## 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.## References

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## Bibliographic Information

**David Henry**- Affiliation: School of Mathematical Sciences, University College Cork, Cork, Ireland
- MR Author ID: 766545
- Email: d.henry@ucc.ie
**Tony Lyons**- Affiliation: Department of Computing & Mathematics, Waterford Institute of Technology, Waterford, Ireland
- MR Author ID: 973283
- Email: tlyons@wit.ie
- Received by editor(s): May 4, 2020
- Received by editor(s) in revised form: August 4, 2020
- Published electronically: January 21, 2021
- Additional Notes: The first author acknowledges the support of the Science Foundation Ireland (SFI) grant 13/CDA/2117.
- Communicated by: Catherine Sulem
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**149**(2021), 1175-1188 - MSC (2020): Primary 35Q35, 76B15; Secondary 37N10
- DOI: https://doi.org/10.1090/proc/15309
- MathSciNet review: 4211872