Exact Simple Waves on Shear Flows in a Compressible Barotropic Medium

Self-similar solutions describing simple waves on shear flows in a finite compressible barotropic atmosphere are found. These include the simple waves on shear flows in water as a special case. By making use of a number of transformations it becomes possible to write these solutions in an exact form. This form, though not explicit, is similar to the incomplete Beta function which seems to characterize this class of nonlinear physical problems.