Two-dimensionality of gravity water flows governed by the equatorial f-plane approximation

We show that gravity wave trains governed by the equatorial f -plane approximation propagate at the free surface of a rotational water flow of constant vorticity vector ( Ω 1 , Ω 2 , Ω 3 ) over a flat bed only if the flow is two-dimensional. Owing to the presence of Coriolis effects, our result is a...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2017-12, Vol.196 (6), p.2253-2260
Main Author: Martin, Calin Iulian
Format: Article
Language:English
Subjects:
Approximation
Coriolis effect
Fluid flow
Geophysics
Gravitation
Gravitational waves
Horizontal orientation
Mathematical analysis
Mathematics
Mathematics and Statistics
Two dimensional flow
Vorticity
Water flow
Wave packets
Wave propagation
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Summary:We show that gravity wave trains governed by the equatorial f -plane approximation propagate at the free surface of a rotational water flow of constant vorticity vector ( Ω 1 , Ω 2 , Ω 3 ) over a flat bed only if the flow is two-dimensional. Owing to the presence of Coriolis effects, our result is also true even if the vorticity vector vanishes. This represents a striking difference when compared with the cases without geophysical effects discussed in Constantin (Europhys Lett 86:29001, 2009 , Eur J Mech 30:12–16; 2011 ) and Martin (J Math Fluid Mech 2016 . doi: 10.1007/s00021-016-0306-1 ), where the conclusion about the two-dimensionality of the flow was possible under the assumption of constant nonvanishing vorticity vector. Another upshot is that the only nonzero component of the vorticity that may not vanish is Ω 2 , that is, the one pointing in the horizontal direction orthogonal to the direction of wave propagation.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-017-0663-2