Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics







753Huxley BuildingSouth Kensington Campus






BibTex format

author = {Pier, B and Schmid, PJ},
doi = {10.1017/jfm.2017.58},
journal = {Journal of Fluid Mechanics},
pages = {435--480},
title = {Linear and nonlinear dynamics of pulsatile channel flow},
url = {},
volume = {815},
year = {2017}

RIS format (EndNote, RefMan)

AB - The dynamics of small-amplitude perturbations, as well as the regime of fullydeveloped nonlinear propagating waves, is investigated for pulsatile channel flows.The time-periodic base flows are known analytically and completely determined bythe 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 paperconsiders pulsatile flows with a single oscillating component and hence only threenon-dimensional control parameters are present. Linear stability characteristics areobtained both by Floquet analyses and by linearized direct numerical simulations.In particular, the long-term growth or decay rates and the intracyclic modulationamplitudes are systematically computed. At large frequencies (mainly Wo > 14),increasing the amplitude of the oscillating component is found to have a stabilizingeffect, while it is destabilizing at lower frequencies; strongest destabilization is foundfor Wo ' 7. Whether stable or unstable, perturbations may undergo large-amplitudeintracyclic modulations; these intracyclic modulation amplitudes reach huge valuesat low pulsation frequencies. For linearly unstable configurations, the resultingsaturated fully developed finite-amplitude solutions are computed by direct numericalsimulations of the complete Navier–Stokes equations. Essentially two types ofnonlinear dynamics have been identified: ‘cruising’ regimes for which nonlinearitiesare sustained throughout the entire pulsation cycle and which may be interpreted asmodulated Tollmien–Schlichting waves, and ‘ballistic’ regimes that are propelled intoa nonlinear phase before subsiding again to small amplitudes within every pulsationcycle. Cruising regimes are found to prevail for weak base-flow pulsation amplitudes,while ballistic regimes are selected at larger pulsation amplitudes; at larger pulsationfrequencies, however, the ballistic regime may be bypassed due to
AU - Pier,B
AU - Schmid,PJ
DO - 10.1017/jfm.2017.58
EP - 480
PY - 2017///
SN - 0022-1120
SP - 435
TI - Linear and nonlinear dynamics of pulsatile channel flow
T2 - Journal of Fluid Mechanics
UR -
UR -
UR -
VL - 815
ER -