Equatorial Jet Shear in Shallow-Water Models of Tidally Locked Planetary Atmospheres

Tidally locked planets have a global circulation controlled by standing planetary Rossby and Kelvin waves,. These produce an eastward momentum flux towards the equator which drives an equatorial jet. Previous studies have represented these waves on an equatorial beta plane with zero background flow, so do not include the effect of the jet’s shear or its geostrophic height field.

We solve the shallow-water equations in the presence of a background shear flow. The flow modifies the wave solutions, both in their latitudinal structure and longitudinal phase. We show its effect on the free and forced Rossby and Kelvin modes, its effect on the jet’s own equilibrium speed, and its effect on the global pressure and temperature field. 

We show that this eastward wave shift and the effect of the shear are crucial to understanding the equilibrium height field, and by extension the global circulation, of such planets. We suggest that the hot-spot shift in the atmosphere of a tidally locked planet is not due to a Kelvin wave response to the heating, as previously suggested.

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