Abstract
A new nonasymptotic method is presented that reveals an unexpected richness in the spectrum of acoustic fluctuations in a shear flow with nontrivial (kinematically complex) mean kinematics. The usefulness of the method is illustrated by analysing three different specific cases of compressible hydrodynamic shear flows. The temporal evolution of perturbations spans a wide range of nonexponential behavior from shear-modified oscillations, transitions between oscillatory and nonperiodic (vortical) modes of motion to monotonic growth. The principal characteristic of the revealed acoustic phenomena is their asymptotic persistence. Exotic regimes like "Echoing" as well as unstable (including parametrically driven) solutions are identified. Further areas of application, for both the method and the new physics, are outlined.
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