In situations where permanent magnetisation is not possible, e.g. above the Curie temperature, to maintain a magnetic field  must be large enough such that induction outweighs diffusion.
It is not the absolute magnitude of velocity that is important for induction, but rather the relative differences and shearing in the flow, which stretch and fold magnetic field lines
.  A more appropriate form for the magnetic Reynolds number in this case is therefore
where S is a measure of strain.
One of the most well known results is due to Backus 
which states that the minimum  for generation of a magnetic field by flow in a sphere is such that
where  is the radius of the sphere and  is the maximum strain rate.
This bound has since been improved by approximately 25% by Proctor.
Many studies of the generation of magnetic field by a flow consider the computationally-convenient periodic cube.  In this case the minimum is found to be
where  is the root-mean-square strain over a scaled domain with sides of length .  If shearing over small length scales in the cube is ruled out, then  is the minimum, where  is the root-mean-square value.