The instability of streaks and the generation mechanism of streamwise vorticity in near-wall turbulence

Abstract

The linear stability analysis has been performed at Re.TAU.=180 for a turbulent-channel-type base flow with a periodic undulation in the spanwise direction in order to elucidate the generation mechanism of streamwise vorticity through the instability of streaks in near-wall turbulence. It is found that there appear three different instability modes depending on the spanwise wavenumber of streaks. In the case of the streak with around 100 wall-unit spanwise wavelength its critical velocity amplitude lies at .DELTA.Uc+.IMAGE.3, above which streaky flow is unstable to an infinitesimal sinuous disturbance, i. e. a bending mode along the streamwise direction. The instability is identified to originate from inflection points, i. e. wake-like instability, in the spanwise variation of the streaky flow. In this case, unstable eigenmodes take a form that is inclined towards the streamwise direction from the wall-normal direction, and they directly induce the streamwise vorticity on low- and high-speed streaks. In addition, the streamwise vorticity is secondarily produced pricipally through tilting of the wall-normal disturbance vorticity by the base flow shear across the wall-normal direction.