A Short-Wave Instability Caused by the Approach of a Vortex Pair to a Ground Plane

Daniel M. Harris
Victor A. Miller
Charles H. K. Williamson
Cornell University

The counter-rotating pair of vortices formed from aircraft wingtips in flight presents a potential hazard to other aircraft in the form of a sustained rolling moment.  Such a trailing vortex pair travels downwards under its own self-induced velocity.  Under conditions where an aircraft is close to the ground, at an airport, the vortices can interact with the ground plane.  The inviscid trajectories of the vortices, as originally predicted by Lamb (1932), differ quite significantly from what is observed in experiment.  This is primarily due to the fact that between the vortices and the ground, a boundary layer forms, which can separate to generate secondary vortices of opposite sign.  The secondary vortices significantly influence the trajectories and development of the original vortex pair, an effect originally discovered by Harvey and Perry (1971).

Figure 1 

In the present work (Figure 1), we have developed a novel technique using laser-induced fluorescence to visualize this secondary vorticity in detail, by pooling dye on the ground plane prior to launching the vortex pair from rotating flaps.  In fact, it is possible to mark only the secondary vorticity with dye, in order to highlight this structure, while leaving the primary vortices invisible!

In image below (Figure 2), we show the cross section of the primary vortices.  We also visualise the secondary vortices, which were originally generated by ground interaction, and are now visible above the primary structures. The lower half of the photo shows a mirror image of the vortex system, due to optical reflection in the ground plane.

Figure 2

Our primary motivation is towards an understanding of the development of new 3D instabilities. The first photograph (Figure 1) captures the essence of our technique, as we are able to  visualize the secondary vorticity generated at the wall, as it is induced to rotate around the (invisible) primary structures. Here we are illuminating more clearly the complex periodic deformations due to a short wave 3D instability.  A similar short wave instability was predicted in a numerical simulation completed by Luton and Ragab (1997), and from the very recent work of Duponcheel et al. (2009), but to our knowledge, a precise experimental visualization of this phenomena does not currently exist in literature. In this example, we employ a thin horizontal laser light sheet, which highlights the beauty and periodicity of this 3D instability, for vorticity that has rotated almost one revolution around the primary structures.

The research is partially supported by the Office of Naval Research.

References

Duponcheel, M., Cottin, C., Daeninck G., Winckelmans, G. and Leweke, T. (2009). Three-dimensional dynamics of vortex pairs in ground effect: experiment and numerical simulations. Submitted to Physics of Fluids.

Harvey, J.K. and Perry, F.J. (1971). Flowfield produced by trailing vortices in the vicinity of the ground. AIAA J., 9(8):1659–1660.

Lamb, H. (1932). Hydrodynamics. 6th edition, Dover Publications, New York, NY.

Luton, J.A. and Ragab, S.A. (1997). Three-dimensional interaction of a vortex pair with a wall. Phys. Fluids, 9(10):2967–2980.

Reporters and Editors

Reporters can freely use these images. Credit: Harris, Miller & Williamson (2009).