Hall効果がありかつR_mが小さいときの相似法則と物体のまわりの流れに対する応用

概要

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In order to study qualitatively the characters of the flow with the Hall effect, we consider such a case in which the generalized Ohm's law is valid instead of the usual Ohm's law and the flow is incompressible and steady. Let us assume that the wall is uniform along the z direction, the magnetic Reynolds number R_m very small and the electric conductivity of the wall zero or very small. If the magnetic field H is (0, H_0 (const.), 0) in the undisturbed state and ∂^2H_z/∂x^2 is zero up to the order R_m everywhere in the flow or outside the boundary layer when it exists, the following similaity rules are obtained. (i) The x, y components of velocity are identical with those for the case, in which there is no Hall effect but the magnetic field is weakened by the factror [numerical formula], if [numerical formula], where wτ is the Hall parameter and α the inverse of Alfven number. (ii) The z component of velocity is proportional to [numerical formula], if [numerical formula]. As examples of applications, the flows in the neighbourhood of the stagnation point and about the flat plate are studied in detail.
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