Budgets of scalar fluxes for cloudy boundary layers

Most turbulence closure schemes used in numerical models of the atmosphere are based on truncated budget equations for the second-order moments of fluctuating velocity and scalar fields. Precise knowledge of these second-moment budgets is a necessary prerequisite for successful validation and further development of turbulence schemes. Despite their paramount importance in turbulence modeling, there is a lack of a systematic and comprehensive analysis of the second-moment budgets in atmospheric boundary layer flows, most notably in cloudy boundary layers. The majority of large-eddy simulation (LES) studies emphasized the turbulence kinetic energy (TKE) budget, other second-moment budgets received insufficient attention. To make a step forward, the budgets of all second-order moments (Reynolds stress components as well as fluxes and variances of scalar quantities) are analyzed using very high resolution LES of cumulus-topped and stratocumulus-topped boundary layer flows. Our presentation is focused on the budgets of fluxes of scalar quantities and on the pressure-scalar covariance terms in the flux budgets.

The LES model PALM (PArallelized Large-Eddy Simulation Model) is used to simulate two boundary layer flows containing shallow clouds. The simulation setups are based on the well-documented BOMEX (trade wind shallow cumuli) and DYCOMS-RF01 (nocturnal marine stratocumuli) cases. In both simulations, a grid spacing of 2.5 m in each direction is used, which provides one of the highest resolutions for the above cases achieved so far. Approximations to the ensemble-mean second-moment budgets are computed by averaging the LES data over horizontal planes and several time steps. The sub-grid scale contributions to the budget terms are also accounted for, which allows to keep the budget residual very small.

The budgets of the vertical scalar fluxes are dominated by the mean-gradient production, buoyancy and pressure terms. The pressure gradient-scalar covariances are decomposed into the contributions due to turbulence-turbulence interactions, buoyancy, mean velocity shear, and Coriolis effects, and the relative importance of these contributions is examined. The implications of our findings for modeling turbulence in cloudy boundary layers are discussed.