On the Energy Dissipation Rate of Ensemble Eddy Viscosity Models of Turbulence: Shear Flows

Classical eddy viscosity models add a viscosity term with a turbulent viscosity coefficient developed beginning with the Kolmogorov–Prandtl parameterization. Approximations of unknown accuracy of the unknown mixing lengths and turbulent kinetic energy are typically constructed by solving associated systems of nonlinear convection–diffusion-reaction equations with nonlinear boundary conditions. These often over-diffuse, so additional fixes are added such as wall laws, or different approximations are used in different regions (which must also be specified). Alternately, one can solve an ensemble of NSEs with perturbed data, compute the ensemble mean and fluctuation, and simply directly compute the turbulent viscosity parameterization. This idea is recent. From previous work it seems to be of a lower complexity and greater accuracy. It also produces parameterizations with the correct near-wall asymptotic behavior. The question then arises: Does this ensemble eddy viscosity approach over-diffuse solutions? This question is addressed herein.