Transient Growth for a Shear Flow Model

We investigate transient growth due to the linear interaction between streaks and streamwise vortices for a nine-dimensional ordinary differential equation model for sinusoidal shear flow, in which fluid between two free-slip walls experiences a sinusoidal body force. We determine how such transient energy growth depends on initial conditions, Reynolds number, and aspect ratio, and also the importance of transient growth for turning on nonlinear effects which can lead to sustained turbulence.