Final Technical Report on Grant DE-FG03-00ER15114

The research under this grant has focused on three-dimensional numerical simulations, as well as on computational linear stability analysis. In the following, our main results for each of those areas will be described separately. In addition, copies of reprints are attached with this report

Long-range sediment transport in the world’s oceans by stably stratified turbidity currents

Peer reviewedPublisher PD

Potential Flow Interactions With Directional Solidification

The effect of convective melt motion on the growth of morphological instabilities in crystal growth has been the focus of many studies in the past decade. While most of the efforts have been directed towards investigating the linear stability aspects, relatively little attention has been devoted to experimental and numerical studies. In a pure morphological case, when there is no flow, morphological changes in the solid-liquid interface are governed by heat conduction and solute distribution. Under the influence of a convective motion, both heat and solute are redistributed, thereby affecting the intrinsic morphological phenomenon. The overall effect of the convective motion could be either stabilizing or destabilizing. Recent investigations have predicted stabilization by a flow parallel to the interface. In the case of non-parallel flows, e.g., stagnation point flow, Brattkus and Davis have found a new flow-induced morphological instability that occurs at long wavelengths and also consists of waves propagating against the flow. Other studies have addressed the nonlinear aspects (Konstantinos and Brown, Wollkind and Segel)). In contrast to the earlier studies, our present investigation focuses on the effects of the potential flow fields typically encountered in Hele-Shaw cells. Such a Hele-Shaw cell can simulate a gravity-free environment in the sense that buoyancy-driven convection is largely suppressed, and hence negligible. Our interest lies both in analyzing the linear stability of the solidification process in the presence of potential flow fields, as well as in performing high-accuracy nonlinear simulations. Linear stability analysis can be performed for the flow configuration mentioned above. It is observed that a parallel potential flow is stabilizing and gives rise to waves traveling downstream. We have built a highly accurate numerical scheme which is validated at small amplitudes by comparing with the analytically predicted results for the pure morphological case. We have been able to observe nonlinear effects at larger times. Preliminary results for the case when flow is imposed also provide good validation at small amplitudes

Report on the Program “Fluid-mediated particle transport in geophysical flows” at the Kavli Institute for Theoretical Physics, UC Santa Barbara, September 23 to December 12, 2013

International audienceThe KITP program held at UC Santa Barbara in the fall of 2013 addressed the dynamics of dispersed particulate flows in the environment. By focusing on the prototypes of Aeolian transport and turbidity currents, it aimed to establish the current state of our understanding of such two-phase flows, to identify key open questions, and to develop collaborative research strategies for addressing these questions. Here we provide a brief summary of the program outcome. Introduction Flows of a continuous fluid phase containing dispersed particles represent a ubiquitous phenomenon, with numerous applications in nature and technology. They can give rise to a great variety of qualitatively distinct flow regimes governed by different balances of inertial, viscous, gravitational and interparticle forces, depending on such aspects as the density ratio between particles and fluid, the nature of the particle-particle interactions, on whether the flows are dilute or concentrated, conservative or nonconservative, and Newtonian or non-Newtonian in nature, to name just a few. Even the narrower field of geophysical particle-laden flows covers a wide variety of phenomena, ranging from Aeolian transport, dust storms and powder snow avalanches to volcanic ash plumes, sediment transport in rivers, estuaries and oceans, and dense pyroclastic and debris flows. While all of the above flows have distinctly different features, they nevertheless share a number of common aspects as well. To advance our capabilities to describe flows of this nature, the community will have to draw heavily on such fundamental research areas as the physics of suspensions and granular flows. The KITP program aimed to review the current state of our understanding of such flows, to identify the key open questions that remain, and to develop collaborative research strategies for addressing these questions via a combination of laboratory experiments, computational investigations and field observations

Sustained gravity currents in a channel

Gravitationally driven motion arising from a sustained constant source of dense fluid in a horizontal channel is investigated theoretically using shallow-layer models and direct numerical simulations of the Navier–Stokes equations, coupled to an advection–diffusion model of the density field. The influxed dense fluid forms a flowing layer underneath the less dense fluid, which initially filled the channel, and in this study its speed of propagation is calculated; the outflux is at the end of the channel. The motion, under the assumption of hydrostatic balance, is modelled using a two-layer shallow-water model to account for the flow of both the dense and the overlying less dense fluids. When the relative density difference between the fluids is small (the Boussinesq regime), the governing shallow-layer equations are solved using analytical techniques. It is demonstrated that a variety of flow-field patterns are feasible, including those with constant height along the length of the current and those where the height varies continuously and discontinuously. The type of solution realised in any scenario is determined by the magnitude of the dimensionless flux issuing from the source and the source Froude number. Two important phenomena may occur: the flow may be choked, whereby the excess velocity due to the density difference is bounded and the height of the current may not exceed a determined maximum value, and it is also possible for the dense fluid to completely displace all of the less dense fluid originally in the channel in an expanding region close to the source. The onset and subsequent evolution of these types of motions are also calculated using analytical techniques. The same range of phenomena occurs for non-Boussinesq flows; in this scenario, the solutions of the model are calculated numerically. The results of direct numerical simulations of the Navier–Stokes equations are also reported for unsteady two-dimensional flows in which there is an inflow of dense fluid at one end of the channel and an outflow at the other end. These simulations reveal the detailed mechanics of the motion and the bulk properties are compared with the predictions of the shallow-layer model to demonstrate good agreement between the two modelling strategies.</jats:p

Consolidation of freshly deposited cohesive and non-cohesive sediment: particle-resolved simulations

We analyze the consolidation of freshly deposited cohesive and non-cohesive sediment by means of particle-resolved direct Navier-Stokes simulations based on the Immersed Boundary Method. The computational model is parameterized by material properties and does not involve any arbitrary calibrations. We obtain the stress balance of the fluid-particle mixture from first principles and link it to the classical effective stress concept. The detailed datasets obtained from our simulations allow us to evaluate all terms of the derived stress balance. We compare the settling of cohesive sediment to its non-cohesive counterpart, which corresponds to the settling of the individual primary particles. The simulation results yield a complete parameterization of the Gibson equation, which has been the method of choice to analyze self-weight consolidation.Comment: 16 pages, 9 figures, accepted for Physical Review Fluid

Transition of a Hyperpycnal Flow Into a Saline Turbidity Current Due to Differential Diffusivities

Acknowledgments: E.M. gratefully acknowledges support through NSF grant CBET‐1438052. L.Z. thanks The National Natural Science Foundation of China (11672267) and the China Scholarship Council for providing him with a scholarship to study at UCSB. B.V. was supported by a Feodor‐Lynen scholarship from the Alexander von Humboldt Foundation, Germany. Computational resources for this work were made available by the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF grant TGCTS150053. All of the data employed in this work can be obtained at https://drive.google.com/drive/folders/1pfg-sBgZeXcu3GbbrOa62FX87qcozzyl?usp=sharing.Peer reviewedPublisher PD