Vortex flow regimes and their bifurcations in electromagnetically driven horizontal soap films in an annulus with rotating boundaries

We study nonlinear vortex flow regimes and their bifurcations in electromagnetically driven horizontal electrically conducting soap films spanning the gap between two concentric cylindrical electrodes capable of rotating about their vertical symmetry axes. A steady axisymmetric shear flow is driven by radially distributed Lorentz force when a direct current flows through the film placed in a non-uniform axisymmetric magnetic field orthogonal to the film. When the Reynolds number exceeds a threshold value, an instability sets in the form of vortices that drift either clock- or anti-clockwise depending on the value of the Reynolds number and magnetic field distribution. An interplay between the shear flow due to electromagnetic forcing, centrifugal effects and the boundary rotation leads to rich bifurcation scenarios and intriguing flow patterns consisting of steadily precessing, breathing or bursting vortices. A gradual increase of the Reynolds number leads to a sequence of transitions from a steady flow to drifting periodic vortices to quasi-periodic patterns with two or three incommensurate frequencies followed by the onset of a weak turbulent regime. The latter occurs at Reynolds numbers up to 100 times larger than the critical value for the primary instability of the base flow. Strong turbulent regime characterised by a broadband temporal power spectrum is not detected.