Artificial bottleneck effect in large eddy simulations

Abstract

In Navier-Stokes turbulence, a bottleneck effect in the energy cascade near the viscous cutoff causes an overshoot in the energy spectrum, or spectral bump, relative to Komogorov's −5/3 power-law scaling. A similar spectral overshoot occurs in large-eddy simulations (LES) when an eddy viscosity model is used. It is not a viscous phenomenon, but rather is caused by error in the residual stress model. This artificial bottleneck effect in LES leads to an over-prediction of kinetic energy even if a reliable dynamic procedure is used to accurately capture the spectral decay at the cutoff length scale. Recently, Johnson [J. Fluid Mech. 934, A30 (2022)] introduced a physics-inspired generalization of the concept of spatial filtering that provides a dynamic procedure that does not require a test filter calculation. In this paper, this method of Stokes flow regularization (SFR) is used alongside fundamental considerations related to kinetic energy to generate a range of LES models to explore the artificial bottleneck effect in more detail. The coefficients for each dynamic model are determined locally, without the need of averaging over homogeneous directions. The theory directly provides stabilizing elements such as local averaging of coefficients. A posteriori tests of the models in isotropic turbulence are reported, demonstrating the robustness of the SFR-based dynamic procedure for a range of model forms and providing a framework for fair comparisons between them in terms of their impact on the bottleneck effect. An effective means of mitigating the bottleneck effect is to introduce a nonlinear gradient component in the residual stress closure, forming a dynamic mixed model. One primary reason for the efficacy of this approach is that the nonlinear gradient model is able to accurately capture aspects of the local structure of the residual stresses, leading to a better representation of energy cascade efficiencies.