海洋Internal Wave场：标度不变谱理论
Oceanic Internal Wave Field: Theory of Scale-invariant Spectra
摘要：
基于波动湍流理论，研究了描述海洋内重力波统计特性的动力学方程的定常尺度不变解。在非旋转标度不变的极限下，动力学方程中的碰撞积分对几乎所有的谱幂律指数都是发散的。这些分歧来自最小水平波数和/或最大水平波数与极端尺度分离的共振相互作用。我们确定了一个小的域中的尺度不变的碰撞积分收敛，并在数值上找到一个收敛的幂律解。该数值解接近Garrett-Munk谱。幂律指数，这可能允许之间的平衡的红外线和紫外线的分歧进行了研究。平衡指数的尺度不变的动力学方程，Pelinovsky-Raevsky频谱的精确解的概括。相反符号的发散之间的平衡表明无穷大减去无穷大可以近似等于零。一个小的，但有限的科里奥利参数表示的旋转的影响被引入到动力学方程，以确定解决方案的发散部分的域使用严格的渐近参数。这引起了诱导扩散制度。动力学方程的推导是基于弱非线性的假设。非局部相互作用的主导地位使动力学方程的自洽性处于危险之中。然而，这些弱非线性定态与许多观测证据是一致的。
英文摘要：
Steady scale-invariant solutions of a kinetic equation describing the statistics of oceanic internal gravity waves based on wave turbulence theory are investigated. It is shown in the non-rotating scale-invariant limit that the collision integral in the kinetic equation diverges for almost all spectral power-law exponents. These divergences come from resonant interactions with the smallest horizontal wavenumbers and/or the largest horizontal wavenumbers with extreme scale-separations. We identify a small domain in which the scale-invariant collision integral converges and numerically find a convergent power-law solution. This numerical solution is close to the Garrett--Munk spectrum. Power-law exponents which potentially permit a balance between the infra-red and ultra-violet divergences are investigated. The balanced exponents are generalizations of an exact solution of the scale-invariant kinetic equation, the Pelinovsky--Raevsky spectrum. A balance between oppositely signed divergences states that infinity minus infinity may be approximately equal to zero. A small but finite Coriolis parameter representing the effects of rotation is introduced into the kinetic equation to determine solutions over the divergent part of the domain using rigorous asymptotic arguments. This gives rise to the induced diffusion regime. The derivation of the kinetic equation is based on an assumption of weak nonlinearity. Dominance of the nonlocal interactions puts the self-consistency of the kinetic equation at risk. Yet these weakly nonlinear stationary states are consistent with much of the observational evidence.
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