123 research outputs found
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
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
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
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
Vorticity dynamics during the start-up phase of gravity currents
The flow during the start-up phase of two-dimensional gravity currents is investigated by numerical simulations. The focus of the study is on the dynamics of the initially vertical density interface which is deformed by the
developing convective motion. Two different cases are considered, namely the lock-exchange flow and the release of a finite volume of dense fluid in deep surroundings. The viscous problem is addressed by direct numerical simulations
based on the Boussinesq equations, which are integrated by high-order numerical schemes. The direct simulations are supplemented by vortex dynamics simulations using a vortex blob technique in order to study the underlying inviscid dynamics. Several distinct features of starting gravity currents are identified, among these the formation of
start-up vortices very similar in nature to those observed for unstratified vortex sheets of finite extent. Moreover, the flow is shown to develop a pronounced Kelvin-Helmholtz–like instability at the interface, the details of which
strongly depend on the ratio of buoyancy forces to viscous forces
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