Optimal Energy Growth in Stably Stratified Turbulent Couette Flow

Optimal disturbances of a turbulent stably stratified plane Couette flow in a wide range of Reynolds and Richardson numbers are studied. These disturbances are computed based on a simplified system of equations in which turbulent Reynolds stresses and heat fluxes are approximated by isotropic viscosity and diffusivity with the coefficients obtained from results of direct numerical simulation. Three types of disturbances are considered: large-scale streamwise-elongated rolls converting into streamwise streaks; large-scale vortical structures, inclined in the vertical plane, changing the inclination to the opposite in process of their evolution; near-wall rolls converting into streaks. Large-scale rolls and streaks predominate at neutral or weakly stable stratification while the inclined structures begin to dominate at moderately stable stratification. Near-wall rolls and streaks appear at any stratification and their spanwise size in wall length units does not depend on the values of Reynolds and Richardson numbers. It is shown that the development of inclined optimal disturbances is due to the coupled action of the lift-up effect and the inviscid Orr mechanism. The energetics of the optimal disturbances is discussed. It is shown that inclined optimal disturbances dissipate rapidly after reaching maximum energy amplification.