The evolution of second harmonic waves in oblique transition

Abstract

In this paper, the evolution of second harmonic waves, whose streamwise wavenumbers are twice of the fundamental streamwise wavenumber, is studied during the oblique transition of plane Couette flow. At the initial stage of the transition, the second harmonic waves are amplified in turn by the Orr mechanism and the nonlinear convection of perturbations together with the working of perturbation pressure. At the middle and late stages, the second harmonic waves are reactivated by the instability of the mean flow in the presence of developed streamwise streaks, and their growth rates are dominated later by the nonlinear interactions of the fundamental oblique waves. When the spanwise kinetic energies of the streamwise vortices, streaks, and the fundamental oblique waves are exceeded by those of the second harmonic waves, the streak breakdown occurs, indicating that these second harmonic waves are essential for the oblique transition.