Finite-amplitude effects on steady lee-wave patterns in subcritical stratified flow over topography
Finite-amplitude effects on steady lee-wave patterns in subcritical stratified flow over topography
复制标题
地形上亚临界分层流中稳定背风波模式的有限振幅效应
DOI：
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发表时间：
1996
影响因子：
3.7
通讯作者：
T. Akylas
中科院分区：
文献类型：
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作者：
Tian;T. Akylas
考虑有限深度渠道中连续分层流体流过光滑底部凸起的流动。在弱非线性-弱色散系统中，ε = a/h [Lt ] 1，μ = h/l [Lt ] 1（其中h是通道深度，a、l分别是障碍物的峰值幅度和宽度），参数A = ε/μp（其中p < 0取决于障碍物形状）控制非线性对稳定背风波列的影响，该稳定背风波列在亚临界流速时形成在障碍物下游。当A = O（1）时，当非线性和色散效应同等重要时，障碍物上长波扰动与背风波的相互作用是完全非线性的，用“超越所有阶次”的渐近方法来确定背风波振幅（当μ → 0时呈指数小）。与数值结果的比较表明，渐近理论通常保持相当的精确性，即使是对于μ和ε的适度小的值，在这种情况下，（形式上呈指数小的）背风波振幅由于非线性而大大增强，并且可能相当大。此外，这些发现表明，经典的线性背风波理论（A [Lt ] 1）的有效性范围是相当有限的。
The flow of a continuously stratified fluid over a smooth bottom bump in a channel of finite depth is considered. In the weakly nonlinear-weakly dispersive régime ε = a/h [Lt ] 1, μ = h/l [Lt ] 1 (where h is the channel depth and a, l are the peak amplitude and the width of the obstacle respectively), the parameter A = ε/μp (where p < 0 depends on the obstacle shape) controls the effect of nonlinearity on the steady lee wavetrain that forms downstream of the obstacle for subcritical flow speeds. For A = O(1), when nonlinear and dispersive effects are equally important, the interaction of the long-wave disturbance over the obstacle with the lee wave is fully nonlinear, and techniques of asymptotics ‘beyond all orders’ are used to determine the (exponentially small as μ → 0) lee-wave amplitude. Comparison with numerical results indicates that the asymptotic theory often remains reasonably accurate even for moderately small values of μ and ε, in which case the (formally exponentially small) lee-wave amplitude is greatly enhanced by nonlinearity and can be quite substantial. Moreover, these findings reveal that the range of validity of the classical linear lee-wave theory (A [Lt ] 1) is rather limited.