Dynamic Large Eddy Simulations of the Ekman Layer Based on Stochastic Analysis

Large eddy simulation (LES) of the neutrally stratified turbulent Ekman layer is performed. In particular, we compare three LES models with direct numerical simulation (DNS), which was validated against existing DNS. The models considered are a standard nondynamic LES model, the Smagorinsky model (SM), a standard dynamic LES model, the stabilized dynamic Smagorinsky model (DSM), and a new linear dynamic model (LDM), which was derived from a realizable stochastic turbulence model. The following conclusions are obtained. The SM does not represent an appropriate model for the flow considered. Mean velocity and turbulence intensities are poorly predicted. With respect to instantaneous fields, the SM provides a tilting of turbulence structures in the opposite direction as seen in DNS. The stabilized DSM also suffers from significant shortcomings. First, its behavior depends on the wall distance. Close to the wall, it produces acceptable turbulence structures. Away from the wall, it suffers from the same shortcomings as the SM. Second, it incorrectly describes the effect of grid coarsening. The new LDM is free from the disadvantages of the SM and stabilized DSM. Its predictions of both mean and instantaneous velocity fields agree very well with DNS. The relevant conclusion is the following. The use of a dynamic LES method represents a mean for correctly simulating large-scale structures (means and stresses), but it does not ensure a correct simultaneous simulation of small-scale structures. Our results indicate that a dynamic method designed in consistency with a realizable stress model can correctly simulate both large-scale and small-scale structures.