Simultaneous Eulerian-Lagrangian velocity measurements of particulate pipe flow in transitional regime.

We present a unique pipe flow rig capable of simultaneous particle tracking and flow velocity measurements in a dilute, neutrally buoyant particulate pipe flow in regimes of transition to turbulence. The flow consists of solid glass spheres for the disperse phase and a density-matching fluid for the carrier phase. The measurements are conducted using a bespoke, combined two-dimensional particle image velocimetry and particle tracking velocimetry technique. The technique takes advantage of a phase discrimination approach that involves separating the disperse and carrier phases based on their respective image characteristics. Our results show that the rig and the technique it implements can effectively be employed to study transitional particulate pipe flows at dilute concentrations.

Bounds on the attractor dimension for magnetohydrodynamic channel flow with parallel magnetic field at low magnetic Reynolds number.

We investigate aspects of low-magnetic-Reynolds-number flow between two parallel, perfectly insulating walls in the presence of an imposed magnetic field parallel to the bounding walls. We find a functional basis to describe the flow, well adapted to the problem of finding the attractor dimension and which is also used in subsequent direct numerical simulation of these flows. For given Reynolds and Hartmann numbers, we obtain an upper bound for the dimension of the attractor by means of known bounds on the nonlinear inertial term and this functional basis for the flow. Three distinct flow regimes emerge: a quasi-isotropic three-dimensional (3D) flow, a nonisotropic 3D flow, and a 2D flow. We find the transition curves between these regimes in the space parametrized by Hartmann number Ha and attractor dimension d(att). We find how the attractor dimension scales as a function of Reynolds and Hartmann numbers (Re and Ha) in each regime. We also investigate the thickness of the boundary layer along the bounding wall and find that in all regimes this scales as 1/Re, independently of the value of Ha, unlike Hartmann boundary layers found when the field is normal to the channel. The structure of the set of least dissipative modes is indeed quite different between these two cases but the properties of turbulence far from the walls (smallest scales and number of degrees of freedom) are found to be very similar.

Direct and inverse pumping in flows with homogeneous and non-homogeneous swirl.

The conditions in which meridional recirculations appear in swirling flows above a fixed wall are analysed. In the classical Bodewädt problem, where the swirl tends towards an asymptotic value away from the wall, the well-known "tea-cup effect" drives a flow away from the plate at the centre of the vortex. Simple dimensional arguments applied to a single vortex show that if the intensity of the swirl decreases away from the wall, the sense of the recirculation can be inverted, and that the associated flow rate scales with the swirl gradient. If the flow is quasi-2D, the classical tea-cup effect takes place. This basic theory is confirmed by numerical simulations of a square array of steady, electrically driven vortices. Experiments in the turbulent regimes of the same configuration reveal that these mechanisms are active in the average flow and in its fluctuating part. These mechanisms provide an explanation for previously observed phenomena in electrolyte flows. They also put forward a possible mechanism for the generation of helicity in flows close to two-dimensionality, which plays a key role in the transition between 2D and 3D turbulence.

Appearance of three dimensionality in wall-bounded MHD flows.

We characterize experimentally how three dimensionality appears in wall-bounded magnetohydrodynamic flows. Our analysis of the breakdown of a square array of vortices in a cubic container singles out two mechanisms: first, a form of three dimensionality we call weak appears through differential rotation in individual 2D vortices. Second, strong three dimensionality characterized by vortex disruption leads on the one hand to a remarkable vortex array that is both steady and 3D, and, on the other hand, to scale-selective breakdown of two dimensionality in chaotic flows. Most importantly, these phenomena are entirely driven by inertia, so they are relevant to other flows with a tendency to two dimensionality, such as rotating, or stratified flows in geophysics and astrophysics.

Experiment on a confined electrically driven vortex pair.

An experimental study of the transition to turbulence in a confined quasi-two-dimensional magnetohydrodynamic flow is presented. A pair of counterrotating vortice is electrically driven in the center of a thin horizontal liquid metal layer, enclosed in a cylindrical container and subject to a homogeneous vertical magnetic field. When the forcing is increased, the pair is displaced away from the center. Boundary layer separations from the circular wall appear that trigger a sequence of supercritical bifurcations. These are singled out in numerical calculations based on our previously developed shallow water model as well as in the experiment, and these bifurcations are shown to resemble those observed in flows past a cylindrical obstacle. For the highest forcing, the flow then ends up in a turbulent regime where the dissipation increases drastically, which we could relate to a possible transition from a laminar to a turbulent Hartmann boundary layer. Finally we show the first experimental evidence of a transition to three-dimensionality in liquid metal magnetohydrodynamics (MHD) by comparing velocity measurements on either horizontal sides of the layer as we find that columnar vortice wobble for a high enough forcing.