Numerical Simulations of Coherent Vortices in Turbulence

After presenting the general features of turbulent flows and coherent vortices, we discuss the major progress brought by Computational Fluid Dynamics (CFD) to the understanding of coherent vortices in turbulence. Afterwards, we present some simple vortex dynamics arguments allowing us to understand qualitatively the formation of coherent vortices during the transition to turbulence in shear flows. Of particular interest are the following elementary vortex interactions: roll up of a vortex sheet, pairing, dipole, even longitudinal hairpin, and odd longitudinal hairpin. Then direct numerical or large-eddy simulations of free-shear flows (mixing layers, backstep, jets, wakes), isotropic turbulence, and spatially-developing boundary-layers on a flat plate are presented. Following the editor’s request, these simulations focus mainly on the work done in France in Grenoble, which is however discussed within a broader numerical and experimental context. We show for instance that helical pairings may occur in plane mixing layers. The paper also presents in details the formalism of large-eddy simulations (LES) of turbulence, with the various models developed since Smagorinsky. We see for instance how longitudinal hairpin vortices are taken into account within these LES. Effects of compressibility upon turbulence are also considered: we study in particular mixing layers (where it is shown that helical pairing is inhibited above a certain convective Mach number), strongly heated boundary layers at low Mach number, and supersonic compression ramps within the frame of the HERMES European space-shuttle reentry project. Finally, we look at the influence of solid-body rotation on incompressible turbulence. In the case of a free-shear layer, we study shear/Coriolis linear instability, which, in anticyclonic conditions and at moderate rotation rates, yields a purely longitudinal mode. Numerical simulations show how this mode evolves non-linearly into concentrated longitudinal hairpin vortices of absolute vorticity. We also consider the case of initially isotropic turbulence subject to rotation.