Magnetic Reynolds number
In magnetohydrodynamics, the magnetic Reynolds number (Rm) is a dimensionless quantity that estimates the relative effects of advection or induction of a magnetic field by the motion of a conducting medium to the magnetic diffusion. It is the magnetic analogue of the Reynolds number in fluid mechanics and is typically defined by: R m = U L η ∼ i n d u c t i o n d i f f u s i o n {\displaystyle \mathrm {R} _{\mathrm {m} }={\frac {UL}{\eta }}~~\sim {\frac {\mathrm {induction} }{\mathrm {diffusion} }}} where U {\displaystyle U} is a typical velocity of the flow, L {\displaystyle L} is a typical length scale of the flow, η {\displaystyle \eta } is the magnetic diffusivity.