Courant Institute of Mathematical Sciences, New York University, New York, NY 10012.
Dipartimento di Scienze Matematiche, Politecnico di Torino, I-10129 Torino, Italy.
Proc Natl Acad Sci U S A. 2018 Jan 30;115(5):855-860. doi: 10.1073/pnas.1710670115. Epub 2018 Jan 16.
The appearance of rogue waves in deep sea is investigated by using the modified nonlinear Schrödinger (MNLS) equation in one spatial dimension with random initial conditions that are assumed to be normally distributed, with a spectrum approximating realistic conditions of a unidirectional sea state. It is shown that one can use the incomplete information contained in this spectrum as prior and supplement this information with the MNLS dynamics to reliably estimate the probability distribution of the sea surface elevation far in the tail at later times. Our results indicate that rogue waves occur when the system hits unlikely pockets of wave configurations that trigger large disturbances of the surface height. The rogue wave precursors in these pockets are wave patterns of regular height, but with a very specific shape that is identified explicitly, thereby allowing for early detection. The method proposed here combines Monte Carlo sampling with tools from large deviations theory that reduce the calculation of the most likely rogue wave precursors to an optimization problem that can be solved efficiently. This approach is transferable to other problems in which the system's governing equations contain random initial conditions and/or parameters.
研究了一维修正非线性薛定谔（MNLS）方程在随机初始条件下深海中随机波的出现，这些初始条件假设服从正态分布，其谱与单向海况的实际条件近似。结果表明，可以利用该谱中包含的不完整信息作为先验信息，并利用 MNLS 动力学对其进行补充，以便在以后的时间可靠地估计海面高度尾部的概率分布。我们的结果表明，当系统遇到不太可能的波型口袋时，就会发生随机波，这些波型口袋会引发表面高度的大扰动。这些口袋中的随机波前是规则高度的波型，但具有非常特定的形状，该形状被明确识别，从而可以进行早期检测。这里提出的方法将蒙特卡罗采样与大偏差理论的工具相结合，将最可能的随机波前的计算简化为一个可以有效解决的优化问题。该方法可推广到其他系统控制方程中包含随机初始条件和/或参数的问题。
