16 research outputs found
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
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Laboratory experiments and simulations for solitary internal waves with trapped cores
We perform simultaneous coplanar measurements of velocity and density in solitary internal waves with trapped cores, as well as viscous numerical simulations. Our set-up comprises a thin stratified layer (approximately 15% of the overall fluid depth) overlaying a deep homogeneous layer. We consider waves propagating near a free surface, as well as near a rigid no-slip lid. In the free-surface case, all trapped-core waves exhibit a strong shear instability. We propose that Marangoni effects are responsible for this instability, and use our velocity measurements to perform quantitative calculations supporting this hypothesis. These surface-tension effects appear to be difficult to avoid at the experimental scale. By contrast, our experiments with a no-slip lid yield robust waves with large cores. In order to consider larger-amplitude waves, we complement our experiments with viscous numerical simulations, employing a longer virtual tank. Where overlap exists, our experiments and simulations are in good agreement. In order to provide a robust definition of the trapped core, we propose bounding it as a Lagrangian coherent structure (instead of using a closed streamline, as has been done traditionally). This construction is less sensitive to small errors in the velocity field, and to small three-dimensional effects. In order to retain only flows near equilibrium, we introduce a steadiness criterion, based on the rate of change of the density in the core. We use this criterion to successfully select within our experiments and simulations a family of quasi-steady robust flows that exhibit good collapse in their properties. The core circulation is small (at most, around 10% of the baroclinic wave circulation). The core density is essentially uniform; the standard deviation of the density, in the core region, is less than 4% of the full density range. We also calculate the circulation, kinetic energy and available potential energy of these waves. We find that these results are consistent with predictions from Dubreil-Jacotin-Long theory for waves with a uniform-density irrotational core, except for an offset, which we suggest is associated with viscous effects. Finally, by computing Richardson-number fields, and performing a temporal stability analysis based on the Taylor-Goldstein equation, we show that our results are consistent with empirical stability criteria in the literature
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