Strain-rate development between a co-rotating Lamb-Oseen vortex pair of unequal strength.

To date, several investigations have considered the prospect of enhanced dissipation of a vortex pair due to elliptic (short wave) instabilities. Recent studies indicate that these modes have the potential to significantly reduce the time taken to dissipate vortex pairs. This has generated interest in the aviation industry, where aircraft trailing wakes pose a significant hazard for nearby aircraft. Of note, recent studies have indicated that the growth rate of these short-wave instability modes depends strongly on the strain-rate developed within the core of each vortex. This strainrate has been shown to develop naturally simply due to the presence of both vortices. Studies to date have concentrated on vortex pairs where each vortex has the same magnitude of circulation. We extend this by varying the circulation ratio of the two vortices; the circulation of one vortex is varied while the circulation of the other remains constant. The effect on the strain-rate which develops within each core is considered. Of particular interest are the time-scales involved in both the strain-rate development and in the twodimensional merging process, as sufficient time is required for short-wavelength instabilities to occur prior to merging for the process to successfully reduce dissipation time. A spectral-element method is used to conduct the DNS investigation at a circulation Reynolds number of ReΓ = 20,000