Physics of the amplification of vortex disturbances in shear flows

Abstract

The physics of the linear mechanism of the amplification of vortex disturbances in shear flows, which is due to the nonorthogonality of the eigenfunctions of the problem in the linear dynamics, is described. To obtain the clearest and simplest picture, a parallel flow with a linear velocity shear is studied, and the vortex disturbances are represented in the form of plane waves — spatial Fourier harmonics. On this level our physical approach is consonant with the nonmodal mathematical analysis of linear processes in shear flows, which has been actively cultivated in the last few years. The physics presented explains the non-monotonic growth of vortex disturbances in time at the linear stage of evolution. Moreover, being universal, the “language” employed in this work can also be used to describe the amplification of potential (acoustic) disturbances.