On constant vorticity water flows in the -plane approximation

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.

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Bibliographic Details
Published in:Journal of fluid mechanics 2019-04, Vol.865, p.762-774
Main Author: Martin, Calin Iulian
Format: Article
Language:English
Subjects:
Approximation
Boundary conditions
Fluid mechanics
Free surfaces
Kinematics
Mathematical analysis
Steady flow
Three dimensional flow
Velocity
Velocity distribution
Vortices
Vorticity
Water flow
Water waves
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Description
Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2019.95