Linearly forced fluid flow on a rotating sphere

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.

arXiv comment13 pages, 6 figures

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Cited by in corpus (5)

• Active Flows on Curved Surfaces
• Rototaxis: localization of active motion under rotation
• An optimal complexity spectral method for Navier--Stokes simulations in the ball
• Vortex line entanglement in active Beltrami flows
• Vielbein Lattice Boltzmann approach for fluid flows on spherical surfaces