Constant vorticity water flows in the modified equatorial β -plane approximation
Monatshefte für Mathematik（2021）
摘要
In this paper, we study three-dimensional equatorial flows with constant vorticity beneath a wave train and above a flat bed in the modified β -plane approximation. It is proved that the equatorial flow is necessarily irrotational and the free surface is necessarily flat if it exhibits a constant vorticity, due to the incorporation of a gravitational-correction term in the tangent plane approximation.
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