Nonlinear Response of a Compressible Boundary Layer to Free-stream Vortical Disturbances

Abstract

The nonlinear response of a compressible boundary layer to unsteady free-stream vortical fluctuations of the convected-gust type is investigated. The amplitude of the disturbances is strong enough for nonlinear interactions to be induced within the boundary layer. Attention is focused on the induced low-frequency streamwise-stretched components of the boundary-layer disturbances, known as streaks or Klebanoff modes, which may become unstable and break down to fully developed turbulence. The streaks are described using the mathematical framework of the so-called boundary-region equations, i.e. the asymptotic limit of the Navier-Stokes equations for low-frequency disturbance, developed by Leib et al.1 and extended by Ricco & Wu 2 and Ricco et al.3 to linear perturbations in compressible boundary layers, and nonlinear disturbances in incompressible boundary layers, respectively. In the present work, compressibility is taken into account through aerodynamic heating effects due to the mean-flow velocity being comparable with the speed of sound. Both velocity and thermal (temperature) streaks are generated as well as are a new mean flow and fluctuations of higher frequencies. Nonlinearity attenuates the fluctuations of the streamwise velocity and a similar stabilizing effect is observed on the temperature.This represents the preliminary study which is necessary to carry out the secondary instability analysis on the new unsteady compressible three-dimensional flow generated by the nonlinear interactions.