迈向消除非线性 Kelvin 尾流
Towards eliminating the nonlinear Kelvin wake
AI总结：
本文用受迫 Kadometsev-Petviashvili 方程分析有限深水面运动局域强迫产生的非线性 Kelvin 尾流，并证明可通过选择强迫分布获得稳定、可实验观测的无波解。
摘要：
本文利用受迫 Kadometsev-Petviashvili 方程，研究了在有限深度液体自由表面上以恒定速度运动的局域作用力所引起的非线性扰动。针对该模型方程，本文确立了在作用力下游存在稳定的 V 形 Kelvin 波型，并将楔角刻画为 Froude 数的函数。受这一分析启发，研究表明，通过谨慎选择作用力分布可以消除尾流；而且重要的是，相应的非线性无波解是稳定的，因此有可能在物理实验中被观察到。其稳定性通过一个初值问题的数值解得到证明，在该问题中，长时间极限下达到了稳定的无波状态。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
