Abstract

The initial and boundary value problem for the equations of free internal inertia-gravity waves in an unconfined basin of constant depth is numerically calculated in the Boussinesq approximation in the presence of a two-dimensional, vertically-inhomogeneous flow. The boundary value problem for the vertical velocity amplitude includes complex coefficients and is solved both numerically and within the framework of perturbation theory. With reference to the example of the calculations of the decay rate of internal waves and wave-induced momentum fluxes it is shown that the exact numerical calculations provide considerably better estimates than those obtained using the perturbation method. In particular, at minimum disagreement of the dispersion curves obtained using the two calculation methods the imaginary parts of the wave frequency interpreted as the decay rates can differ by two-three orders. The vertical wave-induced momentum fluxes are comparable with turbulent fluxes and can be even greater than those. In this case, the results obtained using numerical methods are almost an order smaller than those calculated by the method of perturbation theory.

中文翻译：

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内惯性重力波边值问题的数值求解

摘要

在存在二维垂直非均匀流的情况下，采用 Boussinesq 近似对恒定深度的无约束盆地中自由内惯性重力波方程的初始和边值问题进行了数值计算。垂直速度幅值的边值问题包括复系数，并且可以在数值上和摄动理论框架内求解。参考内波衰减率和波感生动量通量的计算示例，表明精确的数值计算提供了比使用摄动方法获得的估计更好的估计。特别是，在使用两种计算方法获得的频散曲线的最小差异下，解释为衰减率的波频率的虚部可能相差两到三个数量级。垂直波引起的动量通量与湍流通量相当，甚至可能大于湍流通量。在这种情况下，用数值方法得到的结果几乎比用微扰理论方法计算的结果小一个数量级。