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On constant vorticity water flows in the $\unicode[STIX]{x1D6FD}$-plane approximation

Published online by Cambridge University Press:  26 February 2019

Calin Iulian Martin Open the ORCID record for Calin Iulian Martin [Opens in a new window]
Calin Iulian Martin*
Affiliation:
School of Mathematical Sciences, University College Cork, Cork, T12 XF62, Ireland
*
†Email address for correspondence: calin.martin@ucc.ie
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Abstract

We consider here three-dimensional water flows in the $\unicode[STIX]{x1D6FD}$-plane approximation. In a quite general setting we show that the only flow exhibiting a constant vorticity vector is the stationary flow with vanishing velocity field and flat free surface.

JFM classification

Geophysical and Geological Flows: Gravity currents Geophysical and Geological Flows: Waves in rotating fluids Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 762 - 774
Copyright
© 2019 Cambridge University Press 

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