The interpenetration of light and heavy liquids has been studied in a long tube inclined at small angles ␣ to the horizontal. For angles greater than a critical angle ␣ c ͑whose value decreases when the density contrast measured by the Atwood number At increases͒, the velocity of the interpenetration front is controlled by inertia and takes the steady value V f = k i ͑At gd͒ 1/2 , with k i Ӎ 0.7. At lower angles, the front is initially controlled by inertia, but later limited by viscous effects. The transition occurs at a distance X fc , which increases indefinitely as ␣ increases to ␣ c. Once the viscous effects act, the velocity of the front decreases in time to a steady value V f ϱ which is proportional to sin ␣. For a horizontal tube in the viscous regime, the velocity of the front decreases to zero as t −1/2. At the same time, the profile of the interface h͑x , t͒ only depends on the reduced variable x / t 1/2. A quasi-unidirectional model reproduces well the variation of the velocity of the front and the profiles of the interface, both in inclined and horizontal tubes. In the inclined tube, the velocity of the front is determined by matching rarefaction waves to a shock wave.

Buoyancy-driven turbulent mixing of fluids of slightly different densities [At=Δρ/(2⟨ρ⟩)=1.15×10−2] in a long circular tube tilted at an angle θ=15° from the vertical is studied at the local scale, both experimentally from particle image velocimetry and laser induced fluorescence measurements in the vertical diametrical plane and numerically throughout the tube using direct numerical simulation. In a given cross section of the tube, the axial mean velocity and the mean concentration both vary linearly with the crosswise distance z from the tube axis in the central 70% of the diameter. A small crosswise velocity component is detected in the measurement plane and is found to result from a four-cell mean secondary flow associated with a nonzero streamwise component of the vorticity. In the central region of the tube cross section, the intensities of the three turbulent velocity fluctuations are found to be strongly different, that of the streamwise fluctuation being more than twice larger than that of the spanwise fluctuation which itself is about 50% larger than that of the crosswise fluctuation. This marked anisotropy indicates that the turbulent structure is close to that observed in homogeneous turbulent shear flows. Still in the central region, the turbulent shear stress dominates over the viscous stress and reaches a maximum on the tube axis. Its crosswise variation is approximately accounted for by a mixing length whose value is about one-tenth of the tube diameter. The momentum exchange in the core of the cross section takes place between its lower and higher density parts and there is no net momentum exchange between the core and the near-wall regions. A sizable part of this transfer is due both to the mean secondary flow and to the spanwise turbulent shear stress. Near-wall regions located beyond the location of the extrema of the axial velocity (|z|≳0.36 d) are dominated by viscous stresses which transfer momentum toward (from) the wall near the top (bottom) of the tube.

The buoyancy driven interpenetration of two fluids of different densities has been studied in a long tilted tube in the strong mixing regime for which the mean concentration profile along the tube length satisfies a macroscopic diffusion equation. Variations of the corresponding macroscopic diffusion coefficient D and of the front velocity V f are studied as a function of the Atwood number At, the viscosity , the tube diameter d, and the tilt angle . Introducing the characteristic inertial velocity V t and the Reynolds number Re t , the normalized front velocity V f / V t and dispersion coefficient D / ͑V t d͒ are observed to scale, respectively, as Re t −3/4 and Re t −3/2 for Re t Շ 1000. Also, V f increases linearly with tan and the ratio ͑D / V f 2 ͒ remains of the order of ͑35± 10͒d / V t in a wide range of values of the tilt angle and of the other control parameters. This close relation observed between the variations of D and V f 2 is discussed in terms of the characteristic time for transverse mixing across the flow channel.

Buoyancy driven mixing of fluids of different densities ͑ 1 and 2 ͒ in a long circular tube is studied experimentally at the local scale as a function of the tilt angle from vertical ͑15°Յ Յ 60°͒ and of the Atwood number ͓10 −3 Յ At= ͑ 2 − 1 ͒ / ͑ 2 + 1 ͒ Յ 10 −2 ͔. Particle Image Velocimetry ͑PIV͒ and Laser Induced Fluorescence ͑LIF͒ measurements in a vertical diametral plane provide the velocity and the relative concentration ͑and, hence, density͒ fields. A map of the different flow regimes observed as a function of At and has been determined: as At increases and is reduced, the regime varies from laminar to intermittent destabilizations and, finally, to developed turbulence. In the laminar regime, three parallel stable layers of different densities are observed; the velocity profile is linear and well predicted from the density profile. The thickness of the intermediate layer can be estimated from the values of At and . In the turbulent regime, the density varies slowly with z in the core of the flow: there, transverse turbulent momentum transfer is dominant. As At decreases and increases, the density gradient ␤ in the core ͑and, hence, the buoyancy forces͒ becomes larger, resulting in higher extremal velocities and indicating a less efficient mixing. While the mean concentration varies with time in the turbulent regime, the mean velocity remains constant. In the strong turbulent regime ͑highest At and lowest values͒, the transverse gradient of the mean concentration and the fluctuations of concentration and velocity remain stationary, whereas they gradually decay with time when turbulence is weaker.

This study employs three-dimensional particle-tracking velocimetry (3D-PTV) for experimental investigation of the existence and properties of periodic lines in 3D lid-driven time-periodic flows inside a cylindrical cavity. These periodic lines, consisting of material points that periodically return to their initial position, play a central role in the transport properties of laminar flows, yet their existence has so far been demonstrated only in numerical simulations. The formation and characteristics of periodic lines are inextricably linked with spatiotemporal symmetries of the flow. 3D-PTV measurements determined that relevant symmetries, identified with previous symmetry analyses, are satisfied within experimental error bounds. These measurements subsequently isolated periodic lines in the designated symmetry planes, thus offering first experimental evidence of their physical existence and their fundamental reliance on symmetries. Experimental periodic lines are topologically equivalent to those in simulated flows with identical symmetries and exhibit the same response to changes in forcing conditions. The laboratory experiments by these observations bridge the gap from theoretical and numerical predictions on periodic lines to real 3D flows.

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