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In this study we analyze the phase and group velocity of three-dimensionallinear traveling waves in two sheared flows, the plane channel and the wakeflows. This was carried out by varying the wave number over a large interval ofvalues at a given Reynolds number inside the ranges 20-100, 1000-8000, for thewake and channel flow, respectively. Evidence is given about the possiblepresence of both dispersive and non-dispersive effects which are associatedwith the long and short ranges of wavelength. We solved the Orr-Sommerfeld andSquire eigenvalue problem and observed the least stable mode. It is evidentthat, at low wave numbers, the least stable eigenmodes in the left branch ofthe spectrum beave in a dispersive manner. By contrast, if the wavenumber isabove a specific threshold, a sharp dispersive to non-dispersive transition canbe observed. Beyond this transition, the dominant mode belongs to the rightbranch of the spectrum. The transient behavior of the phase velocity of smallthree-dimensional traveling waves was also considered. Having chosen theinitial conditions, we then show that the shape of the transient highly dependson the transition wavelength threshold value. We show that the phase veloctycan oscillate with a frequency which is equal to the frequency width of theeigenvalue spectrum. Furthermore, evidence of intermediate self-similarity isgiven for the perturbation field.

Dispersive to non-dispersive transition and phase velocity transient for linear waves in plane wake and channel flows