The paper is devoted to the theoretical investigation of the possible existence of
stationary mixing layers and of their structure in nearly perfectly conducting, nearly
inviscid fluids with a longitudinal magnetic field. A system of two equations is used,
which generalizes the well-known Blasius equation (for flow around a semi-infinite
plate) to the case under consideration. The system depends on the magnetic Prandtl
number, Pm=ν/νm, where ν and νm are the usual and the magnetic viscosities,
respectively.
For the existence of stationary flows the ratio between the flow velocity vx and
the Alfvén velocity cA=Hx/(4πρ)1/2 (ρ being the fluid density) plays a critical role.
Super-Alfvén (vx>cA) flows are possible at any value of Pm and for any values of vx
and Hx on the layer boundaries. Sub-Alfvén (vx<cA) stationary flows are impossible
at any value of Pm and for any values of the differences in vx and Hx across the
layer, except for two cases: Pm=0 and Pm=1. When Pm=0, i.e. when the fluid is
strictly inviscid, ν=0, flow is possible in both the super- and sub-Alfvén regimes;
however, the magnetic field must be uniform, Hx=const, Hy=0 in this case. For
Pm=1 both flow regimes are also possible; however, the sub-Alfvén flow is possible
only for a definite relationship between the magnetic field and velocity differences:
ΔHx=−δvx (in corresponding units). For the case where the relative differences in
vx and Hx across the layer are small, Δvx[Lt ]vx, ΔHx[Lt ]Hx, solutions are obtained in
explicit form for arbitrary Pm (here vx and Hx are averaged over the layer). For the
specific case Pm=1, exact analytical solutions of basic system are found and studied
in detail.
