Instability of secondary flows in an electromagnetically forced curved duct

In this presentation, we investigated the secondary flow forced electromagnetically between two fixed copper cylinders. The gap geometry corresponds to a rectangular curved duct with a large aspect ratio. We have performed low Hartmann number runs ($M<500$) and we used ultrasonic probes to access the azimuthal and axial velocity profiles. We have characterized a transition between magnetohydrodynamic and hydrodynamic regimes. These regimes are controlled by the Elsasser number. The hydrodynamic regime corresponds to a classic flow in rectangular curved duct presenting a single pair of stable contra-rotative vortices (2-cell mode) and shows a transition to double pair of vortices (4-cell mode) for large enough magnetic Dean number $K_M$ (Dean number adjusted by the magnetic field). We have explored the experimental stability diagram for $100