Eigenvalue Solution Algorithm
S. P. Lin · 2003
For purely temporal disturbances k is real, and if it is given together with the complete set of the flow parameters, then we can solve the complex wave frequency ω from (10.26) as the eigenvalue. The IMSL library routine GVLCG has been used to obtain ω. We characterize the spatial-temporal disturbances of a given wave number k r for a given set of flowparameters with the spatial amplification curves ω r = 0. There are at least two such curves for a given set of flow parameters in the case of convective instability. One corresponds to the sinuous mode and the other to the varicose mode. For each mode, we start with an initial guess of k i for a given k r . Then solve for ω r and ω i using the IMSL routine GVCCG. If ω r = 0 the guess was perfect, if not we find k i by using the Newton integration method with a reduced value of ∣ω r ∣. With the new k i and the original k r we update (ω r , ω i ) by means of the IMSL routine GVCCG. We repeat this procedure until the IMSL routine gives ω r = 0.