Additional Advection Research Articles

Fractionation by Spatially Heterogeneous Diffusion: Experiments and the Two-Component Random Walk Model.

The fundamental question regarding the fractionation phenomenon is whether diffusion alone is responsible for it or whether an additional advection dynamic is involved. We studied the fractionation by diffusion of particles in spatially heterogeneous environments. By experimentally observing the time-sequential fractionation patterns of dye particles diffusing across a solid-solid interface of varying polyacrylamide gel densities, we found that the two-component diffusion model accurately captures the observed fractionation dynamics. In contrast, single-component diffusion models by Fick, Wereide, and Chapman do not. Our results indicate that diffusion alone can explain the fractionation phenomenon and that additional advection dynamics are not involved. The underlying physics in the fractionation phenomenon is discussed by using a two-component random walk model.

On the hydrostatic limit of stably stratified fluids with isopycnal diffusivity

This article is concerned with rigorously justifying the hydrostatic limit for continuously stratified incompressible fluids under the influence of gravity. The main distinction of this work compared to previous studies is the absence of any (regularizing) viscosity contribution added to the fluid-dynamics equations; only thickness diffusivity effects are considered. Motivated by applications to oceanography, the diffusivity effects in this work arise from an additional advection term, the specific form of which was proposed by Gent and McWilliams in the 1990s to model the effective contributions of geostrophic eddy correlations in non-eddy-resolving systems. The results of this paper heavily rely on the assumption of stable stratification. We establish the well-posedness of the hydrostatic equations and the original (non-hydrostatic) equations for stably stratified fluids, along with their convergence in the limit of vanishing shallow-water parameter. These results are obtained in high but finite Sobolev regularity and carefully account for the various parameters involved. A key element of our analysis is the reformulation of the systems using isopycnal coordinates, enabling us to provide meticulous energy estimates that are not readily apparent in the original Eulerian coordinate system.

Enforcing accurate volume conservation in VOF‐based long‐term simulations of turbulent bubble‐laden flows on coarse grids

AbstractThis study proposes two different strategies to enforce accurate volume conservation in volume‐of‐fluid (VOF)‐based simulations of turbulent bubble‐laden flows on coarse grids. It is demonstrated that, without a correction, minimal volume errors on a time‐step level, caused by the under‐resolution of the interface, can accumulate to significant deviations from the intended flow conditions despite the comparably good volume conservation properties of the geometric VOF method. In particular, large volume errors are observed for challenging setups combining coarse grid resolutions and comparably high Reynolds and Eötvös numbers. The problem is reinforced for long‐term simulations in periodic domains, which are often performed to collect flow statistics of bubbly flows. The first proposed volume conservation method simply corrects the volume error of a bubble by uniformly adding or removing the respective amount of gas volume in the interface cells. The second proposed method performs an additional reconstruction and advection step of the VOF field using a non‐divergence‐free velocity field, which can be interpreted as a slight dilatation or contraction of the bubble. A comparison between the global flow statistics as well as the individual bubble dynamics for both volume conservation methods reveals that the results are quasi‐identical for a number of challenging test cases, while the gas volume is accurately conserved. The proposed methods allow to perform numerical simulations of freely deformable bubbles in turbulent flows for setups that have previously been out of reach for this numerical framework.

A conservative network element method for diffusion-advection-reaction problems

We derive a conservative network element method for heterogeneous and anisotropic diffusion problems by modifying the non-conservative version, and extend it to the approximation of an additional advection term. The numerical scheme possesses the flux formulation reminiscent of classical finite volume methods. Its convergence is naturally governed by the network element theory. Numerical results illustrate the good behavior of the method even on distorted point clouds.

Lagrangian Modeling of Marine Microplastics Fate and Transport: The State of the Science

Microplastics pollution has led to irreversible environmental consequences and has triggered global concerns. It has been shown that water resources and marine food consumers are adversely affected by microplastics due to their physico-chemical characteristics. This study attempts to comprehensively review the structure of four well-known Lagrangian particle-tracking models, i.e., Delft3D—Water Quality Particle tracking module (D-WAQ PART), Ichthyoplankton (Ichthyop), Track Marine Plastic Debris (TrackMPD), and Canadian Microplastic Simulation (CaMPSim-3D) in simulating the fate and transport of microplastics. Accordingly, the structure of each model is investigated with respect to addressing the involved physical transport processes (including advection, diffusion, windage, beaching, and washing-off) and transformation processes (particularly biofouling and degradation) that play key roles in microplastics’ behavior in the marine environment. In addition, the effects of the physical properties (mainly size, diameter, and shape) of microplastics on their fate and trajectories are reviewed. The models’ capabilities and shortcomings in the simulation of microplastics are also discussed. The present review sheds light on some aspects of microplastics’ behavior in water that were not properly addressed in particle-tracking models, such as homo- and hetero-aggregation, agglomeration, photodegradation, and chemical and biological degradation as well as additional advection due to wave-induced drift. This study can be regarded as a reliable steppingstone for the future modification of the reviewed models.

Visual Simulation of Turbulent Foams by Incorporating the Angular Momentum of Foam Particles into the Projective Framework

In this paper, we propose an angular momentum-based advection technique that can express the turbulent foam effect. The motion of foam particles, which are strongly bound to the motion of the underlying fluid, is viscous, and sometimes clumping problems occur. This problem is a decisive factor that makes it difficult to express realistic foam effects. Since foam particles, which are secondary effects, depend on the motion of the underlying water, in order to exaggerate the foam effects or express more lively foam effects, it is inevitable to tune the motion of the underlying water and then readjust the foam particles. Because of such a cumbersome process, the readjustment of the foam effects requires a change in the motion of the underlying water, and it is not easy to produce such a scene because the water and foam effects must change at the same time. In this paper, we present a method to maintain angular momentum-based force from water particles without tuning the motion of the underlying water. We can restore the lost turbulent flow by additional advection of foam particles based on this force. In addition, our method can be integrated with screen-space projection frameworks, allowing us to fully embrace all the advantages of this approach. In this paper, the turbulence of the foam particles was improved by minimizing the viscous motion of the foam particles without tuning the motion of the underlying water, and as a result, lively foam effects can be expressed.

Cloud advection model of solar irradiance smoothing by spatial aggregation

Solar generation facilities are inherently spatially distributed and therefore aggregate solar irradiance in both space and time, smoothing its variability. To represent the spatiotemporal aggregation process, most existing studies focus on the reduced correlation in solar irradiance throughout a plant's spatial distribution. In this paper, we derived a cloud advection model that is instead based upon lagging correlations between upwind/downwind portions of a distributed plant, induced by advection of a fixed cloud pattern over the plant. We use the model to calculate a plant transfer function that can be used to predict the smoothing of the time series. The model was validated using the distributed HOPE-Melpitz measurement dataset, which consisted of 50 solar irradiance sensors at 1 s temporal resolution over a 3 × 2 km2 bounding area. The initial validation showed that the advection-based model outperforms other models at predicting the smoothed irradiance time series during manually identified, advection dominated conditions. We also conducted validation on the model against additional advection dominated periods in the dataset that were identified algorithmically. The cloud advection model's performance compared well to models in literature, but degraded slightly as larger cross-wind plant distributions were investigated. The results in this paper highlight the need to incorporate advection effects on spatial aggregation during advection dominated conditions. Future development of spatiotemporal aggregation models is needed to unify advective models with existing correlation reduction models and to identify regimes where each dominate.

Mesh Quality Preserving Shape Optimization Using Nonlinear Extension Operators

In this article, we propose a shape optimization algorithm which is able to handle large deformations while maintaining a high level of mesh quality. Based on the method of mappings, we introduce a nonlinear extension operator, which links a boundary control to domain deformations, ensuring admissibility of resulting shapes. The major focus is on comparisons between well-established approaches involving linear-elliptic operators for the extension and the effect of additional nonlinear advection on the set of reachable shapes. It is moreover discussed how the computational complexity of the proposed algorithm can be reduced. The benefit of the nonlinearity in the extension operator is substantiated by several numerical test cases of stationary, incompressible Navier–Stokes flows in 2d and 3d.

Nonlinear Controllability Assessment of Aerial Manipulator Systems using Lagrangian Reduction

This paper analyzes the nonlinear Small-Time Local Controllability (STLC) of a class of underatuated aerial manipulator robots. We apply methods of Lagrangian reduction to obtain their lowest dimensional equations of motion (EOM). The symmetry-breaking potential energy terms are resolved using advected parameters, allowing full $SE(3)$ reduction at the cost of additional advection equations. The reduced EOM highlights the shifting center of gravity due to manipulation and is readily in control-affine form, simplifying the nonlinear controllability analysis. Using Sussmann's sufficient condition, we conclude that the aerial manipulator robots are STLC near equilibrium condition, requiring Lie bracket motions up to degree three.

Volume-preserving strategies to improve the mixing efficiency of serpentine micromixers

In this study, we have proposed volume-preserving strategies to boost chaoticadvection and improve the mixing efficiency of serpentine micromixers. The proposed strategies revolve around the point that the volume of the micromixer is kept constant during the manipulation. The first strategy involves the utilization of a nozzle-diffuser (ND) shaped microchannel. Using this, the velocity of the fluids fluctuates in an alternating pattern, leading to additional chaotic advection, a decrease in the mixing path, and an increase in the mixing index. The second strategy uses non-aligned inlets to generate swirl inducing effects at the microchannel entrance, where the collision of two fluids generates angular momentum in the flow, providing more chaotic advection. These strategies proved to be effective in boosting the mixing efficiency over wide ranges of Re in which 60% enhancement (from 20.53% to 80.31%) was achieved for Re of 30 by applying an ND shaped microchannel, and 20% enhancement (from 12.71% to 32.21%) was achieved for a critical Re of 15 by applying both of the strategies simultaneously.

Heat Flow Data in an Area of the Eastern Southern Basin and Range in Arizona Contribute to an Analysis of Neogene Lithosphere Thinning Greater than 100 Km

Abstract Heat flow data and thermochronologic derived paleotemperature gradient data are examined to calculate heat flow ~25 Ma and, at present, for a southern Basin and Range location north of Tucson, Arizona. An increase in the surface heat flow is estimated from ~25 Ma to the present; changing from ~47 to ~83 mW m-2. Steady-state conduction temperature vs. depth profiles provide estimates of lithosphere thicknesses both for the present and for ~25 Ma. Different heat transfer models for present heat flow predict present LAB depth that agrees with seismic studies. From these temperature profiles, lithosphere thinning from ~184 km to ~70 km is suggested during the Neogene. Mantle lithosphere thinning caused by thermal phenomena is likely a fundamental driving force for southern Basin and Range extension. Because the mantle lithosphere has likely thinned much more than the crust, it is shown that additional vertical advection, such as an asthenosphere plume, delaminating part of the mantle lithosphere, convection cells, and rising magmas along conduits, add to the vertical advection component of upper mantle lithosphere extension. Interestingly, values of heat flow 25 Ma, lithosphere thicknesses 25 Ma, and Neogene lithosphere thinning are somewhat similar for the Four Corners area of the Colorado Plateau and the southern Basin and Range, even though Neogene tectonic development was quite different, i.e., no Neogene extension in the Colorado Plateau vs. ~57% in the southern Basin and Range. Neogene lithosphere thinning phenomena are likely different in the two regions.

Modeling study of dredging induced sediment plume transport in Hamilton Harbour

To assess and predict the direction and range of a dredging induced contaminated sediment plume on the surrounding environment, a three-dimensional hydrodynamic and mud transport modeling system MIKE 3-FM was used in the Randle Reef area of Hamilton Harbour. Simulations were carried out with the typical local and maximum winds under which the dredging operation would proceed. The dredge plume travel pattern and range in both horizontal and vertical planes are examined under various wind conditions and model mesh resolutions. It was found that the simulated plume extents were very sensitive to transport model mesh resolution due to the additional numerical advection induced in the calculations. Detailed discussion of this particular issue has not been observed in other publications. The results of this simulation provide useful information for remediation project managers in planning and guiding the environmental monitoring of dredging operations. In addition, the methodology used in this study can be adapted to other dredging projects.

A Characteristic-wise Alternative WENO-Z Finite Difference Scheme for Solving the Compressible Multicomponent Non-reactive Flows in the Overestimated Quasi-conservative Form

The fifth, seventh and ninth order characteristic-wise alternative weighted essentially non-oscillatory (AWENO) finite difference schemes are applied to the fully conservative (FC) form and the overestimated quasi-conservative (OQC) form of the compressible multicomponent flows. Several linear and nonlinear numerical operators such as the linear Lax–Friedrichs operator and linearized nonlinear WENO operator and their mathematical properties are defined in order to build a general mathematical (numerical) framework for identifying the necessary and sufficient conditions required in maintaining the equilibriums of certain physical relevant properties discretely. In the case of OQC form, the AWENO scheme with the modified flux can be rigorously proved to maintain the equilibriums of velocity, pressure and temperature. Furthermore, we also show that the FC form cannot maintain the equilibriums without an additional advection equation of auxiliary variable involving the specific heat ratio. Extensive one- and two-dimensional classical benchmark problems, such as the moving material interface problem, multifluid shock-density interaction problem and shock-R22-bubble interaction problem, verify the theoretical results and also show that the AWENO schemes demonstrate less dissipation error and higher resolution than the classical WENO-Z scheme in the splitting form (Nonomura and Fujii in J Comput Phys 340:358–388, 2017).

Tectonic Controls on Gas Hydrate Distribution Off SW Taiwan

AbstractThe northern part of the South China Sea is characterized by widespread occurrence of bottom simulating reflectors indicating the presence of marine gas hydrate. Because the area covers both a tectonically inactive passive margin and the termination of a subduction zone, the influence of tectonism on the dynamics of gas hydrate systems can be studied in this region. Geophysical data show that there are multiple thrust faults on the active margin while much fewer and smaller faults exist in the passive margin. This tectonic difference matches with a difference in the geophysical characteristics of the gas hydrate systems. High hydrate saturation derived from ocean bottom seismometer data and controlled source electromagnetic data and conspicuous high‐amplitude reflections in P‐Cable 3‐D seismic data above the bottom simulating reflector are found in the anticlinal ridges of the active margin. In contrast, all geophysical evidence for the passive margin points to normal to low hydrate saturations. Geochemical analyses of gas samples collected at seep sites on the active margin show methane with heavy δ13C isotope composition, while gas collected at the passive margin shows light carbon isotope composition. Thus, we interpret the passive margin as a typical gas hydrate province fueled by biogenic production of methane and the active margin gas hydrate system as a system that is fueled not only by biogenic gas production but also by additional advection of thermogenic methane from the subduction system.

Modeling the Water-Flushing Properties of the Yangtze Estuary and Adjacent Waters

As a multi-branch estuary system, the Yangtze Estuary presents distinctive characteristics of hydrodynamic processes through co-action among river runoff, tides, wind-waves, and gravitational circulation. To study the pathways of flushing water along all of the estuary’s branches and analyze their differences, especially those due to the influence of seawater intrusion and discharge variations, a free surface flow modeling suite TELEMAC-MASCARET involving passive tracers was applied to the Yangtze Estuary and the adjacent waters. The open boundary conditions were provided by the Nao.99b model (Matsumoto et al., 2000), which was calibrated using observed velocity and salinity data obtained in March 2002. The water age, which was used as the diagnostic tool to study the flushing efficiency of the water body across the estuary, was solved by additional advection- diffusion- reaction equations implemented in the TELEMAC modeling system. The transport properties were investigated under different river discharge scenarios, which represented seasonal impacts; aspects relating to the influence of tide, surface wind stress, and density-induced circulation on age were also investigated. Model results showed that river runoff is one of the dominant factors influencing the spatial distribution of the mean age, while tidal force is another important factor. The horizontal freshwater age distribution demonstrated similarity compared with the salinity distribution; the vertical age distribution resembled the stratification pattern of salinity in all branches where stratification persists. An experimental numerical simulation of tracing saltwater age from the lower reaches of the estuary was conducted, and implicated the connectivity with transport processes of freshwater from upstream. Additionally, a particle tracking algorithm was used to analyze the dynamic characteristics of the four passages. The South Passage and South Channel were found to be significant as main water flow passages, while salinity intrusion in the North Branch was found to cause a return flow that partially joins the South Branch flushing water.

Heat conduction in rotating relativistic stars

In the standard form of the relativistic heat equation used in astrophysics, information propagates instantaneously, rather than being limited by the speed of light as demanded by relativity. We show how this equation nonetheless follows from a more general, causal theory of heat propagation in which the entropy plays the role of a fluid. In deriving this result, however, we see that it is necessary to make some assumptions which are not universally valid: the dynamical timescales of the process must be long compared with the explicitly causal physics of the theory, the heat flow must be sufficiently steady, and the spacetime static. Generalising the heat equation (e.g. restoring causality) would thus entail retaining some of the terms we neglected. As a first extension, we derive the heat equation for the spacetime associated with a slowly-rotating star or black hole, showing that it only differs from the static result by an additional advection term due to the rotation, and as a consequence demonstrate that a hotspot on a neutron star will be seen to be modulated at the rotation frequency by a distant observer.

Transition point prediction in a multicomponent lattice Boltzmann model: Forcing scheme dependencies.

Pseudopotential-based lattice Boltzmann models are widely used for numerical simulations of multiphase flows. In the special case of multicomponent systems, the overall dynamics are characterized by the conservation equations for mass and momentum as well as an additional advection diffusion equation for each component. In the present study, we investigate how the latter is affected by the forcing scheme, i.e., by the way the underlying interparticle forces are incorporated into the lattice Boltzmann equation. By comparing two model formulations for pure multicomponent systems, namely the standard model [X. Shan and G. D. Doolen, J. Stat. Phys. 81, 379 (1995)JSTPBS0022-471510.1007/BF02179985] and the explicit forcing model [M. L. Porter et al., Phys.Rev. E 86, 036701 (2012)PLEEE81539-375510.1103/PhysRevE.86.036701], we reveal that the diffusion characteristics drastically change. We derive a generalized, potential function-dependent expression for the transition point from the miscible to the immiscible regime and demonstrate that it is shifted between the models. The theoretical predictions for both the transition point and the mutual diffusion coefficient are validated in simulations of static droplets and decaying sinusoidal concentration waves, respectively. To show the universality of our analysis, two common and one new potential function are investigated. As the shift in the diffusion characteristics directly affects the interfacial properties, we additionally show that phenomena related to the interfacial tension such as the modeling of contact angles are influenced as well.

An efficient mass-preserving interface-correction level set/ghost fluid method for droplet suspensions under depletion forces

Aiming for the simulation of colloidal droplets in microfluidic devices, we present here a numerical method for two-fluid systems subject to surface tension and depletion forces among the suspended droplets. The algorithm is based on an efficient solver for the incompressible two-phase Navier–Stokes equations, and uses a mass-conserving level set method to capture the fluid interface. The four novel ingredients proposed here are, firstly, an interface-correction level set (ICLS) method; global mass conservation is achieved by performing an additional advection near the interface, with a correction velocity obtained by locally solving an algebraic equation, which is easy to implement in both 2D and 3D. Secondly, we report a second-order accurate geometric estimation of the curvature at the interface and, thirdly, the combination of the ghost fluid method with the fast pressure-correction approach enabling an accurate and fast computation even for large density contrasts. Finally, we derive a hydrodynamic model for the interaction forces induced by depletion of surfactant micelles and combine it with a multiple level set approach to study short-range interactions among droplets in the presence of attracting forces.

Generation of Subsurface Anticyclones at Arctic Surface Fronts due to a Surface Stress

AbstractIsolated anticyclones are frequently observed below the mixed layer in the Arctic Ocean. Some of these subsurface anticyclones are thought to originate at surface fronts. However, previous idealized simulations with no surface stress show that only cyclone–anticyclone dipoles can propagate away from baroclinically unstable surface fronts. Numerical simulations of fronts subject to a surface stress presented here show that a surface stress in the same direction as the geostrophic flow inhibits dipole propagation away from the front. On the other hand, a surface stress in the opposite direction to the geostrophic flow helps dipoles to propagate away from the front. Regardless of the surface stress at the point of dipole formation, these dipoles can be broken up on a time scale of days when a surface stress is applied in the right direction. The dipole breakup leads to the deeper anticyclonic component becoming an isolated subsurface eddy. The breakup of the dipole occurs because the cyclonic component of the dipole in the mixed layer is subject to an additional advection because of the Ekman flow. When the Ekman transport has a component oriented from the anticyclonic part of the dipole toward the cyclonic part then the cyclone is advected away from the anticyclone and the dipole is broken up. When the Ekman transport is in other directions relative to the dipole axis, it also leads to deviations in the trajectory of the dipole. A scaling is presented for the rate at which the surface cyclone is advected that holds across a range of mixed layer depths and surface stress magnitudes in these simulations. The results may be relevant to other regions of the ocean with similar near-surface stratification profiles.

Numerical Study on Flow Distribution in PEMFC with Metal Foam Bipolar Plate

It is important to uniformly supply the fuel gas into the reaction activity area in polymer electrolyte membrane fuel cell (PEMFC). Recent studies have shown that the cell performance can be significantly improved by employing metal foam gas distributor as compared with the conventional bipolar plate types. The metal foam gas distributor has been reported to be more efficient to fuel transport. In this study, three-dimensional computational fluid dynamics (CFD) simulations have been performed to examine the effects of metal foam flow field design on the fuel supply to the reaction site. Darcy's law is used for the flow in the porous media. By solving additional advection equation for fluid particle trajectory, the gas transport has been visualized and examined for various geometrical configuration of metal foam gas distributor. †This work was supported by the International Collaborative Energy Technology R&D Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) (No. 20148520120160)