional high-resolution simulations by Nolan et al (2000), using an adaptivemesh-refinement technique, confirmed these results.…”

“…Admittedly, the interpretation of S as a swirl ratio is problematic, as there is no guarantee that ⍀*L is indicative of the azimuthal velocity in the far field, because by (2.10) L is the height of the domain. It does not necessarily indicate the distance from which fluid travels to arrive in the core of the vortex [although this was indeed the case for Fiedler (1993) and Nolan and Farrell (1999), as the height and width of the convective forcing was matched to the size of the domain in those studies].…”

“…Incompressibility (2.4) is unchanged. Nolan and Farrell (1999) and Nolan et al (2000) used similar equations, but in a nonrotating reference frame, such that the environmental rotation was provided by initializing the flow in solid body rotation and keeping the boundary conditions rotating at the same angular velocity ⍀*. Using the equations with Coriolis terms is helpful to the present discussion because it brings the environmental rotation rate into the equations, where its influence is apparent.…”

“…Dimensional analysis has been used to simplify and understand the results of numerous studies of tornadolike vortices using laboratory models (Ward 1972;Wan and Chang 1972;Church et al 1979; see the review by Church and Snow 1993) and numerical simulations (Bode et al 1975;Rotunno 1979;Walko and Gall 1986;Howells et al 1988;Fiedler 1993Fiedler , 1994Fiedler , 1998Nolan and Farrell 1999). The most widely known result from the earlier studies, both physical and numerical, is that the structure of the low-level vortex is controlled to some extent by a dimensionless parameter known as the swirl ratio, which is the ratio of the circulation of the fluid that feeds into the vortex to the rate at which fluid flows through the vortex.…”

“…Using Fiedler's approach, Nolan and Farrell (1999) explored how the intensity, structure, and behavior of tornado-like vortices depend on the model parameters: the strength of the convective forcing, the environmental rotation rate ⍀, and the kinematic viscosity . They found that the vortex Reynolds number, Re V , which is the ratio of the circulation of the fluid feeding into the low-level vortex to the viscosity, seemed to control the low-level vortex structure rather than the swirl ratio.…”