Abstracts - KTH Mechanics

Experiments on vortex pair dynamics in ground effect
C. Cottin ∗ and T. Leweke ∗
We investigate experimentally the 3D dynamics of a pair of counter-rotating vortices
approaching a solid wall. In addition to its fundamental interest, this configuration
has relevance for the problem of aircraft trailing vortices at take-off and landing.
The vortices are generated in water at the edges of two impulsively rotated flat
plates, and visualised using fluorescent dye. Measurements were performed using
image analysis and Particle Image Velocimetry. The set-up and procedure are similar
to the ones described in Ref. 1. Reynolds numbers, based on the circulation of one
vortex, were in the range 1500-5500.
In the major part of the experiments, the vortex pairs were generated close to
3 vortex separation distances away from the wall. This is short enough for the flow
not to develop long-wavelength displacement instabilities or elliptic core instabilities 1 ,
before the wall effect becomes important. As the vortices approach the surface due
to their mutually induced motion, secondary vorticity is generated at the wall (see
figure 1), which is lifted off the surface and rolls up into a secondary vortex orbiting
the primary one and causing its rebound. During this stage, short-wave perturbations
grow at the periphery of the primary vortices (fig. 1a). At a later time, an instability
with a larger axial wavelength develops on the secondary vortex (fig. 1b), leading to
a rapid decay of the whole system into small-scale structures shortly afterwards. We
will present evidence that these phenomena are caused by a centrifugal instability of
the primary vortex and an elliptic instability of the secondary vortex, respectively.
Some qualitative results on the interaction of a ground effect with the longwavelength
Crow instability will also be presented.
∗ IRPHE, CNRS/Universités Aix-Marseille, B.P. 146, F-13384 Marseille Cedex 13, France.
1 Leweke and Williamson, J. Fluid Mech. 360, 85 (1998)
(a)
(b)
Figure 1: Dye visualisation (side view) and vorticity levels (cross-cut of one vortex
only) of a vortex pair in ground effect at Re = 3500. (a) t ∗ = 4.5, (b) t ∗ =6.4.
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