Generation of Magnetic Field in the Couette-Taylor System

Abstract

The governing equation for the magnetic field B in an electrically conducting fluid with conductivity σ and velocity v is the so-called induction equation

$$ \frac{{\partial B}} {{\partial t}} = curl(v{\text{ x B) + }}\frac{1} {{\mu _0 \sigma }}\Delta B $$

((1))

) which follows from Maxwell equations and Ohm’s law. The solution B = 0 may become unstable for some critical value Re_mc of the magnetic Reynolds number,

$$ \operatorname{Re} _m = \mu _0 \sigma LV, $$

((2))

) L and V being respectively typical length and velocity scales.