Statistical Analysis of Dynamic Subgrid Modeling Approaches in Large Eddy Simulation

Abstract

In large eddy simulation (LES) of turbulent flows, dynamic subgrid models would account for an average cascade of kinetic energy from the largest to the smallest scales of the flow. Yet, it is unclear which of the most critical dynamical processes can ensure the criterion mentioned above. Furthermore, evidence of vortex stretching being the primary mechanism of the cascade is not out of the question. In this article, we study essential statistical characteristics of vortex stretching. Our numerical results demonstrate that vortex stretching rate provides the energy dissipation rate necessary for modeling subgrid-scale turbulence. We have compared the interaction of subgrid stresses with the filtered quantities among four models using invariants of the velocity gradient tensor. The individual and the joint probability of vortex stretching and strain amplification show that vortex stretching rate is highly correlated with the energy cascade rate. Sheet-like flow structures are correlated with viscous dissipation, and vortex tubes are more stretched than compressed. The overall results indicate that the stretching mechanism extracts energy from the large-scale straining motion and passes it onto small-scale stretched vortices.

Interaction of vortex stretching with wind power fluctuations

“…However, challenges include the availability of fewer measurement data and even fewer numerical studies of the mechanism that transfers kinetic energy from the largest-scale motions, where it is produced, to the smallest-scale activities, where it dissipates. Most importantly, the dynamical characteristics of energy cascade 8,25 , especially for the efficient reduced-order representation of turbulence in practical applications, such as optimal design of wind farms, is of high importance.…”

“…Our recent works 22,26,27 developed immersed boundary methods for large eddy simulation (LES) of orographic influence in the atmospheric boundary layer. Unlike classical LESs using the Smagorinsky model, which considers only the 'strain portion' of the velocity gradient tensor, our approach considers both the 'strain tensor' and the 'rotation tensor' to model the eddy viscosity 8 . This approach allows us to dynamically adapt the energy dissipation rates to the scale of the energetic eddies in the roughness sublayer.…”

“…Second, we investigate the scale-adaptivity of dissipation rates 36 in LES of wind farms, where we utilize the transfer of energy via vortex stretching 8,25,37 . Note that LES accurately captures the large-scale unsteady motions in wind farms 38 , using fine grids combined with secondary wall models 39 , thanks to the recent progress in computing power.…”

“…As a result, the local energy cascade rate depends on the skewness of filtered strain plus the stretching of filtered vorticity 37,40 . Energy containing O(L) eddies connect the constrained (or restricted) Euler dynamics to the energy cascade 8,41 . Whereas energy cascading O(∆ les ) eddies, characterized by velocity gradients, extract energy from the large-scale eddies via vortex stretching and pass it onto dissipating eddies of size O(η) 40 .…”

“…The interaction between wind farms and the atmospheric boundary layer produces finescale vortices [1][2][3][4][5] . Turbulence kinetic energy (TKE) is progressively moved toward small scale flow features when a vortex stretches [6][7][8] . Representing the nature of energy cascade in atmospheric computational models is vital for understanding the impact of atmospheric turbulence in large wind farms 9,10 .…”