Turbulence Structure and Mixing in Strongly Stable Boundary-Layer Flows over Thermally Heterogeneous Surfaces

Direct numerical simulations (DNS) at bulk Reynolds number Re=10⁴ and bulk Richardson number Ri=0.25 are performed to analyze the structure and mixing intensity in strongly stable boundary-layer flows over thermally homogeneous and heterogeneous surfaces. An idealized plane Couette flow set-up is used as a proxy for real-world flows. The flow is driven by a fixed velocity at the upper surface, while the lower surface is at rest. The temperature at the horizontal upper and lower surfaces is either homogeneous or varies sinusoidally in the streamwise direction, while the horizontal-mean temperature is the same in the homogeneous and heterogeneous cases. 

The stratification is strong enough to quench turbulence over homogeneous surfaces, resulting in velocity and temperature profiles that vary linearly with height. However, turbulence survives over heterogeneous surfaces. Both the molecular diffusion and the turbulence contribute to the downward, i.e., the down-gradient, transfer of horizontal momentum. The total (diffusive plus turbulent) heat flux is directed downward. However, the turbulent contribution to the heat flux appears to be positive, i.e., up the gradient of the mean temperature. An analysis of the second-order velocity and temperature covariances and of the vertical-velocity and temperature skewness suggests that the counter-gradient heat transport is due to quasi-organized cell-like vortex motions generated by the surface thermal heterogeneity. These motions act to transfer heat upwards similar to quasi-organized cell-like structures that transfer heat upwards in atmospheric convective boundary layers. Thus, the flow over heterogeneous surface features local convective instabilities and upward eddy heat transport, although the overall stratification remains stable and the heat is transported downward in the mean. The DNS results are compared to the results from the large-eddy simulation study of weakly stable boundary layer (Mironov and Sullivan 2016, J. Atmos. Sci., 73, 449-464). The DNS findings corroborate the pivotal role of the temperature variance in setting the structure and transport properties of the stably-stratified flow over heterogeneous surfaces, and the importance of third-order transport of temperature variance.

The analysis is focused on the flow configuration where the crests of the surface temperature waves are normal to the mean flow. Work is underway to analyze the effect of the surface heterogeneity orientation (e.g., temperature-wave crests normal vs. parallel to the mean flow) on the flow structure and mixing intensity. 

Implications for modeling (parameterizing) strongly stable boundary layers in large-scale atmospheric models are discussed.