Strong echo effect and nonlinear transient growth in shear flows
Strong echo effect and nonlinear transient growth in shear flows
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DOI：
10.1063/1.869664
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发表时间：
1998-06-01
影响因子：
4.6
通讯作者：
Warn, T
中科院分区：
文献类型：
--
作者：
Vanneste, J;Morrison, PJ;Warn, T
在二维库埃特流中，连续激发两个扰动的非线性相互作用导致了瞬态能量增长。这种现象被称为回波效应，存在于其他几个物理系统中，它很有趣，因为在与原始扰动相关的能量衰减很久之后，能量增长才出现。本文对非线性响应与两种激励具有相同数量级的情况下的回波效应进行了解析和数值研究。推导了描述三种剪切模态间非线性相互作用的振幅方程组，并应用该方程组来研究回波的物理机制。通过数值仿真验证了该系统的定性有效性。文中还考虑了粘滞耗散对回波效应的影响。(C) 1998美国物理研究所。
The nonlinear interaction of two disturbances excited successively in a two-dimensional Couette flow is shown to lead to a transient energy growth. This phenomenon, which is called the echo effect and exists in several other physical systems, is interesting because the energy growth appears long after the energy associated with the original disturbances has decayed. Here, the echo effect is studied analytically and numerically in a situation where the nonlinear response has the same order of magnitude as the two excitations. A system of amplitude equations describing the nonlinear interactions between three sheared modes is derived and employed to examine the physical mechanism of the echo. The qualitative validity of this system is confirmed by numerical simulations. The influence of viscous dissipation on the echo effect is also considered. (C) 1998 American Institute of Physics.