Simulations of decaying compressible turbulent flows have been performed using the PPM algorithm on grids of 5123 and 10243 computational cells. Although the run on the finer grid has not yet been carried out to a time large enough for the spectra to relax fully, it adds significantly to the results on the coarser grid by lengthening the range of wave numbers in which the flow exhibits a self-similar character. There is an inertial range of scales in the decaying flow on the finer mesh that is free from direct effects of dissipation, forcing, boundary conditions, or initial conditions. Favre averaging of the high resolution data is performed on different scales from which the vorticity structures in the inertial range may be visualized and characterized without confusion from the smaller-scale features of the near dissipation range. We find that the vorticity structures of the inertial range are filamentary as well, but qualitatively different - shorter and more curved - than those of the dissipation range. Quantitative evidence of the action of vortex stretching in developed turbulence is also presented.