Thin-tube vortex simulations for sinusoidal instability in a counter-rotating vortex pair

A thin-tube vortex method is developed to investigate the intrinsic instability within a counter-rotating vortex pair system and the e ects from the core size and the wavenumbers (or wavelengths). The numerical accuracy and the advantages of the scheme are theoretically estimated. A nearest-neighbour-image method is employed in this three-dimensional vortex simulation. Agreement with Crow’s instability analysis has been achieved numerically for the long-wave cases. A short-wave instability for the zeroth radial mode of bending instability has also been found using the thin-tube vortex simulations. Then, the combinations of longand short-wave instability are investigated to elucidate the non-linear e ects due to the interactions of two di erent modes. It is shown that instability is enhanced if both longand short-wave instabilities occur simultaneously. Although the method used in the paper is not capable of including e ects such as axial ow, vortex core deformation and other complicated viscous e ects, it e ectively predicts and clari es the rst-order factor that dominates the sinusoidal instability behaviour in a vortex pair. Copyright ? 2002 John Wiley & Sons, Ltd.