Mutual Transformation of Waves in Smooth Shear Flows

Abstract

Abstract The purpose of this report is to outline a new linear mechanism of mutual transformations of waves in smooth shear flows. The mechanism is closely related to non-normality of linear dynamics of waves in shear flows and is best interpreted in the framework of a nonmodal approach- by tracing of evolution of spatial Fourier harmonics (SFH’s) of waves in time. The core of the phenomenon may be specified as follows: Wave frequency is a certain function (specified by its’ dispersion) of the wave numbers. Mean flow velocity shear results (even in linear approximation) the variation of a wave number(s) of each SFH in time, due to the effect of the shearing background on the wave crest. With this variation it follows that the frequency of SFH varies in time - it “slides along” the dispersion curve of the wave mode. As a result, for definite parameters of the system, if the dispersion curves of the wave modes pass nearby one another, wave frequencies will be closely related in a limited time interval. It is this fact which causes the mutual transformation of the waves in case of a slow variation of waves frequencies. Phenomenon of linear transformation of waves should be realized in a wide variety of terrestrial and astrophysical shear flows and grant significant diversity to processes taking place in these flows.