Scale dependence of subgrid-scale model coefficients: An a priori study

Abstract

Dynamic subgrid-scale models require an a priori assumption about the variation in the model coefficients with filter scale. The standard dynamic model assumes independence of scale while the scale dependent model assumes power-law dependence. In this paper, we use field experimental data to investigate the dependence of model coefficients on filter scale for the Smagorinsky and the nonlinear models. The results indicate that the assumption of a power-law dependence, which is often used in scale dependent dynamic models, holds very well for the Smagorinsky model. For the nonlinear model, the power-law assumption seems less robust but still adequate. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2992192͔ I. BACKGROUNDThe dynamic approach introduced by Germano et al. 1represents a significant milestone in the development of generalized subgrid scale ͑SGS͒ turbulence models for large eddy simulations ͑LES͒. The approach computes an optimal model coefficient based on information from the smallest resolved scales in a simulation using the Germano identity. Although the approach was formulated for the Smagorinsky model, 2 the Germano identity can be applied to other SGS models as well ͑see, for example, Armenio and Piomelli 3 ͒. The traditional dynamic approach makes the assumption of scale invariance, i.e., that the coefficients do not depend on filter scale. The same coefficients determined from the smallest resolved scale are used for the SGS. This scale invariance assumption has been found to break down under various conditions where the filter cutoff scale falls near a transition scale rather than in the inertial subrange. 4,5 To overcome this deficiency, scale dependent dynamic models have been formulated [5][6][7][8][9] and are beginning to be implemented for various applications. [10][11][12][13] As with the traditional dynamic models, the smallest resolved scales are used to obtain the model coefficient. However, scale dependent formulations also interrogate the smallest resolved scale about the variation of the model coefficient with filter scale. This is done by using two test filtering operations that yield the coefficient values at two resolved scales ͑the classic dynamic approach uses only one test filter scale͒. The information at the two test filter scales is then extrapolated to compute an optimal model coefficient that applies to the unresolved scales.An assumption has to be made in the scale dependent formulations regarding the functional dependence of the SGS model coefficients on scale. A power-law functional dependence has been used in all previous scale dependent model implementations. Previously reported a priori tests of the scale dependent model 14 already suggested that it can accurately predict optimal Smagorinsky model coefficients for the velocity field ͑as determined by matching measured and modeled SGS TKE dissipations͒, while the scale invariant formulation underpredicted the coefficients. In addition, a posteriori tests also show that simulations with scale dependent dynamic m...

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Large-Eddy Simulation of Stably-Stratified Flow Over a Steep Hill

“…To achieve that, the scale-dependent dynamic model assumes a power-law dependence of the coefficient with scale. It is important to note that this power-law dependence is only applied to a small range of resolved scales (between the filter scale and a test filter scale) and has been shown to be a realistic assumption in a priori field studies (Porté-Agel et al 2001b;Bou-Zeid et al 2008). Simulations of neutral boundary-layer flow over both flat surfaces (Porté-Agel et al 2000;Porté-Agel 2004;Bou-Zeid et al 2005;Stoll and Porté-Agel 2006) and simple topography (Wan et al 2007) have shown that the scale-dependent dynamic model improves the level of SGS dissipation (rate of energy transfer from the resolved to the subgrid scales), which results in more realistic simulated velocity and scalar statistics.…”

Field study of the dynamics and modelling of subgrid-scale turbulence in a stable atmospheric surface layer over a glacier

“…Mahrt (1998) and Derbyshire (1999) noted the lack of experimental data that can be used to test SGS models for stable ABLs. Since then, the gap has been partially bridged with several studies looking at the performance of several SGS models under stable conditions and investigating the effect of stability on the value of optimal SGS model coefficients using either direct numerical simulation (DNS) data (Dubrulle et al 2002) or, more frequently, field experimental data (Tong, Wyngaard & Brasseur 1999;Porte-Agel et al 2001a, b;Sullivan et al 2003;Kleissl, Meneveau & Parlange 2003;Horst et al 2004;Kleissl, Parlange & Meneveau 2004;Chamecki, Meneveau & Parlange 2007;Bou-Zeid et al 2008;Higgins, Meneveau & Parlange 2009). …”