Ivan Delbende

Direct numerical simulation of helical vortices

We herein present a direct numerical simulation method aimed at describing the dynamics of helical vortices such as those developing in the wake of propellers and wind turbine or helicopter rotors. By enforcing a helical symmetry, the 3D incompressible Navier-Stokes equations are reduced to a 2D problem which we solve using a generalised vorticity/streamfunction formulation. In this framework, we simulate the viscous dynamics of one or several helical vortices and describe quasi-steady states as well as long-time (or far-wake) dynamics. In particular, several types of merging in the two helical vortex systems are identified.

Effect of stretching on vortices with axial flow

It is shown that a weak time-dependent stretching might rapidly destabilise a vortex, thus providing a mechanism for vortex bursts observed in turbulent flows. This study addresses the three-dimensional stability of a stretched viscous Batchelor vortex. In a fashion quite similar to Lundgren’s transformation, the strain field is almost eliminated from the linear equations that govern three-dimensional perturbations. Such transformed equations, which are reminiscent of those for the swirling jet instability, are then numerically solved in the simple case of a compression phase followed by a stretching phase. Simulations qualitatively demonstrate how strain and azimuthal vorticity cooperate to destabilise the vortex.

Bursting of a Swirling Jet Stemming from a Localized Perturbation

The present study is aimed at understanding the mechanisms which lead coherent vortex structures to burst, as observed in fully turbulent flows [2]. A single structure is considered here, modeled by a Batchelor-vortex flow. The linear and nonlinear evolution of an initially localized perturbation is followed by DNS. As already known [5], the flow is linearly unstable towards helicoidal disturbances. Vortical helices are found to arise from the saturation of this primary instability. At the same time, the vortex bursts in the neighborhood of the initial perturbation location, where numerous linear instability modes grow in place, the interaction of which is likely to cause rapid vortex dissipation.