The collapse of turbulence in the nocturnal boundary layer is studied by means of a simple bulk model that describes the basic physical interactions in the surface energy balance. It is shown that for a given mechanical forcing, the amount of turbulent heat that can be transported downward is limited to a certain maximum. In the case of weak winds and clear skies, this maximum can be significantly smaller than the net radiative loss minus soil heat transport. In the case when the surface has low heat capacity, this imbalance generates rapid surface cooling that further suppresses the turbulent heat transport, so that eventually turbulence largely ceases (positive feedback mechanism). The model predicts the minimum wind speed for sustainable turbulence for the so-called crossing level. At this level, some decameters above the surface, the wind is relatively stationary compared to lower and higher levels. The critical speed is predicted in the range of about 5-7 m s 21 , depending on radiative forcing and surface properties, and is in agreement with observations at Cabauw. The critical value appears not very sensitive to model details or to the exact values of the input parameters. Finally, results are interpreted in terms of external forcings, such as geostrophic wind. As it is generally larger than the speed at crossing height, a 5 m s 21 geostrophic wind may be considered as the typical limit below which sustainable, continuous turbulence under clear-sky conditions is unlikely to exist. Below this threshold emergence of the very stable nocturnal boundary layer is anticipated.

The collapse of turbulence in a pressure driven, cooled channel flow is studied by using 3-D 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 case 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 to explain this collapse from 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 eventually will cause a regeneration of turbulence, thus in contrast with the aforementioned DNS results. Also it predicts that the flow should be able to survive 'supercritical' cooling rates, in case when sufficient momentum is applied on the initial state. Here, both predictions are confirmed using DNS simulations. It is shown that also in DNS a recovery of turbulence will occur naturally, provided that perturbations of finite amplitude are imposed to the laminarized state and provided that sufficient time for flow acceleration is allowed. As such, it is concluded 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 parameterized, 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 to study atmospheric physics in addition to tools which are able to represent high Reynolds number flows like Large Eddy Simulation.

In analogy to the nocturnal atmospheric boundary layer, a flux-driven, cooled channel flow is studied using direct numerical simulations. In agreement with earlier studies, turbulence collapses when the surface cooling exceeds a critical value. In that case, laminarization occurs. Here, the so-called maximum sustainable heat flux (MSHF) hypothesis is tested. It explains why laminarization will occur at strong cooling rates. It states that in stratified flows the downward heat flux is limited to a maximum, which, in turn, is determined by the momentum of the flow. If the heat extraction at the surface exceeds this maximum, near-surface stability will increase rapidly, which hampers efficient vertical heat transport further. This positive feedback eventually causes turbulence to be suppressed fully by the intensive density stratification. This framework is used to predict the collapse of turbulence and a good agreement between theory and simulations is found. Therefore, it is concluded that the maximum sustainable heat flux mechanism explains the collapse of turbulence in this kind of flow. In future work, there is the need for an extension to more realistic configurations, allowing for Coriolis effects and more realistic surface boundary conditions.

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