海洋紫外线灾害的起源
On the Origins of the Oceanic Ultraviolet Catastrophe
摘要：
我们提供了一个第一性原理分析的能量通量在海洋内部波场。由此产生的公式是非常相似的著名的现象学公式在海洋中的湍流耗散率，这是众所周知的细尺度参数化。预测的基础是内部重力波的波动理论和一种新的方法，设计用于计算相关的能量通量。在波能量密度的标准谱表示中，在二维垂直波数-频率域中，发现与稳态相关联的能量通量在两个坐标中被向下引导，在函数形式和幅度上紧密匹配精细尺度参数化公式。这些能量转移是由一个“本地”和一个“规模分离”的贡献，而前者是量化的数字，后者是由诱导扩散过程中占主导地位，是服从分析处理。与以前的结果相反，表明从高频到低频的逆能量级联，与观测结果不一致，我们对扩散张量的所有非零系数的分析预测了直接的能量级联。此外，通过相同的分析，被认为是“无通量”解决方案的基本光谱恢复到“恒定降尺度通量”解决方案的状态。这对于理解符合精细尺度参数化观测范式的能量通量、源和汇是重要的，同时解决了两个长期存在的悖论，这两个悖论被称为“海洋紫外线灾难”。
英文摘要：
We provide a first-principles analysis of the energy fluxes in the oceanic internal wavefield. The resulting formula is remarkably similar to the renowned phenomenological formula for the turbulent dissipation rate in the ocean which is known as the Finescale Parameterization. The prediction is based on the wave turbulence theory of internal gravity waves and on a new methodology devised for the computation of the associated energy fluxes. In the standard spectral representation of the wave energy density, in the two-dimensional vertical wavenumber - frequency domain, the energy fluxes associated with the steady state are found to be directed downscale in both coordinates, closely matching the Finescale-Parameterization formula in functional form and in magnitude. These energy transfers are composed of a `local' and a `scale-separated' contributions; while the former is quantified numerically, the latter is dominated by the Induced Diffusion process and is amenable to analytical treatment. Contrary to previous results indicating an inverse energy cascade from high frequency to low, at odds with observations, our analysis of all non-zero coefficients of the diffusion tensor predicts a direct energy cascade. Moreover, by the same analysis fundamental spectra that had been deemed `no-flux' solutions are reinstated to the status of `constant-downscale-flux' solutions. This is consequential for an understanding of energy fluxes, sources and sinks that fits in the observational paradigm of the Finescale Parameterization, solving at once two long-standing paradoxes that had earned the name of `Oceanic Ultraviolet Catastrophe'.
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