Sudden death of turbulence at night

This project is inspired by a remarkable meteorological phenomenon. Consider a clear sky nighttime situation.  In this case two processes compete: the long-wavelength radiative cooling of the land creates a pool of cold heavy air near this surface.  On the other hand, the large-scale wind creates turbulence that mixes the cold with warm air from larger heights.  Depending on the relative importance of these processes, either a turbulent or a laminar boundary layer will occur.  The evening starts turbulent, but then turbulence suddenly dies, resulting in the view showing quietly grazing cows.

Runaway of turbulence

At first sight, a turbulent situation is stable. In the well-mixed turbulent boundary layer, any change of the flux of energy into the ground will be offset by heat transport.  However, we should realize that the ability of the turbulent boundary layer to transport heat is determined by turbulent mixing. 

In turn, the turbulent mixing efficiency is determined by the heat flux. The runaway course of events leading to the cows grazing in a completely still atmosphere may then be easily imagined: an increasing temperature gradient reduces the intensity of turbulent mixing and we expect a maximum heat flux that can be sustained by the turbulent boundary layer.  More cooling will then lead to the total collapse of turbulence and the night turns quiet.

A bifurcation

Clearly, turbulence can switch between mutiple stable states of its mean properties. It is as if turbulence acts as a laminar flow, exhibiting bifurcations and changes of stability.  Surprisingly, the state changes of the nocturnal atmosphere can be predicted by stability analysis, with the transitions from stable to unstable states illustrated in the figure.