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Non-existence of time-dependent three-dimensional gravity water flows with constant non-zero vorticity
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Date
2018-10-08
Authors
Martin, Calin I.
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AIP Publishing
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Abstract
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.
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Keywords
Three-dimensional gravity water flow , Constant non-vanishing vorticity vector , Free surface , Pressure , Velocity field , Orthogonal , Direction of motion
Citation
Martin, C. I. (2018) ‘Non-existence of time-dependent three-dimensional gravity water flows with constant non-zero vorticity’, Physics of Fluids, 30(10), 107102 (6pp). doi: 10.1063/1.5048580
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© 2018, the Author. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Martin, C. I. (2018) ‘Non-existence of time-dependent three-dimensional gravity water flows with constant non-zero vorticity’, Physics of Fluids, 30(10), 107102 (6pp). doi: 10.1063/1.5048580, and may be found at https://aip.scitation.org/doi/10.1063/1.5048580