Accounting for transverse flow in the theory of geometrical shock dynamics

Source abstract

Abstract The theory of geometrical shock dynamics is deduced as a formal approximation to the equations of gas dynamics in two dimensions, thus overcoming the approximation of quasi-one-dimensional flow utilized in the original derivation. Successive approximations may be obtained by using the truncation scheme developed by Best (1991) for considering shock propagation down a tube of slowly varying cross section. The zero-order approximation yields the theory as developed by Whitham (1957). The first-order approximation includes a term which is additional to those appearing in the equations derived by Best (1991). The characteristic speeds for disturbances propagating on the shock are computed and a hierarchical wave structure is evident. In view of this structure, comment is made upon the problem of blast diffraction by a convex corner.