Deep-water sediment wave formation: Linear stability analysis of coupled flow/bed interaction

International audienceA linear stability analysis is carried out for the interaction of an erodible sediment bed with a sediment-laden, stratified flow above the bed, such as a turbidity or bottom current. The fluid motion is described by the full, two-dimensional Navier-Stokes equations in the Boussinesq approximation, while erosion is modelled as a diffusive flux of particles from the bed into the fluid. The stability analysis shows the existence of both Tollmien-Schlichting and internal wave modes in the stratified boundary layer. For the internal wave mode, the stratified boundary layer acts as a wave duct, whose height can be determined analytically from the Brunt-Val frequency criterion. Consistent with this criterion, distinct unstable perturbation wavenumber regimes exist for the internal wave mode, which are associated with different numbers of pressure extrema in the wall-normal direction. For representative turbidity current parameters, the analysis predicts unstable wavelengths that are consistent with field observations. As a key condition for instability to occur, the base flow velocity boundary layer needs to be thinner than the corresponding concentration boundary layer. For most of the unstable wavenumber ranges, the phase relations between the sediment bed deformation and the associated wall shear stress and concentration perturbations are such that the sediment waves migrate in the upstream direction, which again is consistent with field observations. © 2011 Cambridge University Press

Variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells. Part 2. Nonlinear simulations

Direct numerical simulations of the variable density and viscosity Navier-Stokes equations are employed, in order to explore three-dimensional effects within miscible displacements in horizontal Hele-Shaw cells. These simulations identify a number of mechanisms concerning the interaction of viscous fingering with a spanwise Rayleigh-Taylor instability. The dominant wavelength of the Rayleigh-Taylor instability along the upper, gravitationally unstable side of the interface generally is shorter than that of the fingering instability. This results in the formation of plumes of the more viscous resident fluid not only in between neighbouring viscous fingers, but also along the centre of fingers, thereby destroying their shoulders and splitting them longitudinally. The streamwise vorticity dipoles forming as a result of the spanwise Rayleigh-Taylor instability place viscous resident fluid in between regions of less viscous, injected fluid, thereby resulting in the formation of gapwise vorticity via the traditional, gap-averaged viscous fingering mechanism. This leads to a strong spatial correlation of both vorticity components. For stronger density contrasts, the streamwise vorticity component increases, while the gapwise component is reduced, thus indicating a transition from viscously dominated to gravitationally dominated displacements. Gap-averaged, time-dependent concentration profiles show that variable density displacement fronts propagate more slowly than their constant density counterparts. This indicates that the gravitational mixing results in a more complete expulsion of the resident fluid from the Hele-Shaw cell. This observation may be of interest in the context of enhanced oil recovery or carbon sequestration application

Spiral vortex breakdown as a global mode

International audienceThe spiral form of vortex breakdown observed in the numerical simulations of Ruith et al. (J. Fluid Mech., vol. 486, 2003, p. 331) is interpreted as a nonlinear global mode originating at the convective/absolute instability transition point in the lee of the vortex breakdown bubble. The local absolute frequency at the transition station is shown to yield a satisfactory prediction of the precession frequency measured in the three-dimensional direct numerical simulations. © 2006 Cambridge University Press

Rheology of mobile sediment beds sheared by viscous, pressure-driven flows

We present a detailed comparison of the rheological behaviour of sheared sediment beds in a pressure-driven, straight channel configuration based on data that was generated by means of fully coupled, grain-resolved direct numerical simulations and experimental measurements reviously published by Aussillous {\it et al.} (J. Fluid Mech., vol. 736, 2013, pp. 594-615). The highly-resolved simulation data allows to compute the stress balance of the suspension in the streamwise and vertical directions and the stress exchange between the fluid and particle phase, which is information needed to infer the rheology, but has so far been unreachable in experiments. Applying this knowledge to the experimental and numerical data, we obtain the statistically-stationary, depth-resolved profiles of the relevant rheological quantities. The scaling behavior of rheological quantities such as the shear and normal viscosities and the effective friction coefficient are examined and compared to data coming from rheometry experiments and from widely-used rheological correlations. We show that rheological properties that have previously been inferred for annular Couette-type shear flows with neutrally buoyant particles still hold for our setup of sediment transport in a Poiseuille flow and in the dense regime we found good agreement with empirical relationships derived therefrom. Subdividing the total stress into parts from particle contact and hydrodynamics suggests a critical particle volume fraction of 0.3 to separate the dense from the dilute regime. In the dilute regime, i.e., the sediment transport layer, long-range hydrodynamic interactions are screened by the porous media and the effective viscosity obeys the Einstein relation

Settling of cohesive sediment: particle-resolved simulations

We develop a physical and computational model for performing fully coupled, particle-resolved Direct Numerical Simulations of cohesive sediment, based on the Immersed Boundary Method. The model distributes the cohesive forces over a thin shell surrounding each particle, thereby allowing for the spatial and temporal resolution of the cohesive forces during particle-particle interactions. The influence of the cohesive forces is captured by a single dimensionless parameter in the form of a cohesion number, which represents the ratio of cohesive and gravitational forces acting on a particle. We test and validate the cohesive force model for binary particle interactions in the Drafting-Kissing-Tumbling (DKT) configuration. The DKT simulations demonstrate that cohesive particle pairs settle in a preferred orientation, with particles of very different sizes preferentially aligning themselves in the vertical direction, so that the smaller particle is drafted in the wake of the larger one. To test this mechanism in a system of higher complexity, we perform large simulations of 1,261 polydisperse settling particles starting from rest. These simulations reproduce several earlier experimental observations by other authors, such as the accelerated settling of sand and silt particles due to particle bonding. The simulations demonstrate that cohesive forces accelerate the overall settling process primarily because smaller grains attach to larger ones and settle in their wakes. For the present cohesion number values, we observe that settling can be accelerated by up to 29%. We propose physically based parametrization of classical hindered settling functions proposed by earlier authors, in order to account for cohesive forces. An investigation of the energy budget shows that the work of the collision forces can substantially modify the relevant energy conversion processes.Comment: 39 page

Characteristics and controls of the runout behaviour of non-Boussinesq particle-laden gravity currents – A large-scale experimental investigation of dilute pyroclastic density currents

One of the most dangerous aspects of explosive volcanism is the occurrence of dilute pyroclastic density currents that move at high velocities of tens to about a hundred of metres per second outwards from volcanic vents. Predicting the runout behaviour of these turbulent flows of hot particles and air is complicated by strong changes in the flow density resulting from entrainment of ambient air, sedimentation of particles, as well as heating and expansion of the gas phase. Current hazard models that are based on the behaviour of aqueous gravity currents cannot capture all aspects of the flow dynamics, and thus pyroclastic density current dynamics remain comparatively poorly understood. Here we interrogate the runout behaviour of dilute pyroclastic density currents in large-scale experiments using hot volcanic material and gas. We demonstrate that the flows transition through four dynamic regimes with distinct density and force characteristics. The first, inertial regime is characterized by strong deceleration under high density differences between the flow and ambient air where suspended particles carry a main proportion of the flows' momentum. When internal gravity waves start to propagate from the flow body into the advancing flow front, the currents transition into a second, inertia-buoyancy regime while flow density continues to decline. In this regime, subsequent arrivals of fast-moving internal gravity waves into the front replenish momentum and lead to sudden short-lived front accelerations. In the third regime, when the density ratio between flow and ambient air decreases closer to a value of unity, buoyancy forces become negligible, but pressure drag forces are large and constitute the main flow retarding force. In this inertia-pressure drag regime, internal gravity waves cease to reach the front. Finally, and with the density ratio decreasing below 1, the current transitions into a buoyantly rising thermal in regime 4. Unlike for aqueous gravity currents, the Froude number is not constant and viscous forces are negligible in these gas-particle gravity currents. We show that, in this situation, existing Boussinesq and non-Boussinesq gravity current models strongly underpredict the front velocity for most of the flow runout for at least half of the flow propagation. These results are not only important for hazard mitigation of pyroclastic density currents but are also relevant for other turbulent gas-particle gravity currents, such as powder snow avalanches and dust storms