The ensemble mean limit of the one-dimensional turbulence model and application to residual stress closure in finite volume large-eddy simulation

In order to gain insight into the one-dimensional turbulence (ODT) model of Kerstein [1] as it pertains to residual stress closure in large-eddy simulation (LES), we develop ensemble mean closure (EMC), an algebraic stress closure based on the mappings and time scale physics employed in ODT. To allow analytic determination of the stress the ODT model is simplified, conceptually, such that eddy events act upon a velocity field linearized by the local resolved scale strain. EMC can account for viscous effects, addressing the laminar flow finite eddy viscosity problem without implementation of the dynamic procedure [2]. The algebraic form of the model lends itself to analysis [3] and we are able to derive a theoretical value for the eddy rate constant. This value is a bound on the rate constant for full ODT subgrid closure and yields good results in LES of decaying isotropic turbulence with EMC.