Two‐dimensional Models for Nonlinear Vorticity Waves in Shear Flows
Two‐dimensional Models for Nonlinear Vorticity Waves in Shear Flows
复制标题
剪切流中非线性涡度波的二维模型
DOI：
10.1111/1467-9590.00067
复制
发表时间：
1998
影响因子：
2.7
通讯作者：
Y. Stepanyants
中科院分区：
文献类型：
--
作者：
V. Voronovich;V. Shrira;Y. Stepanyants
研究了大雷诺数下分层流体剪切流中弱非线性波动扰动的演化。研究的重点是涡度波，即，由平均流涡度梯度引起的波动。本文考虑了大洋上层的一种典型情况，假定切变流只局限于海面附近，没有拐点。层结的垂直尺度远大于切变流的垂直尺度。基本上三维波扰动的动力学描述通过系统的渐近过程简化为（2+1）维的单个非线性演化积分微分方程。小参数是切变的垂直尺度与扰动的典型波长的比值和振幅参数。该方程不包含粘性项，但它所描述的演化状态是由于小但有限的粘性而发生的。粘性抑制了临界层中强非线性涡的产生。研究了该方程局部化二维定常解的可能存在性。在分层消失的极限下，得到了任意深度流体的轴对称孤子解。在分层流中，剪切流扰动和内波之间的线性共振相互作用被发现起主要作用。由于这些共振引起的涡量波的辐射阻尼使得分层流体中不可能存在类似的块状孤立结构。
The evolution of weakly nonlinear wave perturbations in shear flows of stratified fluid is investigated for large Reynolds numbers. The study is focused on the vorticity waves, i.e., the wave‐like motions caused by the mean flow vorticity gradient. A situation typical of the upper ocean is considered.The shear flow is supposed to be localized near the surface and to have no inflection points. The vertical scale of stratification is much larger than that of the shear current. Description of the dynamics of essentially three‐dimensional wave perturbations is reduced by a systematic asymptotic procedure to a single nonlinear evolution integrodifferential equation for (2+1)‐dimensions. The small parameters are the ratio of the vertical scale of the shear to the typical wavelength of the perturbations and the amplitude parameter. The equation does not contain viscous terms, but the regime of evolution it describes occurs owing to small but finite viscosity. The viscosity inhibits generation of strongly nonlinear vortices in the critical layer. Possible existence of localized two‐dimensional stationary solutions of the equation is investigated. Axially symmetric soliton solutions are found for a fluid of arbitrary depth in the limit of vanishing stratification. In stratified flows a linear resonant interaction between shear flow perturbations and internal waves is found to play the major role. The radiation damping of vorticity waves due to these resonances makes the existence of similar lump solitary structures in stratified fluid impossible.