Collapse of turbulence in stably stratified channel flow: a transient phenomenon

Abstract

The collapse of turbulence in a pressure‐driven, cooled channel flow is studied by using 3D direct numerical simulations (DNS) in combination with theoretical analysis using a local similarity model. Previous studies with DNS reported a definite collapse of turbulence in cases when the normalized surface cooling h/L (with h the channel depth and L the Obukhov length) exceeded a value of 0.5. A recent study by the present authors succeeded in explaining this collapse using the so‐called maximum sustainable heat flux (MSHF) theory. This states that collapse may occur when the ambient momentum of the flow is too weak to transport enough heat downward to compensate for the surface cooling. The MSHF theory predicts that, in pressure‐driven flows, acceleration of the fluid after collapse will eventually cause a regeneration of turbulence, in contrast with the aforementioned DNS results. It also predicts that the flow should be able to survive ‘supercritical’ cooling rates, in cases when sufficient momentum is applied to the initial state. Here, both predictions are confirmed using DNS simulations. It is also shown that in DNS a recovery of turbulence will occur naturally, provided that perturbations of finite amplitude are imposed on the laminarized state and provided that sufficient time for flow acceleration is allowed. As such, we conclude that the collapse of turbulence in this configuration is a temporary, transient phenomenon for which a universal cooling rate does not exist. Finally, in the present work a one‐to‐one comparison between a parametrized, local similarity model and the turbulence‐resolving model (DNS) is made. Although local similarity originates from observations that represent much larger Reynolds numbers than those covered by our DNS simulations, both methods appear to predict very similar mean velocity (and temperature) profiles. This suggests that in‐depth analysis with DNS can be an attractive complementary tool with which to study atmospheric physics, in addition to tools that are able to represent high Reynolds number flows like large‐eddy simulations.