Axisymmetric Modelling of Tornado-Like Vortices with Adaptive Mesh Refinement

Axisymmetric simulations continue to provide insight into how the structure, dynamics and maximum windspeeds of tornado-like vortices are influenced by the surrounding environment. Such work is continued here with a numerical model for axisymmetric incompressible flow that incorporates adaptive mesh refinement (AMR). The model dynamically increases or decreases the resolution as determined by a specified refinement criterion. Here, the criterion is based on the cell Reynolds number, so the flow is guaranteed to be laminar on the scale of the grid spacing.

We show that for short times a simulation with a low base resolution and AMR can accurately reproduce the vortex dynamics of a simulation with high resolution everywhere. For long times, the AMR model can also reproduce the statistical results of a full-resolution model, giving mean maximum windspeeds and the depth of the boundary layer within 1% of those predicted by the full-resolution model. We then use the AMR model to explore the effects on the vortex of the domain size, the location and geometry of the convective forcing, and the value of the Reynolds number. The results show that the structure and dynamics of the resulting vortex are controlled by only three parameters: the intensity of the convective forcing, the far-field circulation, and the eddy vicosity.

The figure below shows the azimuthal velocity field for a simulation with dimensional scales similar to the tornado environment. Tornado-like vortices are reproduced, using a constant eddy viscosity with values such as 20 m²s^-1, which have radii of maximum winds and boundary layer depths similar to those recently observed with portable Doppler radar.