Aligned-fields magnetogasdynamic wakes

Abstract

The effect of compressibility is included here in a study of wakes created in two-dimensional, steady, aligned-fields, magnetogasdynamic flow past obstacles. The gas is assumed to be viscous, resistive, and thermally conducting. With the Oseen type of approximation as well as the magnetogasdynamic boundary-layer approximation, a great simplification in the formulation of wakes results. The boundary-layer equations, although linearized, still retain the coupling between the velocity, the magnetic, and the temperature fields. The solution of the magnetogasdynamic wake, in general, is a superposition of three individual-wake components, each satisfying a diffusion type of equation. Only one of them is capable of extending upstream. Hence the wake picture is generally characterized by a conventional downstream wake with also the possibility of the existence of an upstream one.To be sure, the general features of the magnetogasdynamic wakes in aligned-fields flows are similar to those of an incompressible fluid; however, the flow now, instead of just being subalfvénic, must be subcritical for the upstream wake to occur. That is, the flow condition corresponding to the occurrence of the upstream wake is such that the sum of the square of the Mach number M∞ and the square of the Alfvén number A∞ is less than unity. Evidently it is the mechanism of magneto-sonic-wave propagation that modifies the transition of wakes from the Alfvénic point A∞ = 1 (for an incompressible fluid) to the subcritical are $A^2_\infty + M^2_\infty = 1$ in the Taniuti-Resler diagram.

Finite-magnetic-Reynolds-number effects in magnetogasdynamic flows

“…Its algebraic decay in x is x~5/2. This does not appear to agree with the decay of x~3/2 predicted by Fan [8] for a body of general shape. A study of the discrepancy reveals, however, that this is entirely due to the fore-and-aft symmetry of the body we have chosen and which annihilates the coefficient of the x~3/2 term.…”