Motion of an electrically conducting fluid in a magnetic field generates electric currents and produces Lorentz force, which affects the flow. We consider this interaction for the technologically interesting case of low magnetic Reynolds number, in which the additional magnetic field induced by the fluid motion is weak. The results illustrate the spectacular and, often, unexpected way, in which the applied magnetic field transforms familiar hydrodynamic phenomena, such as the mixing layer instability, transient growth in a channel, and ideal flow in an ellipsoid.
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