Abstract
We first discuss the concept of coherent vortex. Some elementary vortex interactions which appear in transitional or turbulent shear flow are described such as the formation of spiral vortices, and the pairing of two vortices of same sign. The three-dimensional stretching and turning mechanisms leading to longitudinal hairpin vortices (aligned or staggered mode) are presented. Then the formalism of large-eddy simulations (LES) is recalled in details and classical as well as more recent subgrid-scale models are considered: Smagorinsky’s model, Kraichnan’s spectral eddy-viscosity model, structure-function models, and the dynamic model. Various examples of numerically-simulated three-dimensional flows and of coherent vortices imbedded in them are displayed such as three-dimensional isotropic turbulence, free-shear flows, separated flows and boundary-layers. Comparisons with experimental data are presented and geophysical and industrial applications are discussed. We finally show how a solid-body rotation may drastically modify the free-shear layer topology. The shear/Coriolis linear instability yields a purely longitudinal mode for anticyclonic moderate rotation. Numerical simulations show how this mode evolves non-linearly into concentrated longitudinal hairpin vortices of absolute vorticity.
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