Evaluation of subgrid-scale models in decaying rotating stratified turbulence

Abstract

The results of large eddy simulation (LES) using four sub-grid scale (SGS) models, namely: constant coefficient Smagorinsky (CS), dynamic Smagorinsky (DS), a dynamic Clark (DC) model, and dynamic Lund-Novikov II-term model (DLN2M) for rotating stratified turbulence in the absence of forcing using large-scale isotropic initial conditions, are reported here. Three cases with varying ratios of Brunt-Väisälä frequency to the inertial wave frequency, $\mathcal{N}/f$, have been chosen to evaluate the performance of SGS models. The Reynolds number and $\mathcal{N}/f$ are chosen as (a) Case 1: Re=3704, $\mathcal{N}/f=5$, (b) Case 2: Re=6667, $\mathcal{N}/f=40$ and (c) Case 3: Re=6667, $\mathcal{N}/f=138$. Various quantities including turbulent kinetic energy (tke), turbulent potential energy (tpe), total dissipation, potential and total energy spectra, and their fluxes, are analyzed. It is observed that the increase in the value of $\mathcal{N}/f$ leads to increased oscillations in the evolution of kinetic and potential energy. Our results suggest that the inclusion of the rotation rate tensor in SGS modeling leads to overall improvements in energy evolution predictions. The CS model produces the largest errors, while the DS and the DC models are more comparable to each other. Spectral analysis of total energy and their fluxes shows that the CS, DS and DC models can reasonably predict the large-scale motion ($\kappa <10$), while the DLN2M model improves the energy prediction in the wavenumber range ($10<\kappa <64$) in comparison to other SGS models.

Keywords:

• Turbulence
• LES
• rotating and stratified flows
• SGS models

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Additional information

Funding

The authors gratefully acknowledge the financial support provided by the Science and Engineering Board (SERB) of the Department of Science and Technology (DST) of the Government of India under the framework of the Startup Research Grant Science and Engineering Research Board (SRG), No. SRG/2019/000009. Rahul Agrawal acknowledges support from National Aeronautics and Space Administration NASA's Transformational Tools and Technologies project under Grant No. 80NSSC20M0201 for his graduate studies.