ABSTRACT
Previous to the application of the substitution principle, exact rotational solutions of the Euler equations were rare (or nonexistent). Such solutions are therefore of intrinsic interest, particularly when they are simple and represent extensions of well-known irrotational flows. These solutions are obtained by means of the substitution principle, which holds for the three-dimensional, steady Euler equations with no body force and where the gas is perfect. Moreover, the flow field may be subsonic, transonic, or supersonic and may contain shock waves, contact surfaces, and slipstreams. In brief, the principle enables us to transform an irrotational, homenergetic, and homentropic flow field into one that is rotational, nonhomenergetic, and nonhomentropic. Both flows are exact solutions of the steady Euler equations. Generating rotational flows from irrotational flows is but one use of the principle. A number of homework problems illustrate alternate applications.
