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 Kolmogorov's -5/3 scaling. A similar overshoot occurs in large-eddy simulations (LES) when an eddy viscosity model is used. It is not a viscous phenomenon but is caused by error in the residual stress model. This artificial bottleneck effect in LES leads to an over-prediction of kinetic energy even when a dynamic procedure is used to capture the spectral decay at the cutoff scale. Recently, Johnson [2022, J. Fluid Mech., 934, A30] introduced a generalization of spatial filtering that provides a dynamic procedure without a test filter. In this paper, this method of Stokes flow regularization (SFR) is used with kinetic energy considerations to generate a range of LES models and explore the bottleneck effect in more detail. The coefficients for each dynamic model are determined locally, without averaging over homogeneous directions. A posteriori tests of the models in isotropic turbulence are reported, demonstrating the robustness of the SFR-based procedure for different model forms and enabling fair comparisons in terms of their impact on the bottleneck effect. An effective way to mitigate the bottleneck is to add a nonlinear gradient component in the residual stress closure, forming a dynamic mixed model. This approach improves representation of residual stress structure and energy cascade efficiencies.