Phase Transition to Turbulence in Spatially Extended Shear Flows.

Directed percolation (DP) has recently emerged as a possible solution to the century old puzzle surrounding the transition to turbulence. Multiple model studies reported DP exponents, however, experimental evidence is limited since the largest possible observation times are orders of magnitude shorter than the flows' characteristic timescales. An exception is cylindrical Couette flow where the limit is not temporal, but rather the realizable system size. We present experiments in a Couette setup of unprecedented azimuthal and axial aspect ratios. Approaching the critical point to within less than 0.1% we determine five critical exponents, all of which are in excellent agreement with the 2+1D DP universality class. The complex dynamics encountered at the onset of turbulence can hence be fully rationalized within the framework of statistical mechanics.

The influence of invariant solutions on the transient behaviour of an air bubble in a Hele-Shaw channel.

We hypothesize that dynamical systems concepts used to study the transition to turbulence in shear flows are applicable to other transition phenomena in fluid mechanics. In this paper, we consider a finite air bubble that propagates within a Hele-Shaw channel containing a depth-perturbation. Recent experiments revealed that the bubble shape becomes more complex, quantified by an increasing number of transient bubble tips, with increasing flow rate. Eventually, the bubble changes topology, breaking into multiple distinct entities with non-trivial dynamics. We demonstrate that qualitatively similar behaviour to the experiments is exhibited by a previously established, depth-averaged mathematical model and arises from the model's intricate solution structure. For the bubble volumes studied, a stable asymmetric bubble exists for all flow rates of interest, while a second stable solution branch develops above a critical flow rate and transitions between symmetric and asymmetric shapes. The region of bistability is bounded by two Hopf bifurcations on the second branch. By developing a method for a numerical weakly nonlinear stability analysis we show that unstable periodic orbits (UPOs) emanate from the first Hopf bifurcation. Moreover, as has been found in shear flows, the UPOs are edge states that influence the transient behaviour of the system.

The rise of fully turbulent flow.

Over a century of research into the origin of turbulence in wall-bounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow. At moderate flow speeds, turbulence is confined to localized patches; it is only at higher speeds that the entire flow becomes turbulent. The origin of the different states encountered during this transition, the front dynamics of the turbulent regions and the transformation to full turbulence have yet to be explained. By combining experiments, theory and computer simulations, here we uncover a bifurcation scenario that explains the transformation to fully turbulent pipe flow and describe the front dynamics of the different states encountered in the process. Key to resolving this problem is the interpretation of the flow as a bistable system with nonlinear propagation (advection) of turbulent fronts. These findings bridge the gap between our understanding of the onset of turbulence and fully turbulent flows.

Turbulent spots in channel flow: an experimental study: large-scale flow, inner structure and low-order model.

We present new experimental results on the development of turbulent spots in channel flow. The internal structure of a turbulent spot is measured, with Time Resolved Stereoscopic Particle Image Velocimetry. We report the observation of travelling-wave-like structures at the trailing edge of the turbulent spot. Special attention is paid to the large-scale flow surrounding the spot. We show that this large-scale flow is an asymmetric quadrupole centred on the spot. We measure the time evolution of the turbulent fluctuations and the mean flow distortions and compare these with the predictions of a nonlinear reduced order model predicting the main features of subcritical transition to turbulence.

Experimental scaling law for the subcritical transition to turbulence in plane Poiseuille flow.

We present an experimental study of the transition to turbulence in a plane Poiseuille flow. Using a well-controlled perturbation, we analyze the flow by using extensive particle image velocimetry and flow visualization (using laser-induced fluorescence) measurements, and use the deformation of the mean velocity profile as a criterion to characterize the state of the flow. From a large parametric study, four different states are defined, depending on the values of the Reynolds number and the amplitude of the perturbation. We discuss the role of coherent structures, such as hairpin vortices, in the transition. We find that the minimal amplitude of the perturbation triggering transition scales asymptotically as Re(-1).