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Super- and sub-rotating equatorial jets in shallow water models of Jovian atmospheres: Newtonian cooling versus Rayleigh friction

Published online by Cambridge University Press:  07 June 2017

Emma S. Warneford  and
Paul J. Dellar Open the ORCID record for Paul J. Dellar [Opens in a new window]
Emma S. Warneford
Affiliation:
OCIAM, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK
Paul J. Dellar*
Affiliation:
OCIAM, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK
*
†Email address for correspondence: [email protected]
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Abstract

Numerical simulations of the shallow water equations on rotating spheres produce mixtures of robust vortices and alternating zonal jets, as seen in the atmospheres of the gas giant planets. However, simulations that include Rayleigh friction invariably produce a sub-rotating (retrograde) equatorial jet for Jovian parameter regimes, whilst observations of Jupiter show a super-rotating (prograde) equatorial jet that has persisted over several decades. Super-rotating equatorial jets have recently been obtained in shallow water simulations that include a Newtonian relaxation of perturbations to the layer thickness to model radiative cooling to space, and in simulations of the thermal shallow water equations that include a similar relaxation term in their temperature equation. Simulations of global quasigeostrophic forms of these different models produce equatorial jets in the same directions as the parent models, suggesting that the mechanism responsible for setting the direction lies within quasigeostrophic theory. We provide such a mechanism by calculating the effective force acting on the thickness-weighted zonal mean flow due to the decay of an equatorially trapped Rossby wave. Decay due to Newtonian cooling creates an eastward zonal mean flow at the equator, consistent with the formation of a super-rotating equatorial jet, while decay due to Rayleigh friction leads to a westward zonal mean flow at the equator, consistent with the formation of a sub-rotating equatorial jet. In both cases the meridionally integrated zonal mean of the absolute zonal momentum is westward, consistent with the standard result that Rossby waves carry westward pseudomomentum, but this does not preclude the zonal mean flow being eastward on and close to the equator.

JFM classification

Geophysical and Geological Flows: Geostrophic turbulence Geophysical and Geological Flows: Shallow water flows Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
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Journal of Fluid Mechanics , Volume 822 , 10 July 2017 , pp. 484 - 511
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© 2017 Cambridge University Press 

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