无穷多海洋表面波共振的Zakharov方程  

Zakharov-Type Equations for Resonances of an Infinite Number of Ocean Surface Waves

作　　者：黄虎[1,2] 

机构地区：[1]上海大学上海市应用数学和力学研究所 [2]上海市力学在能源工程中的应用重点实验室,上海200072

出　　处：《应用数学和力学》2014年第10期1143-1150,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11172157);上海市浦江人才计划(12PJD001);上海高校创新团队建设资助项目~~

摘　　要：从基本的波之"能量、动量、作用量"守恒定律出发,遵照普适的"对称性决定相互作用"法则和"Hamilton"结构,运用Hamilton海洋表面波复正则方程、正则变换及其Poisson括号条件,并结合经典的3-4-5-波共振条件,推导出两大类"无穷多海洋表面波相互作用的共振条件";相应地就建立了两大类"无穷多海洋表面波共振的Zakharov方程".以此,就为最具根本性、普遍性的海洋波湍流搭建了一个必备、先行和完备的理论框架.Based on the fundamental wave conservation laws of energy, momentum and ac- tion, together with the law of symmetry deciding interactions and the Hamilton structure, 2 main categories of resonance conditions for an infinite number of wave interactions and the cor- responding 2 major Zakharov-type equations for an infinite number of wave resonances were de- rived by means of the complex Hamiltonian canonical equation for ocean surface waves, the ca- nonical transformation and the Poisson bracket conditions. The presented Zakharov-type equa- tions, in connection with the classical conditions for the 3-, 4- and 5-wave resonances, there- fore build an indispensable, advanced and complete theoretical framework for the most funda- mental and universal ocean wave turbulence.

关 键 词：ZAKHAROV方程 共振条件 无穷多海洋表面波 能量 动量和作用量守恒 

分 类 号：O353.2[理学—流体力学]