Spatiotemporal Intermittency in Pulsatile Pipe Flow

Despite its importance in cardiovascular diseases and engineering applications, turbulence in pulsatile pipe flow remains little comprehended. Important advances have been made in the recent years in understanding the transition to turbulence in such flows, but the question remains of how turbulence behaves once triggered. In this paper, we explore the spatiotemporal intermittency of turbulence in pulsatile pipe flows at fixed Reynolds and Womersley numbers (Re=2400, Wo=8) and different pulsation amplitudes. Direct numerical simulations (DNS) were performed according to two strategies. First, we performed DNS starting from a statistically steady pipe flow. Second, we performed DNS starting from the laminar Sexl–Womersley flow and disturbed with the optimal helical perturbation according to a non-modal stability analysis. Our results show that the optimal perturbation is unable to sustain turbulence after the first pulsation period. Spatiotemporally intermittent turbulence only survives for multiple periods if puffs are triggered. We find that puffs in pulsatile pipe flow do not only take advantage of the self-sustaining lift-up mechanism, but also of the intermittent stability of the mean velocity profile.

Patterns, Bifurcations, Multistability and Hysteresis in an Inhomogeneous Coupled Map Lattice

We investigate local interaction between logistic maps in an inhomogeneous lattice numerically with respect to an inhomogeneity parameter [Formula: see text] and the coupling constant [Formula: see text]. In our model, the inhomogeneity appears in the form of different values of the map parameter at different sites. The phase diagram of the model in the [Formula: see text]–[Formula: see text] plane gives seven qualitatively different patterns. These are: synchronized patterns, steady (fixed in time) patterns with spatial period-two, spatially chaotic together with temporally periodic patterns, spatially coherent accompanied with temporally quasi-periodic patterns, spatial intermittency with temporal period-two patterns, spatiotemporal intermittency patterns or spatiotemporal chaotic patterns. Our system exhibits, tangent bifurcations in the transition from synchronized patterns to steady patterns, period-doubling bifurcation from steady patterns to temporal periodic patterns and Neimark–Sacker (Hopf) bifurcation from steady patterns to temporal quasi-periodic patterns. The system also shows the possibility of multistable attractors and the phenomena of hysteresis for some parameter values. We identify our results using techniques such as time series, space-time plot, Fourier transform, bifurcation diagram, stability analysis.