摘要：

An investigation of the accuracy of a numerical model for the development of three-dimensional localized disturbances in unstable flows is presented. A dispersion relation is defined for the linear evolution of the disturbances, with a simplification that saddle points can be determined algebraically. Closed-form approximate solutions are deduced for a wave-packet and are shown to be free from scaling assumptions. Comparisons are made with exact solutions obtained by eigenvalues computed by plane Poiseuille flow, revealing accuracy in growth rate approximations and an 11% error in the frequency of the most unstable mode. Methods for improving the values for the eigenvalues are introduced and an acceptable accuracy is achieved. Further consideration is given to the possibility that the unstable mode splits into two regions of maximum amplitude.

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