Thomas Bonometti

Transition from spherical cap to toroidal bubbles

Large gas bubbles rising under the effect of buoyancy are known to adopt either a spherical cap shape or to undergo a topological transition after which they become toroidal. We carry out an axisymmetric numerical investigation of the evolution of such large bubbles in the presence of both capillary and viscous effects. The numerical approach is of the volume of fluid type (it solves the Navier-Stokes equations on a fixed grid and transports the local volume fraction of one of the fluids), but does not involve any explicit reconstruction of the interface. The transition from spherical cap to toroidal bubbles is studied in the parameter space built on the Bond (Bo) and Archimedes (Ar) numbers, which compare the strength of inertial effects to that of capillary and viscous effects, respectively. Preliminary tests show that the position of this transition is very sensitive to the grid resolution; these tests are used to select grid characteristics that yield grid-independent results. Two markedly different transition scenarios, corresponding to the limit of large Ar and large Bo, respectively, are then identified. In the first case, the front of the bubble is pierced by an upward jet coming from the rear of the bubble. In contrast, in the limit of large Bo, a downward jet develops at the front part and pierces the rear of the bubble, unless viscous effects are sufficient to stabilize the front. We also determine the position of the transition for intermediate values of Bo and Ar and discuss the connection between present axisymmetric results and experimental situations in which the bubble is followed by a turbulent wake. We finally examine a puzzling feature of these large bubbles which is that, given an initial gas volume, the final bubble topology appears to depend dramatically on the initial conditions. Indeed, we find that initially oblate bubbles may result in stable spherical cap bubbles for values of Bo and Ar well beyond those for which initially spherical bubbles of similar volume undergo the topological transition. This remarkable influence of the initial shape is shown to be due to the influence of the oblateness on both the bubble acceleration and the hydrostatic pressure difference between the two bubble poles.

Wall effects in non-Boussinesq density currents

We report on the results of a numerical study of nearly immiscible contrasted density currents aimed at shedding light on the influence of wall effects on current dynamics in the lock-exchange configuration. The numerical approach is an interface-capturing method which does not involve any explicit reconstruction of the interface. Navier-Stokes equations are solved on a fixed grid and a hyperbolic equation is used for the transport of the local volume fraction of one of the fluids. This allows us to describe the density currents for the complete range of density contrast 10⁻³ ≤ρL/ρH≤ 0.99 (ρL and ρH being the density of the light and heavy fluids) and a wide range of Reynolds number 70 ≤Re≤ 5×10⁴ (based on the channel height and the viscosity of the heavy fluid). The use of free-slip vs. no-slip boundary conditions enables us to separate the dissipation at the interface from the dissipation at the boundaries. Present results reveal that wall effects play a significant role on the propagation of contrasted density currents, unlike dissipation at the interface. It is first shown that when wall friction can be neglected, theoretical models based on the inviscid shallowwater approximations and Benjamins steady-state result describe fairly well the light and heavy front velocities of density currents for the complete range of density ratio. However, when wall friction cannot be neglected, the results depart significantly from the prediction of inviscid theories. It is observed that most of the dissipation in highly contrasted currents takes place at the bottom wall and is a maximum at the head of the heavy current. This dissipation is shown to be responsible for the decrease of the front velocity. We propose a simple model based on Benjamins analysis that includes wall friction. Keeping in mind the simplicity and limitations of the present model, the prediction of the front velocity of the heavy and light currents is observed to be in good agreement with the numerical results for the complete range of density contrast. This gives further support to the idea that wall effects are the crucial ingredient for accurately predicting the front velocity of highly contrasted density currents.

A numerical investigation of high-Reynolds-number constant-volume non-Boussinesq density currents in deep ambient

The time-dependent behaviour of non-Boussinesq high-Reynolds-number density currents, released from a lock of height h0 and length x0 into a deep ambient and spreading over horizontal flat boundaries, is considered. We use two-dimensional Navier–Stokes simulations to cover: (i) a wide range of current-to-ambient density ratios, (ii) a range of length-to-height aspect ratios of the initial release within the lock (termed the lock aspect ratio λ=x0/h0) and (iii) the different phases of spreading, from the initial acceleration phase to the self-similar regimes. The Navier–Stokes results are compared with predictions of a one-layer shallow-water model. In particular, we derive novel insights on the influence of the lock aspect ratio (λ) on the shape and motion of the current. It is shown that for lock aspect ratios below a critical value (λcrit ), the dynamics of the current is significantly influenced by λ. We conjecture that λcrit depends on two characteristic time scales, namely the time it takes for the receding perturbation created at the lock upon release to reflect back to the front, and the time of formation of the current head. A comparison of the two with space–time diagrams obtained from the Navier–Stokes simulations supports this conjecture. The non-Boussinesq effect is observed to be significant. While the critical lock aspect ratio (λcrit ) is of order 1 for Boussinesq currents, its value decreases for heavy currents and increases significantly (up to about 20) for light currents. We present a simple analytical model which captures this trend, as well as the observation that for a light current the speed of propagation is proportional to λ1/4 when λ

Kelvin–Helmholtz instability in the presence of variable viscosity for mudflow resuspension in estuaries

The temporal stability of a parallel shear flow of miscible fluid layers of different density and viscosity is investigated through a linear stability analysis and direct numerical simulations. The geometry and rheology of this Newtonian fluid mixing can be viewed as a simplified model of the behavior of mudflow at the bottom of estuaries for suspension studies. In this study, focus is on the stability and transition to turbulence of an initially laminar configuration. A parametric analysis is performed by varying the values of three control parameters, namely the viscosity ratio, the Richardson and Reynolds numbers, in the case of initially identical thickness of the velocity, density and viscosity profiles. The range of parameters has been chosen so as to mimic a wide variety of real configurations. This study shows that the Kelvin–Helmholtz instability is controlled by the local Reynolds and Richardson numbers of the inflection point. In addition, at moderate Reynolds number, viscosity stratification has a strong influence on the onset of instability, the latter being enhanced at high viscosity ratio, while at high Reynolds number, the influence is less pronounced. In all cases, we show that the thickness of the mixing layer (and thus resuspension) is increased by high viscosity stratification, in particular during the non-linear development of the instability and especially pairing processes. This study suggests that mud viscosity has to be taken into account for resuspension parameterizations because of its impact on the inflection point Reynolds number and the viscosity ratio, which are key parameters for shear instabilities.

Propagation and deposition of non-circular finite release particle-laden currents

The dynamics of non-axisymmetric turbidity currents is considered here for a range of Reynolds numbers of O(10^4) when based on the initial height of the release. The study comprises a series of experiments and highly resolved simulations for which a finite volume of particle-laden solution is released into fresh water. A mixture of water and polystyrene particles of mean diameter dp=300 μm and mixture density ρc=1012 kg/m^3 is initially confined in a hollow cylinder at the centre of a large tank filled with fresh water. Cylinders with two different cross-sectional shapes, but equal cross-sectional areas, are examined: a circle and a rounded rectangle in which the sharp corners are smoothened. The time evolution of the front is recorded as well as the spatial distribution of the thickness of the final deposit via the use of a laser triangulation technique. The dynamics of the front and final deposit are significantly influenced by the initial geometry, displaying substantial azimuthal variation especially for the rectangular case where the current extends farther and deposits more particles along the initial minor axis of the rectangular cross-section. Several parameters are varied to assess the dependence on the settling velocity, initial height aspect ratio and volume fraction. Even though resuspension is not taken into account in our simulations, good agreement with experiments indicates that it does not play an important role in the front dynamics, in terms of velocity and extent of the current. However, wall shear stress measurements show that incipient motion of particles and particle transport along the bed are likely to occur in the body of the current and should be accounted to properly capture the final deposition profile of particles.

Simulation of an Avalanche in a Fluid with a Soft-sphere/Immersed Boundary Method Including a Lubrication Force

The present work aims at reproducing the local dynamics of a dense granular media evolving in a viscous fluid from the grain scale to that of thousands of grains, encountered in environmental multiphase flows. To this end a soft-sphere collision/immersed-boundary method is developed. The methods are validated alone through various standard configurations including static and dynamical situations. Then, simulations of binary wall-particle collisions in a fluid are performed for a wide range of Stokes number ranging in [10-1, 104]. Good agreement with available experimental data is found provided that a local lubrication model is used. Finally, three- dimensional simulations of gravity/shear-driven dense granular flows in a viscous fluid are presented. The results open the way for a parametric study in the parameter space initial aspect ratio-initial packing.

Numerical Modeling of a Granular Collapse Immersed in a Viscous Fluid

Numerical simulations can help to further understand particles-fluid flows which are encountered in many industrial and natural applications. An immersed boundary and a soft-sphere discrete element methods are coupled to resolve the fluid flow around moving non-deformable particles and to solve the Lagrangian motion of the particles, including grain–grain interactions, respectively. A lubrication force is added to the equation of the grains motion to properly capture rebound interactions in a fluid. An a priori simple configuration of gravity-driven grains-fluid mixture flows, namely, the unsteady collapse of a granular column in an incompressible Newtonian fluid, is investigated by three-dimensional simulations. The scale of the system is \({\mathcal{O}}\left( {10^{3} } \right)\) particles. In the present simulations, the collapse dynamics is controlled by the viscous time in agreement with the experimental classification of granular regimes in a fluid proposed by du Pont et al. Phys. Rev. Lett. 90, 044301 (2003). Good agreement is found with experiments of Rondon et al. Phys. Fluids, 23(7), 073301 (2011) regarding the final form of the granular deposit, which may be triangular or trapezoidal depending on aspect ratio and initial packing fraction. In addition, the fluid pressure at the bottom of the granular column, as well as the lengths of the granular deposits, measured in present simulations are in quantitative agreement with experiments. The phenomenon of pore pressure feedback is captured for the first time in simulation results.

Turbulent structures in cylindrical density currents in a rotating frame of reference

ABSTRACT Gravity currents are flows generated by the action of gravity on fluids with different densities. In some geophysical applications, modeling such flows makes it necessary to account for rotating effects, modifying the dynamics of the flow. While previous works on rotating stratified flows focused on currents of large Coriolis number, the present work focuses on flows with small Coriolis numbers (i.e. moderate-to-large Rossby numbers). In this work, cylindrical rotating gravity currents are investigated by means of highly resolved simulations. A brief analysis of the mean flow evolution to the final state is presented to provide a complete picture of the flow dynamics. The numerical results, showing the well-known oscillatory behavior of the flow (inertial waves) and a final state lens shape (geostrophic adjustment), are in good agreement with experimental observations and theoretical models. The turbulent structures in the flow are visualized and described using, among others, a stereoscopic visualization and videos as supplementary material. In particular, the structure of the lobes and clefts at the front of the current is presented in association to local turbulent structures. In rotating gravity currents, the vortices observed at the lobes front are not of hairpin type but are rather of Kelvin-Helmholtz type.