Non-existence of time-dependent three-dimensional gravity water flows with constant non-zero vorticity

We show that in a three-dimensional gravity water flow with a constant non-vanishing vorticity vector (Ω1, Ω2, Ω3), the free surface, the pressure, and the velocity field present no variations in the direction orthogonal to the direction of motion. In addition, the second component of the velocity f...

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Bibliographic Details
Published in:Physics of fluids (1994) 2018-10, Vol.30 (10)
Main Author: Martin, Calin Iulian
Format: Article
Language:English
Subjects:
Fluid dynamics
Free surfaces
Gravitation
Physics
Surface waves
Three dimensional flow
Time dependence
Velocity distribution
Vorticity
Water flow
Wave propagation
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Summary:We show that in a three-dimensional gravity water flow with a constant non-vanishing vorticity vector (Ω1, Ω2, Ω3), the free surface, the pressure, and the velocity field present no variations in the direction orthogonal to the direction of motion. In addition, the second component of the velocity field is constant throughout the flow. Moreover, we prove that the vertical component, Ω3, of the vorticity vector has to vanish. This latter fact turns out to be of crucial importance in proving the absence of variations of the flow in the direction that is orthogonal to the direction of the surface wave propagation. Our results are obtained under general assumptions: both the free surface and the flow beneath are allowed to be time dependent in the most general way.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.5048580