Dissipative-centrifugal instability of the Burgers vortex core and cyclone-anticyclone vortex asymmetry

TL;DR

This paper introduces a new exact solution for the Burgers vortex that incorporates medium rotation and friction, revealing a dissipative-centrifugal instability and a cyclone-anticyclone asymmetry similar to planetary atmospheres.

Contribution

The paper presents a novel exact solution of hydrodynamic equations for the Burgers vortex, accounting for rotation and friction, and identifies a new instability and vortex asymmetry phenomenon.

Findings

Identification of a nonlinear dissipative-centrifugal instability condition.

Discovery of cyclone-anticyclone vortex asymmetry during DCI.

Similarity of vortex asymmetry to planetary atmosphere phenomena.

Abstract

A new exact solution of the hydrodynamic equations is obtained in the form of the Burgers vortex generalization (BVG)accounting for the medium rotation as a whole and linear uniform friction. The nonlinear dissipative-centrifugal instability(DCI)condition, associated with some superthreshold rotation angular velocity and nonzero friction, for solid-body rotating core of BVG is obtained. The new effect of cyclone-anticyclone vortex asymmetry, arising during DCI of BVG vortex core, is shown to be similar to that observed for the atmospheres of high speed rotating planets and laboratory experiments.