Numerical simulation of supercritical trapped internal waves over topography
Numerical simulation of supercritical trapped internal waves over topography
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DOI：
10.1063/1.3521532
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发表时间：
2010-11-01
影响因子：
4.6
通讯作者：
Stastna, Marek
中科院分区：
文献类型：
--
作者：
Soontiens, Nancy;Subich, Christopher;Stastna, Marek
本文研究了垂直方向有限的流体中分层流体在地形上的定常流动，以具有刚性盖的实验水槽或刚性盖近似下的海洋为代表，我们不指定上游分层或背景流的函数形式，并推导出Dubreil-Reintin的一般版本。这个椭圆方程是强非线性的，我们发展了一种有效的，伪谱的，迭代方法来求解它的数值解。振幅大于流体深度50%的捕获波我们发现，当存在背景剪切流或地形足够窄时，多个稳态是可能的，并且我们通过使用全时变欧拉方程的积分来证实这一发现。我们讨论了具有闭合流线的波的实例，发现剪切的存在允许具有涡核的波在随时间变化的模拟中持续很长时间，并且与定常理论的解很好地匹配。相反，在没有上游剪切的情况下流线翻转仅发生在表面附近分层的流动中，并且在这种情况下，时变模拟产生的非定常堆芯与定常结果不匹配（C）2010美国物理研究所[doi 10 1063/1 3521532]
We consider the steady flow of a stratified fluid over topography in a fluid of finite vertical extent, as typified by experimental flumes with a rigid lid or the ocean under the rigid lid approximation We do not specify a functional form of the upstream stratification or background current and derive a general version of the Dubreil-Jacotin-Long equation appropriate for the problem This elliptic equation is strongly nonlinear and we develop an efficient, pseudospectral, iterative method for its numerical solution The method allows us to compute laminar, trapped waves with amplitudes more than 50% of the depth of the fluid We find that when either a background shear current is present or the topography is narrow enough, multiple steady states are possible and we confirm this finding by using integrations of the full time-dependent Euler equations We discuss instances of waves with closed streamlines, finding that the presence of shear allows for waves with vortex cores that persist for long times in time-dependent simulations and match well with solutions of the steady theory In contrast, streamline overturning in the absence of upstream shear only occurs for flows that are stratified near the surface and in this instance, time-dependent simulations yield unsteady cores that do not match steady results very well (C) 2010 American Institute of Physics [doi 10 1063/1 3521532]