急流和流氓波上被困波的非线性动力学
Nonlinear dynamics of trapped waves on jet currents and rogue waves
摘要：
用解析和数值方法研究了反向喷流捕获的表面重力波的非线性动力学。对于频率窄但角分布不一定窄的波场，发展了基于（V.Shrira，A. Slunyaev，J. Fluid. Mech，738，65，2014）导出了单模自聚焦型的一维修正非线性薛定谔方程。它的解决方案，如包络孤立子和呼吸被认为是原型的流氓波，这些解决方案，在没有电流的情况下，相对于波是强大的横向扰动，这表明潜在的更高的概率流氓波。通过对位势欧拉方程的直接数值模拟，验证了调制俘获波和孤立波群形式的长寿命解析解的鲁棒性。
英文摘要：
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonlinear theory based on the modal approach of (V. Shrira, A. Slunyaev, J. Fluid. Mech, 738, 65, 2014) leads to the one-dimensional modified nonlinear Schrödinger equation of self-focusing type for a single mode. Its solutions such as envelope solitons and breathers are considered to be prototypes of rogue waves; these solutions, in contrast to waves in the absence of currents, are robust with respect to transverse perturbations, which suggests potentially higher probability of rogue waves. Robustness of the long-lived analytical solutions in form of the modulated trapped waves and solitary wave groups is verified by direct numerical simulations of potential Euler equations.
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