Stability Properties and Nonlinear Mappings of Two and Three‐Layer Stratified Flows
Stability Properties and Nonlinear Mappings of Two and Three‐Layer Stratified Flows
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二层和三层分层流的稳定性特性和非线性映射
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
C. Turner
中科院分区：
文献类型：
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作者：
L. Chumakova;F. E. Menzaque;P. Milewski;R. Rosales;E. Tabak;C. Turner
研究了静水平衡中分层流的两层和三层模型。对于前者，非线性变换可以将具有刚性顶盖和底盖或垂直周期性的[斜压]双层流映射为[正压]单层浅水自由表面流。我们之前已经证明，理查森数大于 1 的双层流是非线性稳定的，在以下意义上：当系统在给定时间适定时，它通过非线性演化保持适定。在这里，我们给出了混合型系统非线性稳定性的一般必要条件。对于具有垂直周期性的三层流，确定了局部稳定域，并且表明系统不满足非线性稳定性的必要条件。这意味着存在演变成剪切不稳定流的波动。
Two and three‐layer models of stratified flows in hydrostatic balance are studied. For the former, nonlinear transformations are found that map [baroclinic] two‐layer flows with either rigid top and bottom lids or vertical periodicity, into [barotropic] single‐layer, shallow water free‐surface flows. We have previously shown that two‐layer flows with Richardson number greater than one are nonlinearly stable, in the following sense: when the system is well‐posed at a given time, it remains well‐posed through the nonlinear evolution. Here, we give a general necessary condition for the nonlinear stability of systems of mixed type. For three‐layer flows with vertical periodicity, the domains of local stability are determined and the system is shown not to satisfy the necessary condition for nonlinear stability. This means that there are wave‐motions that evolve into shear unstable flows.