On the stability of large-scale streaks in turbulent Couette and Poiseulle flows

The linear secondary stability of large-scale optimal streaks in turbulent Couette flow at Re τ = 52 and Poiseulle flow at Re τ = 300 is investigated. The streaks are computed by solving the nonlinear two-dimensional Reynolds-averaged Navier–Stokes equations using an eddy-viscosity model. Optimal initial conditions leading the largest linear transient growth are used, and as the amplitude of the initial vortices increases, the amplitude of streaks gradually increases. Instabilities of the streaks appear when their amplitude exceeds approximately 18 % of the velocity difference between walls in turbulent Couette flow and 21 % of the centerline velocity in turbulent Poiseuille flow. When the amplitude of the streaks is sufficiently large, the instabilities attain significant growth rates in a finite range of streamwise wavenumbers that shows good agreement with the typical streamwise wavenumbers of the large-scale motions in the outer region.