基于广义拉格朗日平均的波均原始方程
Explicit wave-averaged primitive equations using a Generalized Lagrangian Mean
摘要：
广义拉格朗日平均理论提供了三维中一般波浪-湍流-平均流相互作用的精确方程。在实际应用中，这些方程必须通过指定波浪强迫项来封闭。在小的表面坡度，弱的水平梯度的水深和平均流，和弱曲率的平均流剖面的假设下，这里得到一个近似的封闭。这些假设产生了平均动量和压力强迫项的解析表达式，这些项可以用波谱表示。然后应用坐标的垂直变化以获得在笛卡尔坐标中具有非发散质量输运的glm 2 z-RANS方程（55）和（57）。最低阶，协议被发现与欧拉平均理论，本近似提供了一个明确的扩展已知的波平均方程的波场的短尺度变化，和垂直变化的电流仅限于弱或本地化的轮廓曲率。此外，基本的精确方程为有限波幅和任何实际情况的扩展提供了一个自然的框架。近似的准确性进行了讨论，使用精确的数值解的线性波在任意底坡，方程仍然是准确的，当适当占部分驻波的比较。对于有限振幅波，发现近似解对于海洋混合层模拟和浅化波可能是准确的，只要设计适当的湍流闭合。然而，对于碎波区的应用，由于波浪非线性对波浪强迫项的垂直剖面有很大的影响，预计近似值只能给出定性的结果。
英文摘要：
The generalized Langrangian mean theory provides exact equations for general wave-turbulence-mean flow interactions in three dimensions. For practical applications, these equations must be closed by specifying the wave forcing terms. Here an approximate closure is obtained under the hypotheses of small surface slope, weak horizontal gradients of the water depth and mean current, and weak curvature of the mean current profile. These assumptions yield analytical expressions for the mean momentum and pressure forcing terms that can be expressed in terms of the wave spectrum. A vertical change of coordinate is then applied to obtain glm2z-RANS equations (55) and (57) with non-divergent mass transport in cartesian coordinates. To lowest order, agreement is found with Eulerian-mean theories, and the present approximation provides an explicit extension of known wave-averaged equations to short-scale variations of the wave field, and vertically varying currents only limited to weak or localized profile curvatures. Further, the underlying exact equations provide a natural framework for extensions to finite wave amplitudes and any realistic situation. The accuracy of the approximations is discussed using comparisons with exact numerical solutions for linear waves over arbitrary bottom slopes, for which the equations are still exact when properly accounting for partial standing waves. For finite amplitude waves it is found that the approximate solutions are probably accurate for ocean mixed layer modelling and shoaling waves, provided that an adequate turbulent closure is designed. However, for surf zone applications the approximations are expected to give only qualitative results due to the large influence of wave nonlinearity on the vertical profiles of wave forcing terms.
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