Simulation of the Kolmogorov inertial subrange using an improved subgrid model

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Abstract
A subgrid model is developed and applied to a large‐eddy simulation of the Kolmogorov inertial subrange. Currently popular subgrid models are derived from models of the turbulent energy equation, resulting in a significant loss of information as a consequence of the statistical averaging performed in going from the Navier–Stokes equation to the energy equation. The subgrid model developed here is based directly on a model of the Navier–Stokes equation. The improved subgrid model contains two terms: an eddy viscosity and a stochastic force. These terms are computed from the EDQNM stochastic model representation of the momentum equation, and from a fully resolved direct numerical simulation. Use of the subgrid model in a forced large‐eddy simulation results in an energy spectrum that exhibits a clear k − 5 / 3 power‐law subrange with an approximate value Ko=2.1 of the Kolmogorov constant.