Exact solutions for unsteady axisymmetric vortex motions governing atmospheric vortices

Abstract

In this paper, attempts have been made to provide non-steady generalisation to some of the existing solutions for azimuthal velocity of vortex motion representing different rotational motions occurring in the nature. The existing solutions, viz., Rankine combined vortex and Burgers-Rott vortex steady models are extended to include non-steady effects. The derived expressions reduce to those available in the existing literature. It is concluded from the unsteady model extended from the Rankine combined model that when time tends to infinity, the core radius vanishes for inviscid flows. However, the unsteady viscous flow model, extended from the Burgers-Rott model, reveals that, when time tends to infinity, the core radius becomes infinitely large for zero axial pressure gradient but stabilises if the axial pressure gradient is non-zero. Thus, it is concluded that a vortex survives with time only when the flow is viscous and the axial pressure gradient is non-zero. © 2018 Elsevier B.V.