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Optimal Disturbances in the Development of the Instability of a Free Shear Layer and a System of Two Counter-Streaming Jet Flows
Fluid Dynamics ( IF 0.9 ) Pub Date : 2020-03-01 , DOI: 10.1134/s0015462820020068
M. V. Kalashnik , O. G. Chkhetiani

Abstract— An analytical approach to the determination of optimal disturbances is developed. The approach, suitable for flows with piecewise-constant vorticity distributions, is based on the equation of disturbance energy balance and explicit expressions for the growth rate of the energy or the final-to-initial energy ratio. The corresponding expressions are functions of the initial parameters and the optimal disturbance parameters are determined from an extremization of these functions. Within the framework of the approach the classical Rayleigh problem of the free shear layer instability and the problem of the instability of a system consisting of two counter-streaming jet flows in a rotating shallow water layer are considered. The parameters of the optimal disturbances are compared with those of growing normal modes.

中文翻译:

自由剪切层和两个逆流射流系统不稳定性发展的最佳扰动

摘要:开发了一种确定最佳扰动的分析方法。该方法适用于具有分段恒定涡度分布的流动,它基于扰动能量平衡方程和能量增长率或最终与初始能量比的显式表达式。相应的表达式是初始参数的函数,并且从这些函数的极值化确定最优扰动参数。在该方法的框架内,考虑了自由剪切层不稳定性的经典瑞利问题和旋转浅水层中由两个逆流喷射流组成的系统的不稳定性问题。将最优扰动的参数与生长正常模式的参数进行比较。
更新日期:2020-03-01
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