Pollard waves with underlying currents

Henry, David; Lyons, Tony

doi:10.1090/proc/15309

Pollard waves with underlying currents
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by David Henry and Tony Lyons

Proc. Amer. Math. Soc. 149 (2021), 1175-1188

DOI: https://doi.org/10.1090/proc/15309

Published electronically: January 21, 2021

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Abstract:

We construct an exact solution of the geophysical fluid dynamics governing equations which models waves in the presence of underlying currents, extending Pollard’s wave solution to admit underlying meridional and vertical currents at mid-latitudes. We show that these currents cannot be prescribed arbitrarily, but rather must be constant and form a velocity vector which is parallel to the Earth’s rotation vector. At the equator, there is freedom to prescribe a meridional current term which may vary both zonally and vertically.

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