The minimum wind speed for sustainable turbulence in the nocturnal boundary layer

The collapse of turbulence in the nocturnal boundary layer is studied by means of a simple bulk model that describes the basic physical interactions between the atmospheric boundary layer and the underlying surface.

It is shown that for a given mechanical forcing, the amount of turbulent heat that can be transported downward is limited to a 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 diurnal wind cycle is weak as compared to lower and higher levels. The critical speed is predicted in the range of about 5–7 m/s, depending on radiative forcing and surface properties. The predictions are in good agreement climatological observations from Cabauw. It is explained why the model prediction are robust in a sense that they do not depend critically to model details or to the exact values of the input parameters. Finally, it will be discussed how the ‘maximum sustainable heat flux' hypothesis can be tested in a more formal setting e.g. by using Direct Numerical Simulations or LES.