Stability of a pair of co-rotating vortices with axial flow

International audienceThe three-dimensional linear temporal stability properties of a flow composed of two corotating q-vortices (also called Batchelor vortices) are predicted by numerical stability analysis. As for the corresponding counter-rotating case, when the axial flow parameter is increased, different instability modes are observed and identified as a combination of resonant Kelvin modes of azimuthal wavenumbers m and m+2 within each vortex. In particular, we show that the sinuous mode, which is the dominant instability mode without axial flow, is stabilized in the presence of a moderate axial flow. Different types of mode with a large amplitude in the critical layer are also identified. For small separation distances (above the merging threshold), unstable eigenmodes, corresponding to axial wavenumbers that cannot be easily identified with simple resonant interactions of Kelvin modes, are also observed. Their growth rate is a substantial fraction of the growth rates of low-order resonant modes. The effects of the Reynolds number and vortex separation distance on the growth rate parameter map are considered. Finally, we analyze the similarities and differences between the stability characteristics of co- and counter-rotating vortex pairs