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arXiv 1406.3779physics.flu-dynnlin.PS
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流体表面弱非线性重力-毛细波系综的能谱

Energy spectrum of ensemble of weakly nonlinear gravity-capillary waves on a fluid surface

Elena Tobisch

备注：
Accepted for publication in JETP Letters. arXiv admin note: text overlap with arXiv:1005.2067 by other authors
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摘要：

本文考虑非线性参数为$\varepsilon \sim 0.1 ÷0.25$的非线性重力-毛细波。对于这种非线性，时间尺度分离不会发生，动力学波动方程不成立。在这种情况下的能量级联建立在动态时间尺度（D-级联），并计算的增量链方程方法首先介绍了\emph{Kartashova, \emph{EPL} \textbf{97} (2012), 30004.}我们计算的第一次非线性重力毛细波的能量谱的解析表达式作为一个显式函数依赖于表面张力的比例重力加速度。它表明，它的两个极限-纯毛细和纯重力波的流体表面-与以前得到的结果相吻合。本文还讨论了D-级联模型与非线性波理论中几个已知模型如Zakharov方程、非线性Stokes修正频率的模共振和Benjamin-Feir指数的关系。这些连接是至关重要的理解和预测的各种多分量波动力学，从海洋学光学，从等离子体物理声学的能量传输的细节。

英文摘要：

In this Letter we regard nonlinear gravity-capillary waves with parameter of nonlinearity being $\varepsilon \sim 0.1 ÷0.25$. For this nonlinearity time scale separation does not occur and kinetic wave equation does not hold. An energy cascade in this case is built at the dynamic time scale (D-cascade) and is computed by the increment chain equation method first introduced in \emph{Kartashova, \emph{EPL} \textbf{97} (2012), 30004.} We compute for the first time an analytical expression for the energy spectrum of nonlinear gravity-capillary waves as an explicit function depending on the ratio of surface tension to the gravity acceleration. It is shown that its two limits - pure capillary and pure gravity waves on a fluid surface - coincide with the previously obtained results. We also discuss relations of the model of D-cascade with a few known models used in the theory of nonlinear waves such as Zakharov's equation, resonance of the modes with nonlinear Stokes corrected frequencies and Benjamin-Feir index. These connections are crucial in the understanding and forecasting specifics of the energy transport in a variety of multi-component wave dynamics, from oceanography to optics, from plasma physics to acoustics.

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