# Séminaire de Mécanique d'Orsay

## Le Jeudi 7 juillet à 14h00 - Salle de conférences du LIMSI

### Instabilities in electromagnetically driven flows: From laminar to
turbulent regimes in electromagnetic pumps

## Paola Rodriguez Imazio

Laboratoire de Physique Statistique, École Normale Supérieure de Paris

The MHD flow driven by a travelling magnetic field (TMF) in an annular channel is investigated
numerically. Laminar and turbulent regimes of the flow are studied, using both axisymmetric and
3D simulations. At low hydrodynamical Reynolds numbers Re, it is seen that for sufficiently large
magnetic Reynolds number Rm, or if a large enough pressure gradient is externally applied, the
system undergoes an instability in which the flow rate in the channel dramatically drops from
synchronism with the wave to much smaller velocities. This transition takes the form of a saddle-
node bifurcation for the time-averaged quantities. We characterize the bifurcation, and study the
stability of the flow as a function of several parameters. We show that the bifurcation of the flow
involves a bistability between Poiseuille-like and Hartman-like regimes, and relies on magnetic flux
expulsion. Based on this observation, new predictions are made for the occurrence of this stalling
instability. For large Re, and with more realistic boundary conditions, we show that the instability
takes the form of a large axisymmetric vortex flow in the (r; z)-plane, in which the fluid is locally
pumped in the direction opposite to the one of the magnetic field. Close to the marginal stability
of this vortex flow, a low-frequency pulsation is generated. For 3D simulations, it is shown that the
strong shear produced by the local stalling of the flow leads to a 3D destabilization in the azimuthal
direction, characterized by the growth of nonaxisymmetric modes of the velocity field. Finally,
these results are compared to theoretical predictions and are discussed within the framework of
experimental annular linear induction electromagnetic pumps.