Linearly forced fluid flow on a rotating sphere

TL;DR

This paper studies analytically and numerically the behavior of linearly driven fluid flows on rotating spheres, revealing stationary jets and Rossby waves similar to planetary atmospheres, with results matching theoretical predictions.

Contribution

It extends the analysis of generalized Navier-Stokes equations to include linear driving on rotating spheres, providing exact solutions and numerical validation.

Findings

Exact solutions for stationary jets and Rossby waves.

Numerical simulations confirm stationary states and wave phase speeds.

Agreement between simulation results and analytical predictions.

Abstract

We investigate generalized Navier-Stokes (GNS) equations that couple nonlinear advection with a generic linear instability. This analytically tractable minimal model for fluid flows driven by internal active stresses has recently been shown to permit exact solutions on a stationary two-dimensional sphere. Here, we extend the analysis to linearly driven flows on rotating spheres. We derive exact solutions of the GNS equations corresponding to time-independent zonal jets and superposed westward-propagating Rossby waves, qualitatively similar to those seen in planetary atmospheres. Direct numerical simulations with large rotation rates obtain statistically stationary states close to these exact solutions. The measured phase speeds of waves in the GNS simulations agree with analytical predictions for Rossby waves.