Velocity structure function in a geostrophic coherent vortex under strong rotation

TL;DR

This paper analytically investigates the anisotropic velocity structure function of turbulent pulsations within a geostrophic vortex in a rapidly rotating fluid, revealing how rotation and vortex dynamics influence turbulence statistics at small scales.

Contribution

It provides an analytical description of the pair structure function in a geostrophic vortex, highlighting anisotropy caused by rotation and vortex shear effects.

Findings

Velocity gradient is largest radially and smallest streamwise.

Anisotropy in structure function due to rotation effects.

Turbulence behavior resembles shear flow without rotation.

Abstract

We consider analytically pair structure function of turbulent pulsations on the background of a coherent geostrophic vortex in a fast rotating fluid. The statistics of the turbulent pulsation is determined by their dynamics which is the dynamics of inertia waves affected by the differential rotation in the vortex and weak viscous damping. Our consideration is restricted by the smallest scales, where the velocity field remains smooth. We establish the anisotropy of the structure function. The velocity gradient of the turbulent pulsations achieves its largest value for the radial direction and its smallest value in the streamwise direction, resembling its behaviour in turbulent flow with mean shear component without imposed rotation.