On the resonant generation of large-amplitude internal solitary and solitary-like waves
On the resonant generation of large-amplitude internal solitary and solitary-like waves
复制标题
DOI：
10.1017/s002211200500652x
复制
发表时间：
2005-11
影响因子：
3.7
通讯作者：
M. Stastna;W. Peltier
中科院分区：
文献类型：
--
作者：
M. Stastna;W. Peltier
在本文中，我们讨论了连续分层流体中流过孤立地形而产生大振幅孤立波的数值模拟。我们采用内孤立波的完全非线性理论对模态 1 波的数值结果进行分类，并与两类近似理论进行比较：弱非线性理论导致 Korteweg-deVries 和 Gardner 方程以及共轭流理论，它没有对非线性进行近似，而是完全忽略色散。我们发现这两种弱非线性理论的适用范围都是有限的。相比之下，共轭流理论预测了限制上游传播响应（无耗散孔）的性质，成功地描述了孔的垂直结构，并给出了流入速度值 $c_j$，高于该值则不可能出现上游传播响应。数值实验证明，当流入速度超过 $c_j$ 时，存在一类大振幅响应结构，这些结构会在地形上产生和捕获。虽然在结构上与完全非线性孤立波相似，但这些捕获的扰动可以引起比限制孤立波在保持层流时引起的等重位移大 100% 以上。我们开发了一种理论来描述这些受困扰动波峰处的垂直结构并描述其有效性范围。最后，我们转向 2 型孤立波的生成。模式 2 波不可能是真正的孤立波，因为存在一个小的模式 1 尾部，该尾部在波的下游辐射能量。我们证明，对于由单个密斜层主导的层结，2 型波耗散主要由波破碎主导，而不是 1 型波辐射。我们提出了一种基于弱非线性理论的唯象准则，以测试给定分层是否会产生 2 型波。
In this paper we discuss numerical simulations of the generation of large-amplitude solitary waves in a continuously stratified fluid by flow over isolated topography. We employ the fully nonlinear theory for internal solitary waves to classify the numerical results for mode-1 waves and compare with two classes of approximate theories, weakly nonlinear theory leading to the Korteweg–deVries and Gardner equations and conjugate flow theory which makes no approximation with respect to nonlinearity, but neglects dispersion entirely. We find that both weakly nonlinear theories have a limited range of applicability. In contrast, the conjugate flow theory predicts the nature of the limiting upstream propagating response (a dissipationless bore), successfully describes the bore's vertical structure, and gives a value of the inflow speed, $c_j$, above which no upstream propagating response is possible. The numerical experiments demonstrate the existence of a class of large-amplitude response structures that are generated and trapped over the topography when the inflow speed exceeds $c_j$. While similar in structure to fully nonlinear solitary waves, these trapped disturbances can induce isopycnal displacements more than 100% larger than those induced by the limiting solitary wave while remaining laminar. We develop a theory to describe the vertical structure at the crest of these trapped disturbances and describe its range of validity. Finally, we turn to the generation of mode-2 solitary-like waves. Mode-2 waves cannot be truly solitary owing to the existence of a small mode-1 tail that radiates energy downstream from the wave. We demonstrate that, for stratifications dominated by a single pycnocline, mode-2 wave dissipation is dominated by wave breaking as opposed to mode-1 wave radiation. We propose a phenomenological criterion based on weakly nonlinear theory to test whether mode-2 wave generation is to be expected for a given stratification.