The stability analysis of vortex flows

The stability of rotating inviscid flows with realistic, continuously differentiable velocity and vorticity profiles is investigated using linear stability analysis. Two different types of flow are studied, V = V_(r) and V = V_(r,z). The former case was further divided into two different flow profiles. It was found that all of the flowfields considered are stable in respect to the linear disturbances. This result is not in agreement with previous studies of segmented velocity profiles of similar type. This suggests that instability found in previous analytical studies may be due to the discontinuity in assumed flow profiles.

It was concluded that if the flow satisfies the Rayleigh Criterion and is modelled as a continuous and continuously differentiable one-dimensional profile, it is stable with respect to linear disturbances. Therefore, the instability of natural rotating flows such as tornados and dust devils depend crucially on the three-dimensional nature of the basic flowfield.