© 1965 by Oxford University Press
UPSTREAM INFLUENCE EFFECTS IN THE FLOW OF A CONDUCTING FLUID OVER AN INSULATING WALL
( Department of Mathematics, University of Strathclyde )
In conventional gas dynamics there is no great difficulty encountered when studying the propagation of a disturbance through the two-dimensional steady supersonic flow of a perfect gas past a straight-edged wall. A two-dimensional disturbance introduced into the flow travels along the appropriate Mach line to the wall from which it is then reflected downstream. The flow of a uniform stream past a wall convex to the stream is achieved by means of the well-known Prandtl-Meyer expansion. Flows in channels and similar problems can be analysed by the techniques of the method of characteristics.
In magneto-gasdynamics, however, the corresponding problems for the flow of an infinitely conducting gas indicate that situations arise in which disturbances not only propagate upstream in the gas but can also propagate in all directions in the solid wall. One immediate consequence is that the conditions upstream can be continually modified. To obtain a qualitative understanding of these processes a mathematical analysis is presented below.
In a recent paper by Chu (4), the flow everywhere is uniform and the disturbances are created only at the boundary between the gas and the non-conducting solid. The present paper includes the work of Chu (4) as a particular case.