In this paper, we study the interaction of two co-rotating trailing vortices. It is well-known that vortices of like-sign ultimately merge to form a single vortex, and there has been much work on measuring and predicting the initial conditions for the onset of merger, especially concerning the critical vortex core radius. However, the physical mechanism causing this merger has received little attention. In this work, we directly measure the structure of the antisymmetric vorticity field that causes the co-rotating vortices to be pushed towards each other during merger. We discover that the form of the antisymmetric vorticity comprises two counter-rotating vortex pairs, whose induced velocity field readily pushes the two centroids together. The merging velocity computed from the antisymmetric vorticity field agrees closely with the merging velocity measured directly from the total (original) flow field.The co-rotating vortex pair evolves through four distinct phases. The initial stage comprises a diffusive growth, which can be either viscous or turbulent. In either case, the number of turns that they rotate around one another until the vortices start to merge increases with Reynolds number (Re). If one observes the streamlines in a rotating reference frame (moving with the vortices), then one finds an inner and outer recirculating region of the flow bounded by a separatrix streamline. When the vortices grow large enough in the first stage, diffusion across the separatrix places vorticity into the outer recirculating region of the flow, and this leads to the generation of the antisymmetric vorticity, causing convective merger. This second (convective) stage corresponds to the motion of the vortex centroids towards each other, and is a process which is almost independent of viscosity. During the late part of this stage, the antisymmetric vorticity is diminished by a symmetrization process, and the final merging into one vorticity structure is achieved by a second diffusive stage. The fourth and ultimate phase is one where the merged vortex core grows by diffusion.

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Stimulated by experimental observations of vortex merging, we compute a new family of uniform-vorticity steady solutions of the Euler equations in two dimensions. In experiments with two co-rotating vortices, one finds that, prior to the convective merging phase, and the formation of vortex filaments, the initial pair diffuses into a single structure (with two vorticity peaks) in the form of a symmetric ‘dumb-bell’. In the present computations, our exploration of the existence of vortex solutions has been guided by the streamline patterns of the co-rotating reference frame, and by the simple concept that the vortex boundary must be one of these streamlines. By varying the parameters which define the vortex patches, we find a family of vorticity structures which pass from the limiting case of point vortices, through the case of two equal co-rotating uniform vortices (as previously computed by Saffman & Szeto 1980; Overman & Zabusky 1982; Dritschel 1985), to the regime where the vortices touch in the form of a dumb-bell. Further exploration of this family of solutions leads to an elliptic vortex, which joins precisely to the local transcritical bifurcation from elliptic vortices with $n\,{=}\,4$ perturbation symmetry that was found by Kamm (1987) and Saffman (1988). Finally, one reaches a limiting ‘cat's-eye’ vortex patch of two-fold symmetry ($m\,{=}\,2$), which constitutes an extension to the limiting shapes of $m$-fold symmetry ($m \,{>}\, 2$) found by Wu, Overman & Zabusky (1984).

Fluidic oscillating valves have been used in order to apply unsteady boundary layer injection to repair the separated flow of a model diffuser, where the hump pressure gradient represents that of the suction surface of a highly loaded stator vane. The fluidic actuators employed in this study consist of a fluidic oscillator that has no moving parts or temperature limitations and therefore is more attractive for implementation on production turbomachinery. The fluidic oscillators developed in this study generate an unsteady velocity with amplitudes up to 60% RMS of the average operating at non-dimensional blowing frequencies (F+) in the range 0.6 < F+ < 6. These actuators are able to fully reattach the flow and achieve maximum pressure recovery with a 60% reduction of injection momentum required and a 30% reduction in blowing power compared to optimal steady blowing. PIV velocity and vorticity measurements have been performed that show no large-scale unsteadiness in the controlled boundary layer flow.

Fluidic oscillating valves have been used in order to apply unsteady boundary layer injection to “repair” the separated flow of a model diffuser, where the hump pressure gradient represents that of the suction surface of a highly loaded stator vane. The fluidic actuators employed in this study consist of a fluidic oscillator that has no moving parts or temperature limitations and is therefore more attractive for implementation on production turbomachinery. The fluidic oscillators developed in this study generate an unsteady velocity with amplitudes up to 60% rms of the average operating at nondimensional blowing frequencies (F+) in the range of 0.6<F+<6. These actuators are able to fully reattach the flow and achieve maximum pressure recovery with a 60% reduction of injection momentum required and a 30% reduction in blowing power compared with optimal steady blowing. Particle image velocimetry velocity and vorticity measurements have been performed, which show no large-scale unsteadiness in the controlled boundary layer flow.