Large-Eddy Simulations of Longitudinal Vortices in Shear Flows

Abstract

The formation of three-dimensional vortices in mixing layers and boundary layers is investigated in Large-Eddy Simulation, with the aid of the subgrid-scale models presented in (Lesieur and Métais, 1996, Ann. Rev. Fluid Mech., 28, and Lesieur, 1997, Turbulence in fluids, third updated and revised edition). In mixing layers perturbed upstream or initially by small-amplitude random perturbations, two types of flow patterns are obtained depending on the level of three-dimensionality of the perturbations and the spanwise size of the domain. For forcing amplitudes of the order of 1% in turbulent intensity, the natural tendency is the emergence of oblique subharmonic modes yielding the formation of highly-three-dimensional vortex lattices, as in the experiments of Chandrsuda, Mehta, Weir and Bradshaw, 1978, J. Fluid Mech. 85). This trend can be partially inhibitted by taking narrower domains, and sometimes just by making the perturbations more two-dimensional. In this case, a more “canonical” flow pattern is obtained, with quasi-two-dimensional billows undergoing successive pairings while stretching, in between each other, streamwise vortices that form in a succession of stages involving local roll-up and pairing, as conjectured by Lin and Corcos (1984, J. Fluid Mech., 141). The LES of the transition of a spatially-growing boundary layer is also shown, featuring the almost-simultaneous emergence of staggered Λ-vortices and streamwise streaks. The connection between these results and different stability analyses is discussed.