The Magnetic Reynolds number (Rm) is the magnetic analogue of the Reynolds number, a fundamental dimensionless group that
occurs in magnetohydrodynamics. It gives an estimate of the relative effects of advection or induction of a magnetic field by the motion of a conducting medium, often a fluid, to magnetic diffusion. It is typically defined by:
![R_m=\frac{l_0 V_0}{\eta}](/Images/godic/202501/25/5dc83c26e59c1fbcb7dae65c6bca17190238.png")
![l_0](/Images/godic/202501/25/36b8d268d23f69d511cb24f2e295212d0238.png")
和![V_0](/Images/godic/202501/25/e40444a94ae90f2ae253721b8132f9770238.png")
分别是系统的特征尺度和特征速度，![\eta=\frac1{\sigma\nu}](/Images/godic/202501/25/040d89b5994107924541822ec7fcc91c0238.png")
是磁扩散率。![\frac{\partial\boldsymbol{B}}{\partial t}=\nabla\times(\boldsymbol{v}\times\boldsymbol{B})+\eta\nabla^2\boldsymbol{B}](/Images/godic/202501/25/04ed7c601aacf26955af2102fde242470239.png")
![\frac{\partial\boldsymbol{B}}{\partial t}=\eta\nabla^2\boldsymbol{B}](/Images/godic/202501/25/e82e028afda16b0d15ec88f8d266929d0239.png")
![\frac{\partial\boldsymbol{B}}{\partial t}=\nabla\times(\boldsymbol{v}\times\boldsymbol{B})](/Images/godic/202501/25/e2d9d46f06cd09e1928850e4f5355f6f0239.png")