风驱动海洋中的正、逆叶栅
Direct and Inverse Cascades in the Wind-Driven Sea
摘要：
给出了风激重力波平方波幅Hasselmann动力学方程中S（nl）项的一种新形式。S（nl）的这种形式使得有可能以微分形式改写能量、动量和波浪作用的守恒定律，并以自然的方式引入它们的通量。我们发现，固定动力学方程有一个家庭的确切Kolmogorov型的解决方案所管辖的运动常数通量：波浪作用，能量和动量。详细研究了与扩散近似等价的S（nl）项的简单“局部”模型。在这种情况下，Kolmogorov谱被发现在明确的形式。我们表明，一般的解决方案的固定动力学方程背后的光谱峰描述的Kolmogorov型解决方案与频率相关的通量。“逆级联”和“正级联”的区域可以通过自然的方式分离。普适域中的谱接近于$ω^{-4}$。
英文摘要：
We offer a new form for the S(nl) term in the Hasselmann kinetic equation for squared wave amplitudes of wind-driven gravity wave. This form of S(nl) makes possible to rewrite in differential form the conservation laws for energy, momentum, and wave action, and introduce their fluxes by a natural way. We show that the stationary kinetic equation has a family of exact Kolmogorov-type solutions governed by the fluxes of motion constants: wave action, energy, and momentum. The simple "local" model for S(nl) term that is equivalent to the "diffusion approximation" is studied in details. In this case, Kolmogorov spectra are found in the explicit form. We show that a general solution of the stationary kinetic equation behind the spectral peak is described by the Kolmogorov-type solution with frequency-dependent fluxes. The domains of "inverse cascade" and "direct cascade" can be separated by natural way. The spectrum in the universal domain is close to $ω^{-4}$.
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