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Published online by Cambridge University Press: 02 December 2009
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 kr for a given set of flowparameters with the spatial amplification curves ωr = 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 ki for a given kr. Then solve for ωr and ωi using the IMSL routine GVCCG. If ωr = 0 the guess was perfect, if not we find ki by using the Newton integration method with a reduced value of ∣ωr∣. With the new ki and the original kr we update (ωr, ωi) by means of the IMSL routine GVCCG. We repeat this procedure until the IMSL routine gives ωr = 0.
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