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The Structure and Dynamics of Tornado-Like Vortices

David S. NolanDepartment of Mathematics, Lawrence Berkeley National Laboratory, Berkeley, California

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Brian F. FarrellDepartment of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts

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Abstract

The structure and dynamics of axisymmetric tornado-like vortices are explored with a numerical model of axisymmetric incompressible flow based on recently developed numerical methods. The model is first shown to compare favorably with previous results and is then used to study the effects of varying the major parameters controlling the vortex: the strength of the convective forcing, the strength of the rotational forcing, and the magnitude of the model eddy viscosity. Dimensional analysis of the model problem indicates that the results must depend on only two dimensionless parameters. The natural choices for these two parameters are a convective Reynolds number (based on the velocity scale associated with the convective forcing) and a parameter analogous to the swirl ratio in laboratory models. However, by examining sets of simulations with different model parameters it is found that a dimensionless parameter known as the vortex Reynolds number, which is the ratio of the far-field circulation to the eddy viscosity, is more effective than the conventional swirl ratio for predicting the structure of the vortex.

As the value of the vortex Reynolds number is increased, it is observed that the tornado-like vortex transitions from a smooth, steady flow to one with quasiperiodic oscillations. These oscillations, when present, are caused by axisymmetric disturbances propagating down toward the surface from the upper part of the domain. Attempts to identify these oscillations with linear waves associated with the shears of the mean azimuthal and vertical winds give mixed results.

The parameter space defined by the choices for model parameters is further explored with large sets of numerical simulations. For much of this parameter space it is confirmed that the vortex structure and time-dependent behavior depend strongly on the vortex Reynolds number and only weakly on the convective Reynolds number. The authors also find that for higher convective Reynolds numbers, the maximum possible wind speed increases, and the rotational forcing necessary to achieve that wind speed decreases. Physical reasoning is used to explain this behavior, and implications for tornado dynamics are discussed.

* Current affiliation: Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado.

Corresponding author address: Dr. David S. Nolan, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371.

Email: nolan@chandra.atmos.colostate.edu

Abstract

The structure and dynamics of axisymmetric tornado-like vortices are explored with a numerical model of axisymmetric incompressible flow based on recently developed numerical methods. The model is first shown to compare favorably with previous results and is then used to study the effects of varying the major parameters controlling the vortex: the strength of the convective forcing, the strength of the rotational forcing, and the magnitude of the model eddy viscosity. Dimensional analysis of the model problem indicates that the results must depend on only two dimensionless parameters. The natural choices for these two parameters are a convective Reynolds number (based on the velocity scale associated with the convective forcing) and a parameter analogous to the swirl ratio in laboratory models. However, by examining sets of simulations with different model parameters it is found that a dimensionless parameter known as the vortex Reynolds number, which is the ratio of the far-field circulation to the eddy viscosity, is more effective than the conventional swirl ratio for predicting the structure of the vortex.

As the value of the vortex Reynolds number is increased, it is observed that the tornado-like vortex transitions from a smooth, steady flow to one with quasiperiodic oscillations. These oscillations, when present, are caused by axisymmetric disturbances propagating down toward the surface from the upper part of the domain. Attempts to identify these oscillations with linear waves associated with the shears of the mean azimuthal and vertical winds give mixed results.

The parameter space defined by the choices for model parameters is further explored with large sets of numerical simulations. For much of this parameter space it is confirmed that the vortex structure and time-dependent behavior depend strongly on the vortex Reynolds number and only weakly on the convective Reynolds number. The authors also find that for higher convective Reynolds numbers, the maximum possible wind speed increases, and the rotational forcing necessary to achieve that wind speed decreases. Physical reasoning is used to explain this behavior, and implications for tornado dynamics are discussed.

* Current affiliation: Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado.

Corresponding author address: Dr. David S. Nolan, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371.

Email: nolan@chandra.atmos.colostate.edu

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