Empirical analysis of regional growth functions of turbulent waxes

theoretical results in Table 2. These comparisons serve to provide confidence in the validity of the solution. The results obtained using the method presented in this paper are almost identical to the results obtained by Smith. The results shown in Table 2 for the approximate solution were obtained by imposing, on Eq. (2), the condition that (X*/ra) « 1. The exact solutions are shown to be superior to the approximate solutions, especially for those modes having a small number of circumferential waves. Frequencies, for the first four radial modes having one to five circumferential waves, of a particular shell, subjected to the eight sets of boundary conditions of Table 1, are presented in Table 3. The advantages of the "exact" solution presented here over those seen previously are: 1) the arbitrary complex constants in the assumed solution need not be redefined as real constants, and 2) the form of the roots of the auxiliary equation need not be monitored during the solution. These advantages yield a saving of computational time and lead to a more truly "general" solution.