Magnetic Reynolds Number

Magnetohydrodynamics · 1946

Equation: R_m = v·L / η
Field: Magnetohydrodynamics
Named After: Walter Elsasser · after Osborne Reynolds
Year: 1946

Symbols

v flow speed · L size of the system · η magnetic diffusivity · dimensionless — big R_m means the field is frozen into the fluid, small means it slips through

Significance

One number that decides the regime: in Earth's core and the Sun (R_m huge) field lines are frozen into the flow and can be wound up into a dynamo — Elsasser's explanation for why Earth is a magnet at all. In the lab (R_m small) the field barely notices the fluid.