Energy dissipation rates of ensemble eddy viscosity models of turbulence: the periodic box
This addresses the issue of over-diffusion in turbulence modeling for fluid dynamics researchers, offering a proof-based alternative to incremental fixes in existing models.
The paper tackles the problem of over-diffusion in classical eddy viscosity models of turbulence by proposing an ensemble approach that solves Navier-Stokes equations with perturbed data to compute turbulent kinetic energy directly, and proves that this method does not over-diffuse solutions for turbulence in a periodic box.
Classical eddy viscosity models of turbulence add an eddy viscosity term based on the Kolmogorov-Prandtl parameterization by a turbulent length scale $l$ and a turbulent kinetic energy $k^{\prime }$. Approximations of the unknowns $l,k^{\prime }$ are typically constructed by solving multi-parameter systems of nonlinear convection-diffusion-reaction equations. Often these over-diffuse so additional fixes are added. Alternately, one can solve an ensemble of NSE's with perturbed data and simply compute directly $k^{\prime }$(without modeling). The question then arises: Does this ensemble eddy viscosity approach over-diffuse solutions? We prove herein that for turbulence in a periodic box it does not.