Turbulence budget in transitional plane Couette flow with turbulent stripe

On the basis of direct numerical simulations, we report the transport process of Reynolds stresses with respect to the turbulent-stripe structure (TSS) in a plane Couette flow at a transitional Reynolds number. The transitional structure of TSS is partially turbulent with coexisting laminar regions, oriented obliquely to the streamwise direction. To explain the inclination of the turbulent bands against the mean flow direction, we investigated the budgets for the turbulent energy, considering the non-zero Reynolds shear stresses, including v′w′ and w′u′ (here, u′, v′, and w′ denote the velocity fluctuations in the streamwise, wall-normal, and spanwise directions, respectively). We found that, although they hardly contributed to the turbulent production, their spanwise gradient was a key factor in sustaining a secondary flow in the spanwise direction.