The dynamics of small-amplitude perturbations, as well as the regime of fully
developed nonlinear propagating waves, is investigated for pulsatile channel flows.
The time-periodic base flows are known analytically and completely determined by
the Reynolds number Re (based on the mean flow rate), the Womersley number Wo
(a dimensionless expression of the frequency) and the flow-rate waveform. This paper
considers pulsatile flows with a single oscillating component and hence only three
non-dimensional control parameters are present. Linear stability characteristics are
obtained both by Floquet analyses and by linearized direct numerical simulations.
In particular, the long-term growth or decay rates and the intracyclic modulation
amplitudes are systematically computed. At large frequencies (mainly Wo > 14),
increasing the amplitude of the oscillating component is found to have a stabilizing
effect, while it is destabilizing at lower frequencies; strongest destabilization is found
for Wo ' 7. Whether stable or unstable, perturbations may undergo large-amplitude
intracyclic modulations; these intracyclic modulation amplitudes reach huge values
at low pulsation frequencies. For linearly unstable configurations, the resulting
saturated fully developed finite-amplitude solutions are computed by direct numerical
simulations of the complete Navier–Stokes equations. Essentially two types of
nonlinear dynamics have been identified: ‘cruising’ regimes for which nonlinearities
are sustained throughout the entire pulsation cycle and which may be interpreted as
modulated Tollmien–Schlichting waves, and ‘ballistic’ regimes that are propelled into
a nonlinear phase before subsiding again to small amplitudes within every pulsation
cycle. Cruising regimes are found to prevail for weak base-flow pulsation amplitudes,
while ballistic regimes are selected at larger pulsation amplitudes; at larger pulsation
frequencies, however, the ballistic regime may be bypassed due to the stabilizing
effect of the base-flow pulsating component. By investigating extended regions of
a multi-dimensional parameter space and considering both two-dimensional and
three-dimensional perturbations, the linear and nonlinear dynamics are systematically
explored and characterized.