Analysis of Model Variance for Ensemble Based Turbulence Modeling

This report develops an ensemble or statistical eddy viscosity model. The model is parameterized by an ensemble of solutions of an ensemble-Leray regularization. The combined approach of ensemble time stepping and ensemble eddy viscosity modeling allows direct parametrization of the turbulent viscosity coefficient that gives an unconditionally stable algorithm. We prove that the model’s solution approaches statistical equilibrium as t → ∞; the model’s variance → 0 as t → ∞. The ensemble method is used to interrogate a rotating flow, testing its predictability by computing effective averaged Lyapunov exponents.