Non-normal energy amplifications in stratified turbulent channels

Carlo Cossu (1)

1 LHEEA - Laboratoire de recherche en Hydrodynamique, Énergétique et Environnement Atmosphérique

The influence of stable and unstable stratification on the amplification of coherent structures in turbulent channel flows is investigated by computing the linear response to stochastic forcing near the turbulent mean flow. The velocity and thermal responses to momentum and thermal forcing are considered separately. It is found that, consistently with results of previous direct numerical simulations, the influence of the mean flow stratification on stochastic forcing amplifications is nonnegligible only for streamwise-elongated large-scale structures. Unstable stratification is found to enhance the peak variance of the response, except for the velocity response to thermal forcing, and to increase the spanwise wavelength of the most amplified structures. Stable stratification induces opposite effects. The different spanwise wavelengths maximizing the different types of variance amplifications, all converge to approximately six channels half-widths when approaching the linear instability threshold where large-scale coherent rolls become linearly unstable. We show that in the presence of even moderately unstable stratification, the profiles of turbulent buoyancy and momentum fluxes and of rms vertical velocity of all types of most amplified stochastic responses are nearly indistinguishable from those of the critical mode becoming unstable at the critical Richardson number. For all considered stratification levels, the two most energetic POD modes are found to contribute to more than 90% of the variance of the response, except for the thermal response to thermal forcing. We conclude that the same mechanism underlies the onset of the instability of coherent large-scale rolls at the critical Richardson number and the amplification of coherent large-scale structures at subcritical Richardson numbers. The process leading to the onset of the instability of large-scale rolls is therefore gradual and the increasing response variance associated to increasingly unstable mean flow stratification as well as the increase of the optimal spanwise wavelength of the most amplified mechanically forced streaks, can be both interpreted as precursors of the linear instability of large-scale rolls.

Domaines: Mécanique des fluides [physics.class-ph]

Carlo Cossu. Non-normal energy amplifications in stratified turbulent channels. Physical Review Fluids, 2023, 8 (7), pp.074601. ⟨10.1103/PhysRevFluids.8.074601⟩. ⟨hal-04153025⟩