Pollard waves with underlying currents

David Henry, Tony Lyons

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1175-1188
Number of pages14
JournalProceedings of the American Mathematical Society
Issue number3
Publication statusPublished - Mar 2021


  • Exact solution
  • Geophysical fluid dynamics
  • Nonlinear waves
  • Wave-current interactions


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