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arXiv · 2410.01255

Towards eliminating the nonlinear Kelvin wake

Jack Keeler·Benjamin Binder·Mark Blyth
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Abstract

The nonlinear disturbance caused by a localised forcing moving at constant speed on the free surface of a liquid of finite depth is investigated using the forced Kadometsev-Petviashvili equation. The presence of a steady v-shaped Kelvin wave pattern downstream of the forcing is established for this model equation, and the wedge angle is characterised as a function of the Froude number. Inspired by this analysis, it is shown that the wake can be eliminated via a careful choice of the forcing distribution and that, significantly, the corresponding nonlinear wave-free solution is stable so that it could potentially be seen in a physical experiment. The stability is demonstrated via the numerical solution of an initial value problem for which the steady wave-free state is attained in the long-time limit.

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Jack Keeler, Benjamin Binder, Mark Blyth. 2024-10-02. Towards eliminating the nonlinear Kelvin wake. https://arxiv.org/abs/2410.01255

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