Non-equilibrium pressure control of the height of a large-scale, ground-coupled, rotating fluid column

Abstract

When a ground-coupled, rotating fluid column is modeled incorporating non-equilibrium pressure forces in the Navier-Stokes equations, a new exact solution results. The solution has been obtained in a similar manner to the classical equilibrium solution. Unlike the infinite-height, classical solution, the non-equilibrium pressure solution yields a ground-coupled rotating fluid column of finite height. A viscous, non-equilibrium Rankine vortex velocity distribution, developed previously, was used to demonstrate how the viscous and non-equilibrium pressure gradient forces, arising in the vicinity of the velocity gradient discontinuity that is present in the classical Rankine vortex model, effectively isolate the rotating central fluid column from the outer potential vortex region. Thus, the non-equilibrium region acts to confine and shield the central, rigid-body-like, rotating fluid core, justifying this examination of how such a rotating fluid column can interact with the ground. The resulting non-equilibrium ground-coupled, rotating fluid column solution was employed to estimate the central column heights of three well-documented dust devils, and the central column height predictions were consistent with published dust devil height statistics.