Towards eliminating the nonlinear Kelvin wake

Fuente: arXiv
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Main Authors: Keeler, Jack, Binder, Benjamin, Blyth, Mark
Format: Preprint
Published: 2024
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author Keeler, Jack
Binder, Benjamin
Blyth, Mark
author_facet Keeler, Jack
Binder, Benjamin
Blyth, Mark
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_01255
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Towards eliminating the nonlinear Kelvin wake
Keeler, Jack
Binder, Benjamin
Blyth, Mark
Fluid Dynamics
Mathematical Physics
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.
title Towards eliminating the nonlinear Kelvin wake
topic Fluid Dynamics
Mathematical Physics
url https://arxiv.org/abs/2410.01255