Waviness and self-sustained turbulence in plane Couette-Poiseuille flow

Direct numerical simulations of a Couette-Poiseuille flow were performed near the transition to turbulence to investigate the nonlinear relationship between streak waviness and rolls. This relationship is a key step in Waleffe's model for a self-sustaining process (SSP). Simulations were conducted for Reynolds numbers ranging from 500 to 940, and a range of initial perturbation amplitudes were used. In these simulations, the streaks, rolls, and streak waviness initially increase. The optimal time for this growth is close to the linear transient growth period for small perturbations, but much shorter for large, highly nonlinear perturbations. For higher Reynolds numbers and large initial perturbations, the velocity field reaches a turbulent steady state, whereas it relaxes to a laminar state in other cases. The main result is that the waviness of the streaks is a quadratic function of the rolls, provided that its value is sufficiently large.Direct numerical simulations of a Couette-Poiseuille flow were performed near the transition to turbulence to investigate the nonlinear relationship between streak waviness and rolls. This relationship is a key step in Waleffe's model for a self-sustaining process (SSP). Simulations were conducted for Reynolds numbers ranging from 500 to 940, and a range of initial perturbation amplitudes were used. In these simulations, the streaks, rolls, and streak waviness initially increase. The optimal time for this growth is close to the linear transient growth period for small perturbations, but much shorter for large, highly nonlinear perturbations. For higher Reynolds numbers and large initial perturbations, the velocity field reaches a turbulent steady state, whereas it relaxes to a laminar state in other cases. The main result is that the waviness of the streaks is a quadratic function of the rolls, provided that its value is sufficiently large.