An a priori study of the subfilter‐scale conservation equations for the stably stratified atmospheric surface layer

Abstract

We perform an a priori analysis of the subfilter-scale (SFS) conservation equations for the stably stratified atmospheric boundary layer (ABL). Using data from the Horizontal Array Turbulence Studies (HATS) experiment, we build on previous studies by exploring in greater detail the scale dependence of the mean and root-mean-square (r.m.s.) values of the production terms in the SFS stress and flux budgets. Our analysis shows production terms that are the dominant generation mechanisms for the SFS stresses and fluxes in conditions of under-resolved turbulence, also contribute significantly to their fluctuation levels. From the fluctuation levels of the production terms, we infer that fluctuations in terms other than the production terms (i.e. advection, transport and destruction) must be associated with strong auto-correlations or cross-correlations (with the production terms) for filter widths much finer than the length-scale for the most energetic eddies. For filter widths too coarse to resolve the most energetic eddies, we are unable either to confirm or rule out this possibility.The dominant production terms in the SFS stress budgets, upon suitable scaling, exhibit limiting values as we approach the Reynolds-averaged Navier-Stokes (RANS) limit, i.e. when the turbulence resides entirely at the subfilter scales. The values in the RANS limit agree well with both existing analytical arguments and a previous LES study of the moderately convective ABL. The agreement between a priori and a posteriori statistics suggests consistency between the two methods is achievable in the RANS limit with the appropriate choice of scaling parameters.

Estimating Dependence of the Turbulent Length Scales on Model Resolution Based on A Priori Analysis

“…The analysis is confined to application to a convective boundary layer in this study, whereas the proposed approach is available to other situations including a free atmosphere. Ramachandran andWyngaard (2011, 2014) proposed a second-order turbulent model, which predicted all the components of the second-order subgrid covariance, and found that their model showed better performance than a LES using a eddy-diffusivity closure when compared with the data obtained from the Horizontal Array Turbulence Study (HATS; Horst et al 2004) experiment. Nevertheless, a simple analysis in terms of the length scales would partly provide information for constructing a numerical model on the basis of the eddy-diffusivity closure.…”