#
High Reynolds Number Simulations of Axisymmetric Tornado-like Vortices with Adaptive
Mesh Refinement

### David S. Nolan

### Ann S. Almgren

### John B. Bell

### Abstract

Axisymmetric numerical simulations continue to provide new 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 power of adaptive mesh refinement is used to investigate the
effects of the size of the domain, the location and geometry of the
convective forcing, and the effective Reynolds number (based on the
choice of the eddy viscosity nu) on the behavior of the vortex. In
particular, the claim that the vortex Reynolds number Gamma/nu, which the
ratio of the far-field circulation to the eddy viscosity, is the most
important parameter for determining vortex structure and behavior is
found to be valid over a wide variety of domain and forcing
geometries. 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 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 opposite to what had been previously
observed.

The conclusions drawn from these results are applied to dimensional
simulations with scales similar to the tornado environment and with a
more realistic rotating environment. Tornado-like vortices are
reproduced, using a constant eddy viscosity with such values as 20
m^{2}s^{-1}, which have radii of maximum winds and boundary layer depths
which are very similar to those recently observed with portable Doppler
radar.