Theoretical and numerical analysis of wake vortices
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The first part of the paper analyses the linear dynamics of a vortex pair thanks to a normal mode analysis. The basic flow is a superposition of two Lamb-Oseen vortices of radius a and distance b. The long-wave Crow instability and the short-wave Widnall instabilities are fully characterized for different aspect ratios a/b of the vortex pair. In particular, as a/b increases, it is shown that the antisymmetric Widnall instabilities are favoured for short-wave perturbations. This constitutes an explanation for the results obtained by Leweke & Williamson (1998). The second part of the paper deals with turbulence in the Batchelor vortex. A 3D Large Eddy Simulation (LES) shows that, starting from a linearly unstable wake-type vortex, high levels of turbulence can be obtained. But, the mean-flow then rapidly evolves towards a stable state. These results are in accordance with those of Ragab & Sreedhar (1995).
© EDP Sciences, ESAIM, 1999