Point-to-curve raytracing by algebraic rasterization

Boundary-value raytracing problems can be concatenated to a smooth one-parameter family of problems, that can be solved by continuation. This has been the purpose of point-to-curve raytracing. A global approach, based on algorithms taken from computer graphics (algebraic rasterization of implicit curves), has several advantages. Subject to relatively mild assumptions-Lipschitz continuity of the emergence point as function of initial parameters-all solution branches are found, there are no problems with initialization, bifurcation, or closed loop solutions. The algebraic rasterization benefits to boundary value raytracing problems in a wide range of applications: shot-to-profile shooting, VSP raytracing, normal raytracing, and more. The algorithm is sufficiently robust to continue even beyond points where the Lipschitz continuity does not apply, such as faults.     

A comparison of gravity wave phase velocities calculated from the impedance equation and pressure data

Abstract

Marked oscillations in wind speed, wind direction and pressure with periods of between 5 and 15 minutes were recorded on a number of occasions and it is assumed that they were produced by atmospheric gravity waves. Gossard and Munk (1954) have shown that the phase velocity of a gravity wave can be calculated using wind and pressure fluctuation data from a single station by means of the “impedance equation”. It is also possible to measure the phase velocity of a gravity wave using an array of microbarovariographs. In this investigation, the phase velocity of gravity waves calculated using these two different methods are compared and the feasibility of deriving wave characteristics from single point measurements is discussed. The results show that, while in a few isolated cases the two velocities agree reasonably well, the application of the impedance equation to data from a single station is limited due to the superposition of local wind systems upon the wave-induced perturbations.     

Kinematic modelling of shear band localization using discrete finite elements

Modelling shear band is an important problem in analysing failure of earth structures in soil mechanics. Shear banding is the result of localization of deformation in soil masses. Most finite element schemes are unable to model discrete shear band formation and propagation due to the difficulties in modelling strain and displacement discontinuities. In this paper, a framework to generate shear band elements automatically and continuously is developed. The propagating shear band is modelled using discrete shear band elements by splitting the original finite element mesh. The location or orientation of the shear band is not predetermined in the original finite element mesh. Based on the elasto‐perfect plasticity with an associated flow rule, empirical bifurcation and location criteria are proposed which make band propagation as realistic as possible. Using the Mohr–Coulomb material model, various results from numerical simulations of biaxial tests and passive earth pressure problems have shown that the proposed framework is able to display actual patterns of shear banding in geomaterials. In the numerical examples, the occurrence of multiple shear bands in biaxial test and in the passive earth pressure problem is confirmed by field and laboratory observations. The effects of mesh density and mesh alignment on the shear band patterns and limit loads are also investigated. Copyright © 2003 John Wiley & Sons, Ltd.     

Micro‐inertia origin of instabilities in granular materials

Within the framework of the second‐order work theory, the onset of instabilities is explored numerically in loose granular materials through three‐dimensional DEM simulations. Stress controlled directional analysis are performed in Rendulic's plane, and a particular attention is paid to transient evolutions at the microscale. Thanks to a micromechanical analysis, the onset and development of transient mechanical instabilities is explored. It is shown that these instabilities result from the unjamming and bending of a few force chains associated with a local burst of kinetic energy. This burst of kinetic energy propagates to the whole sample and provokes a generalized unjamming of force chains. As force chains buckle, a phase transition from a quasi‐static to an inertial regime is observed. At the macroscopic scale, this results in a transient softening and a loss of controllability. After the collapse of existing force chains, the development of plastic strain is eventually stopped as new stable force chains are built.     

Point-to-curve ray tracing

Point-to-curve ray tracing is an attempt at dealing with multiplicity of solutions to a generic boundary-value problem of ray tracing. In a point-to-curve tracing (P2C) the input parameters of the boundary-value problem (BVP), such as the ends of the ray, are allowed to vary along a curve. The solutions of the BVP automatically wander from one solution branch to another generating a nearly complete multi-valued solution of the BVPs.A procedure for transforming an arbitrary iterative algorithm, solving a ray tracing BVP to a corresponding P2C algorithm, is presented. Bifurcations of the solution curve of the P2C problem at caustics are studied and an algorithm for obtaining the bifurcating branches is developed. In particular, transition from real rays to complex rays in a caustic shadow offers an additional link between otherwise disconnected solution curves of the P2C problem. The topological structure of a generic solution curve and its implications for the algorithm are studied.     

The influence of flow discharge variations on the morphodynamics of a diffluence–confluence unit on a large river

Bifurcations are key geomorphological nodes in anabranching and braided fluvial channels, controlling local bed morphology, the routing of sediment and water, and ultimately defining the stability of their associated diffluence–confluence unit. Recently, numerical modelling of bifurcations has focused on the relationship between flow conditions and the partitioning of sediment between the bifurcate channels. Herein, we report on field observations spanning September 2013 to July 2014 of the three‐dimensional flow structure, bed morphological change and partitioning of both flow discharge and suspended sediment through a large diffluence–confluence unit on the Mekong River, Cambodia, across a range of flow stages (from 13 500 to 27 000 m³ s^?1). Analysis of discharge and sediment load throughout the diffluence–confluence unit reveals that during the highest flows (Q = 27 000 m³ s^?1), the downstream island complex is a net sink of sediment (losing 2600 ± 2000 kg s^?1 between the diffluence and confluence), whereas during the rising limb (Q = 19 500 m³ s^?1) and falling limb flows (Q = 13 500 m³ s^?1) the sediment balance is in quasi‐equilibrium. We show that the discharge asymmetry of the bifurcation varies with discharge and highlight that the influence of upstream curvature‐induced water surface slope and bed morphological change may be first‐order controls on bifurcation configuration. Comparison of our field data to existing bifurcation stability diagrams reveals that during lower (rising and falling limb) flow the bifurcation may be classified as unstable, yet transitions to a stable condition at high flows. However, over the long term (1959–2013) aerial imagery reveals the diffluence–confluence unit to be fairly stable. We propose, therefore, that the long‐term stability of the bifurcation, as well as the larger channel planform and morphology of the diffluence–confluence unit, may be controlled by the dominant sediment transport regime of the system. © 2017 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

An experimental study of discharge partitioning and flow structure at symmetrical bifurcations

Recent research has examined the factors controlling the geometrical configuration of bifurcations, determined the range of stability conditions for a number of bifurcation types and assessed the impact of perturbations on bifurcation evolution. However, the flow division process and the parameters that influence flow and sediment partitioning are still poorly characterized. To identify and isolate these parameters, three‐dimensional velocities were measured at 11 cross‐sections in a fixed‐walled experimental bifurcation. Water surface gradients were controlled, and systematically varied, using a weir in each distributary. As may be expected, the steepest distributary conveyed the most discharge (was dominant) while the mildest distributary conveyed the least discharge (was subordinate). A zone of water surface super‐elevation was co‐located with the bifurcation in symmetric cases or displaced into the subordinate branch in asymmetric cases. Downstream of a relatively acute‐angled bifurcation, primary velocity cores were near to the water surface and against the inner banks, with near‐bed zones of lower primary velocity at the outer banks. Downstream of an obtuse‐angled bifurcation, velocity cores were initially at the outer banks, with near‐bed zones of lower velocities at the inner banks, but patterns soon reverted to match the acute‐angled case. A single secondary flow cell was generated in each distributary, with water flowing inwards at the water surface and outwards at the bed. Circulation was relatively enhanced within the subordinate branch, which may help explain why subordinate distributaries remain open, may play a role in determining the size of commonly‐observed topographic features, and may thus exert some control on the stability of asymmetric bifurcations. Further, because larger values of circulation result from larger gradient disadvantages, the length of confluence–diffluence units in braided rivers or between diffluences within delta distributary networks may vary depending upon flow structures inherited from upstream and whether, and how, they are fed by dominant or subordinate distributaries. Copyright © 2011 John Wiley & Sons, Ltd.     

The existence of internal solitary waves in a two-fluid system near the KdV limit

Abstract

Two fluid layers of constant density lying one over the other on top of a rigid horizontal lower boundary with either a free upper surface or a rigid upper boundary can support solitary waves. The existence of a unique branch of such waves emanating from the horizontal flow at a critical speed U _? is demonstrated in both cases by use of the Nash—Moser implicit function theorem. These results complement the global results of Amick and Turner (1986) and are analogous to the work of Friedrichs and Hyers (1954) and Beale (1977) for surface waves. It is also noted that the most obvious variational principle which characterizes these waves as constrained extremals (Benjamin, 1984) is of indefinite type, having a Hessian with infinitely many positive and infinitely many negative eigenvalues.     

Three‐dimensional numerical modeling of the Bulle effect: the nonlinear distribution of near‐bed sediment at fluvial diversions

The Bulle effect is a phenomenon in which a disproportionately higher amount of near‐bed sediment load at a fluvial diversion moves into the diverted channel, even for cases in which the proportion of water (with respect to the main flow) entering the diversion channel is relatively small. This phenomenon has wide‐ranging implications for both engineered and natural systems: from efficient design of channels to redirect water and sediment for reclaiming sinking deltas, designing navigational channels that do not need frequent dredging, to morphological evolution of river bifurcations. The first ever, and one of the most extensive set of experiments conducted to explore this phenomenon, were conducted by Bulle in 1926 . In the current study the experiments conducted by Bulle have been simulated using an open‐source, free‐surface finite‐element‐based hydrodynamic solver. The main objectives were to explore to what extent the complex phenomenon of the Bulle effect at the scale of a laboratory experiment can be simulated accurately using Reynolds‐averaged Navier–Stokes (RANS)‐based hydrodynamic solver, and to understand the details of the hydrodynamics that Bulle could not analyze through his experiments. The hydrodynamics captured by the simulations were found to match the observations made by Bulle through his experiments, and the distributions of sediment at the diversion predicted by the numerical simulations were found to match the general trend observed in the laboratory experiments. The results from the numerical simulations were also compared with existing one‐dimensional models for sediment distribution at bifurcations, and the three‐dimensional numerical model was found to perform appreciably better. This is expected due to the complex flow features at the diversion, which can only be captured satisfactorily using a three‐dimensional hydrodynamic model. Copyright © 2017 John Wiley & Sons, Ltd.     

Dynamic flood topographies in the Terai region of Nepal

Flood hazard maps used to inform and build resilience in remote communities in the Terai region of southern Nepal are based on outdated and static digital elevation models (DEMs), which do not reflect dynamic river configuration or hydrology. Episodic changes in river course, sediment dynamics, and the distribution of flow down large bifurcation nodes can modify the extent of flooding in this region, but these processes are rarely considered in flood hazard assessment. Here, we develop a 2D hydrodynamic flood model of the Karnali River in the Terai region of west Nepal. A number of scenarios are tested examining different DEMs, variable bed elevations to simulate bed aggradation and incision, and updating bed elevations at a large bifurcation node to reflect field observations. By changing the age of the DEM used in the model, a 9.5% increase in inundation extent was observed for a 20-year flood discharge. Reducing horizontal DEM resolution alone resulted in a <1% change. Uniformly varying the bed elevation led to a 36% change in inundation extent. Finally, changes in bed elevation at the main bifurcation to reflect observed conditions resulted in the diversion of the majority of flow into the west branch, consistent with measured discharge ratios between the two branches, and a 32% change in inundation extent. Although the total flood inundation area was reduced (−4%), there was increased inundation along the west bank. Our results suggest that regular field measurements of bed elevation and updated DEMs following large sediment-generating events, and at topographically sensitive areas such as large river bifurcations, could help improve model inputs in future flood prediction models. This is particularly important following flood events carrying large sediment loads out of mountainous regions that could promote bed aggradation and channel switching across densely populated alluvial river systems and floodplains further downstream. © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd