Here u, b describe the flow velocity vector and the magnetic field vector, respectively, p is a scalar pressure, v > 0 is the kinematic viscosity, and [eta] > 0 is the magnetic diffusivity
, while [u.sub.0] and [b.sub.0] are the given initial velocity and initial magnetic field, respectively, with [nabla] x [u.sub.0] = [nabla] x [b.sub.0] = 0.
is the magnetic diffusivity and introducing explicitly the z-dependence of these quantities.
The relative effect of the magnetic forces is scaled by the magnetic Prandtl number, which is simply the ratio between the magnetic Reynolds number and the Reynolds number [P.sub.m] = [R.sub.m]/[R.sub.e], but is also the ratio between the kinematic viscosity and the magnetic diffusivity. We give the value of the magnetic Prandtl number in the photosphere in Table 2.
Where [eta] represents all parameters involved, in this case, the viscosity, the magnetic diffusivity
, and external magnetic field.