Shock analysis: Three useful new relations

Open Access
Publisher Website
Google Scholar
Abstract
Over the years a variety of methods for analyzing hydromagnetic shocks have been developed. The Rankine‐Hugoniot relations on which the analyses are based are sufficiently complex and involve sufficiently large numbers of variables that in specific instances a decision must be made on how to proceed. Our analyses have tended to emphasize the magnetic field (B) and velocity (V) as the starting point since they are typically the most accurately determined measurables. We have also tended to carry out the analysis in a reference frame aligned, and moving, with the shock. Three new relations have been derived which are generally useful. (1) The shock speed can be calculated from the upstream and downstream values of B and V independent of the shock normal or its direction relative to the upstream field. (2) An explicit relation is derived relating the angles between the jump in velocity, the shock normal, and the upstream field. (3) From the magnetic field and two‐dimensional velocity measurements, which are frequently all that are available, it is possible to infer the third component of the upstream‐downstream velocity jump.