Axisymmetric Shocks in the Newtonian Limit for Nonrigid Boundaries

Abstract

The natural generalization of the snowplow equation in two-dimensional axisymmetric or Cartesian geometries is a Newtonian approximation in which the possibility of surface deformation is admitted. Such a general Newtonian approximation has been derived from the Lagrangian fluid equations, using an ideal-gas model in the limit of strong shock and high density ratio across the shock front. In one dimension the result reduces properly to the snowplow equation. In two dimensions, if the surface is constrained and the motion steady, the result consists of the ``Newtonian plus Busemann'' terms. The general result contains in addition a Coriolis term. The general theory is applied to the evaluation of the pressure on the surface of a conical plasma whose vertex angle is decreasing uniformly with time. Although the results are derived for an ideal-gas model, they are applicable whenever dissociation and ionization are taking place behind a strong shock front.