  Sheared incompressible flows are usually considered non-dispersive media. As
a consequence, the frequency evolution in transients has received much less
attention than the wave energy density or growth factor. By carrying out a
large number of long term transient simulations for longitudinal, oblique and
orthogonal perturbations in the plane channel and wake flows, we could observe
a complex time evolution of the frequency. The complexity is mainly associated
to jumps which appear quite far along within the transients. We interpret these
jumps as the transition between the early transient and the beginning of an
intermediate term that reveals itself for times large enough for the influence
of the fine details of the initial condition to disappear. The intermediate
term leads to the asymptotic exponential state and has a duration one order of
magnitude longer than the early term, which indicates the existence of an
intermediate asymptotics. Since after the intermediate term perturbations die
out or blowup, the mid-term can be considered as the most probable state in the
perturbation life. Long structured transients can be related to the spot
patterns commonly observed in subcritical transitional wall flows. By
considering a large group of 3D waves in a narrow range of wavenumbers, we
superposed them in a finite temporal window with oblique and longitudinal waves
randomly delayed with respect to an orthogonal wave which is supposed to
sustain the spot formation with its intense transient growth. We show that in
this way it is possible to recover the linear initial evolution of the pattern
characterized by the presence of longitudinal streaks. We also determined the
asymptotic frequency and phase speed wavenumber spectra for the channel and
wake flows. The mild dispersion observed can in part explain the different
propagation speeds of the backward and forward fronts of the spot.
