Zakharov-Type Equations for Resonances of an Infinite Number of Ocean Surface Waves
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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.
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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
Abstract: Based on the fundamental wave conservation laws of energy, momentum and action, 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 corresponding 2 major Zakharov-type equations for an infinite number of wave resonances were derived by means of the complex Hamiltonian canonical equation for ocean surface waves, the canonical transformation and the Poisson bracket conditions. The presented Zakharov-type equations, in connection with the classical conditions for the 3,4 and 5-wave resonances, therefore build an indispensable, advanced and complete theoretical framework for the most fundamental and universal ocean wave turbulence. -
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