An Intercomparison of LES Subgrid-Scale Models for Simulations of Slope Flows

We propose an inter-comparison of Smagorinsky type subgrid-scale models for the simulation of high Reynolds number katabatic flows, with the purpose of testing the validity of some of the model's assumptions for the considered application. Katabatic flows arise along sloping surfaces under stably stratified conditions and are a direct consequence of surface cooling. Understanding their structure is of great interest in meteorology because of the broad band of areas and scales that they cover, influencing from local valleys microclimate (e.g. over Salt Lake and Phoenix valleys) to synoptic scale motions (e.g. over Antarctica). Large-eddy simulation (LES), on the other hand, represents an important tool to study high-Reynolds number flows and has undergone significant developments and validations in the past years, confirming its reliability when adopted to simulate a variety of atmospheric (and industrial) flows. The stable stratification of the environment and the complex dynamics that arise close to the surface in katabatic winds – leading eventually to the formation of the so-called low level jet – represent a tough test case for closure models, questioning their applicability over a broad range of filter (grid) scales and motivating the proposed work. The study is performed in the idealized framework of the Prandtl model, the set of normalized, filtered Boussinesq equations is solved on a regular domain, adopting an in-house mixed pseudo-spectral / finite difference code. The original static Smagorinsky model (SMAG), the standard dynamic model with planar averaging of the coefficient (PASI) and the more recent scale-dependent Smagorinsky model with Lagrangian averaging of the coefficients (LASD) are adopted to independently parametrize the subgrid-scale terms for kinematic momentum and energy, which arise from the filtering operation. Results focus on the statistically steady state solution of the problem and show how mean profiles are consistent across subgrid-scale models and most of the discretizations, whereas second order statistics show strong dependence on the spatial resolution, which is partially alleviated once the scale invariance assumption of the model coefficient is relaxed. For the considered resolutions we show that scale-invariance of the model coefficient does in fact not hold – on average – in proximity of the low level jet and close to the wall. At these location of strong shear production the support of the LES filter is approaching the integral scale and the LASD model is therefore expected to provide a more accurate estimation of the Smagorinsky coefficient. Considerations regarding the dissipation rates of the different subgrid-scale models and on mixing efficiency of resolved and modeled turbulence will be discussed.