Linearly forced fluid flow on a rotating sphere

Abstract

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