A-priori testing of alpha regularisation models as subgrid-scale closures for large-eddy simulations

Alpha-type regularisation models provide theoretically attractive subgrid-scale closure approximations for large-eddy simulations of turbulent flow. We adopt the a-priori testing strategy to study three different alpha regularisation models, namely the Navier-Stokes- model, the Leray- model, and the Clark- model. Specifically, we use high-resolution direct numerical simulation data of homogeneous isotropic turbulence to compute the mean subgrid-scale dissipation, the spatial distribution of the subgrid-scale dissipation, and the spatial distribution of elements of the subgrid-scale stress tensor. This is done for different filter parameters and different large-eddy simulation grid resolutions. Predictions of the three regularisation models are compared to the exact values of the subgrid-scale stress tensor, as defined in the filtered Navier-Stokes equations. The potential of the three regularisation models to provide good approximations is quantified using spatial correlation coefficients. Whereas the Clark- model exhibits the highest spatial correlation coefficients for the subgrid-scale dissipation and the subgrid-scale stress tensor elements, the Leray- model provides lower correlation coefficients, and the Navier-Stokes- model exhibits the lowest correlation coefficients of the three models. Our results indicate the presence of an optimal choice of the filter parameter depending on the large-eddy simulation grid resolution.