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Linearly forced fluid flow on a rotating sphere

Published online by Cambridge University Press:  06 April 2020

Rohit Supekar
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA02139, USA Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA02139, USA
Vili Heinonen
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA02139, USA
Keaton J. Burns
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA02139, USA
Jörn Dunkel
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA02139, USA
Corresponding
E-mail address:

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.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Supekar et al. supplementary movie 1

Simulations showing linearly driven flows on a rotating sphere at different rotation rates, as seen in the corotating frame.

Video 10 MB

Supekar et al. supplementary movie 2

Wave propagation in linearly driven zonal flows and corresponding mode excitations of spherical harmonics.

Video 6 MB

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