正压准地转流对内潮的散射
Scattering of internal tides by barotropic quasigeostrophic flows
摘要：
海洋内潮和其他惯性重力波在长度尺度与波长相似的高能湍流中传播。这种流动的平流和折射导致波的散射，在波矢量空间中重新分配它们的能量。结果，最初从源（例如地形脊）辐射的平面波在远离源时变得空间不相干。为了研究这个过程中，我们推导出一个动力学方程，它描述了统计的散射的假设下，流是准地转，正压，以及由一个平稳的均匀随机场。通过计算散射截面来量化能量转移，并将其限制为具有相同频率和相同垂直结构的波，因此具有相同的水平波长。对于各向同性流，散射导致各向同性波场。我们估计这种各向同性的特征时间和长度尺度，并研究它们对参数的依赖性，包括流的能谱。线性浅水模型的平面造波机产生的内潮的模拟证实了这些尺度的相关性。与动力学方程的数值解的比较证明了后者的有效性，并说明了波散射和运输之间的相互作用如何塑造波的统计。
英文摘要：
Oceanic internal tides and other inertia-gravity waves propagate in an energetic turbulent flow whose lengthscales are similar to the wavelengths. Advection and refraction by this flow cause the scattering of the waves, redistributing their energy in wavevector space. As a result, initially plane waves radiated from a source such as a topographic ridge become spatially incoherent away from the source. To examine this process, we derive a kinetic equation which describes the statistics of the scattering under the assumptions that the flow is quasigeostrophic, barotropic, and well represented by a stationary homogeneous random field. Energy transfers are quantified by computing a scattering cross section and shown to be restricted to waves with the same frequency and identical vertical structure, hence the same horizontal wavelength. For isotropic flows, scattering leads to an isotropic wavefield. We estimate the characteristic time and length scales of this isotropisation, and study their dependence on parameters including the energy spectrum of the flow. Simulations of internal tides generated by a planar wavemaker carried out for the linearised shallow-water model confirm the pertinence of these scales. A comparison with the numerical solution of the kinetic equation demonstrates the validity of the latter and illustrates how the interplay between wave scattering and transport shapes the wave statistics.
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