Second-order Cowley-Imai analogy in magnetogasdynamics

Abstract

The extended Cowley–Imai analogy is derived and employed to obtain explicit equations which allow transcription of gasdynamic perturbation solutions into magnetogasdynamic solutions. The transcription is written down to second order for axisymmetric super-Alfvénic flows of a perfect gas at arbitrary Mach numbers. Speed and field perturbations are shown to vanish in the Alfvénic limit for such solutions, although this is not a property of the exact solution. Van Dyke's supersonic-cone-flow solution is then transcribed and compared with the exact numerical solution over the range 1 < A∞, ≥ 20, 1 < M∞, ≥ 20 for a cone of 5° semi-apex angle, showing excellent agreement which improves with increasing field strength. The large-cone-angle behaviour of the solution is also quite good for the upstream state A∞ = M∞ = 2·0.