= Kinematic magnetic dynamo
{title2=$D_t\mathbf B=(\mathbf B\cdot\nabla)\mathbf u$}
= Kinematic dynamo
{synonym}
A <kinematic magnetic dynamo> studies <magnetic field> amplification by a prescribed <fluid flow>, neglecting the field's feedback on the velocity through the <Lorentz force>. With incompressibility and zero <magnetic diffusivity>, a Lagrangian field vector evolves by its local velocity-gradient matrix. A growth law derived in this approximation cannot hold indefinitely once magnetic stresses significantly change the flow.
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