Kartashova Elena, Nazarenko Sergey, Rudenko Oleksii
Weizmann Institute of Science, Rehovot, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1 Pt 2):016304. doi: 10.1103/PhysRevE.78.016304. Epub 2008 Jul 14.
We study exact four-wave resonances among gravity water waves in a square box with periodic boundary conditions. We show that these resonant quartets are linked with each other by shared Fourier modes in such a way that they form independent clusters. These clusters can be formed by two types of quartets: (1) Angle resonances which cannot directly cascade energy but which can redistribute it among the initially excited modes and (2) scale resonances which are much more rare but which are the only ones that can transfer energy between different scales. We find such resonant quartets and their clusters numerically on the set of 1000x1000 modes, classify and quantify them and discuss consequences of the obtained cluster structure for the wave-field evolution. Finite box effects and associated resonant interaction among discrete wave modes appear to be important in most numerical and laboratory experiments on the deep water gravity waves, and our work is aimed at aiding the interpretation of the experimental and numerical data.
我们研究了具有周期性边界条件的方形盒子中重力水波之间精确的四波共振。我们表明，这些共振四重奏通过共享的傅里叶模式相互联系，从而形成独立的簇。这些簇可以由两种类型的四重奏形成：（1）角度共振，它不能直接级联能量，但可以在初始激发模式之间重新分配能量；（2）尺度共振，它更为罕见，但却是唯一能够在不同尺度之间传递能量的共振。我们在1000×1000模式集上通过数值方法找到了这种共振四重奏及其簇，对它们进行分类和量化，并讨论了所获得的簇结构对波场演化的影响。在大多数关于深水重力波的数值和实验室实验中，有限盒子效应以及离散波模式之间相关的共振相互作用似乎很重要，我们的工作旨在帮助解释实验和数值数据。
