Application of the NS-α Model to a Recirculating Flow

In this paper we investigate a subgrid model based on an anisotropic version of the NS-α model using a lid-driven cavity flow at a Reynolds number of 10,000. Previously the NS-α model has only been used numerically in the isotropic form. The subgrid model is developed from the Eulerian-averaged anisotropic equations (Holm, Physica D 133:215, 1999). It was found that when α2 was based on the mesh numerical oscillations developed which manifested themselves in the appearance of streamwise vortices and a ‘mixing out’ of the velocity profile. This is analogous to the Craik–Leibovich mechanism, with the difference being that the oscillations here are not physical but numerical. The problem could be traced back to the discontinuity in α2 encountered when α2 = 0 on the endwalls. A definition of α2 based on velocity gradients, rather than mesh spacing, is proposed and tested. Using this definition the results with the model show a significant improvement. The splitting of the downstream wall jet, rms and shear stress profiles are correctly captured a coarse mesh. The model is shown to predict both positive and negative energy transfer in the jet impingement region, in qualitative agreement with DNS results.