An Evaluation of Algebraic Turbulence Length Scale Formulations

Abstract

Turbulence kinetic energy (TKE) schemes are routinely used for turbulence parameterization in numerical weather prediction models. A key component of these schemes is the so-called turbulence length scale. Novel scale-aware, budget-based diagnostics that account for the cross-scale transfer of variances are used to evaluate the performance of selected turbulence length scale formulations in the gray zone of turbulence. The diagnostics are computed using the coarse-graining method on high resolution large eddy simulation data for selected idealized cases. The vertical profiles and the temporal evolution of the turbulence length scales are analyzed. Additionally, the local normalized root mean square error and a non-local three-component technique tailored specifically to the turbulence length scale profiles are used for the evaluation. Based on our analyses, we recommend using turbulence length-scale formulations that depend not only on the boundary layer height, but also on the TKE and stratification. Such formulations are able to perform satisfactorily in different flow regimes, but their scale-awareness is still limited. Only the Honnert et al. formulation shows a stronger scale-awareness thanks to its cut-off relationship in the gray zone. However, in contrast to the turbulence length scale diagnostics, its resolution dependence does not change with height.