Resonant–triad interaction in a wall jet

Abstract

The subharmonic nonlinear route to transition in a wall jet with respect to the Craik resonant–triad instability is considered theoretically. The general technique based on linear stability theory, allowing one to reveal the resonant triads in a parametric space, was developed and successfully implemented for both the boundary layer and the wall jet. The analysis showed that only resonant interaction between inner instability modes occurring in the vicinity of the wall is prospective for an experimental observation. The detailed calculations were performed for the particular case of the resonant triad consisting of components which all become neutral at the same downstream location. At a sufficiently large initial amplitude of the two-dimensional (2D) Tollmien–Schlichting wave imposed on the basic flow, the rapid emergence of its 3D subharmonics occurs within a few wavelengths of the fundamental. It follows from the present results that a wall jet is very sensitive to the three-dimensional wavy perturbations propagating in a narrow band of wave angles around θ=58°.