Effect of horizontal surface temperature heterogeneity on turbulent mixing in the stably stratified atmospheric boundary layer

Representation of stably-stratified boundary-layer turbulence in numerical models of atmospheric circulation is one of the key unresolved issues that slows down progress in climate modeling, numerical weather prediction, and related applications. Turbulence in a stably stratified boundary layer (SBL) is often weak, episodic in space and time and thus difficult to model. SBL turbulence evolves under the action of larger-scale forcings such as internal gravity waves, Kelvin-Helmholtz instability, and horizontal heterogeneity of the underlying surface. Current SBL models do not include these important effects in a physically meaningful way. In the present study, the effect of horizontal temperature heterogeneity of the underlying surface on the turbulence structure and mixing efficiency in the SBL is analyzed using large-eddy simulation (LES).

Idealized LES of two flows driven by fixed winds and homogeneous and heterogeneous surface temperature are compared (details of the simulation setup are provided in the extended abstract). The LES data are used to compute statistical moments of the fluctuating fields (mean wind and mean potential temperature, second-order and third-order turbulence moments, pressure-velocity and pressure-scalar covariances), to estimate terms in the second-moment budgets, and to assess the relative importance of various terms in maintaining the budgets. It should be noted that the LES-based second-moment budgets are often estimated on the basis of resolved-scale fields only (cf. Mironov et al. 2000, Mironov 2001). However, the sub-grid scale (SGS) contributions may be substantial, particularly in the SBL, and should be retained in order to close the second-moment budgets to a good order. In the present study, the budgets of the turbulence kinetic energy (TKE), of the temperature variance, and of the vertical temperature flux are computed with due regard for the SGS contributions to the various budget terms.

We find the SBL over a heterogeneous surface is more turbulent with larger variances and TKE, is better mixed and is deeper compared to its homogeneous counterpart. The latter results are similar to those described by Stoll and Porte-Agel (2009). Perhaps the most striking difference between the cases is exhibited in the temperature variance and its budget. Due to surface heterogeneity, the third-order moment, i.e. the vertical flux of temperature variance, is non-zero at the surface. Hence, the turbulent transport term (divergence of the above third-order moment) not only redistributes the temperature variance in the vertical, but is a net gain. As a result, the temperature variance in the heterogeneous case is large near the surface. An increase of temperature variance is the key to understanding the enhanced mixing in the SBL over a heterogeneous surface. Motivated by the LES results, possible ways to incorporate the effect of the sub-grid scale surface temperature heterogeneity into the SBL turbulence models (parameterization schemes), including the surface-layer flux-profile relationships, are discussed.

The work was partially supported by the NCAR Geophysical Turbulence Program and by the European Commission through the COST Action ES0905.