Examining the Artificial Bottleneck Effect in Large Eddy Simulations

In Navier-Stokes turbulence, a bottleneck effect in the energy cascade near the viscous cutoff causes an overshoot in the energy spectrum 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.

This work uses Stokes flow regularization (SFR) and kinetic energy considerations to create LES models exploring the artificial bottleneck effect. A posteriori tests in isotropic turbulence compare the models’ impact on this effect. A key strategy of mitigating the bottleneck effect is to introduce a nonlinear gradient component in the residual stress closure, forming a dynamic mixed model. This approach effectively captures the local structure of residual stresses, leading to better representation of energy cascade efficiencies.

Specifically, the mixed model produces vortex tube-like structures that closely resemble those observed in the filtered DNS, whereas the eddy viscosity model produces a significantly different flow structure characterized by more shear layer-like structures (i.e.,vortex sheets rather than vortex tubes). The shear layers produced by the eddy viscosity models may be linked to the inverse cascade vortex thinning mechanism observed in 2D turbulence, suggesting a possible connection between the (artificial) bottleneck effect in 3D turbulence and the inverse cascade in 2D turbulence.