Spectral broadening and flow randomization in free shear layers

Abstract

AbstractIt has been observed experimentally that when a free shear layer is perturbed by a disturbance consisting of two waves with frequencies ${\omega }_{0} $ and ${\omega }_{1} $, components with the combination frequencies $(m{\omega }_{0} \pm n{\omega }_{1} )$ ($m$ and $n$ being integers) develop to a significant level thereby causing flow randomization. This spectral broadening process is investigated theoretically for the case where the frequency difference $({\omega }_{0} \ensuremath{-} {\omega }_{1} )$ is small, so that the perturbation can be treated as a modulated wavetrain. A nonlinear evolution system governing the spectral dynamics is derived by using the non-equilibrium nonlinear critical layer approach. The formulation provides an appropriate mathematical description of the physical concepts of sideband instability and amplitude–phase modulation, which were suggested by experimentalists. Numerical solutions of the nonlinear evolution system indicate that the present theory captures measurements and observations rather well.