Two-phase hydrodynamic and sediment transport modeling of wave-generated sheet flow

This numerical investigation was carried out to advance mechanistic understanding of sediment transport under sheet flow conditions. An Euler–Euler coupled two-phase flow model was developed to simulate fluid–sediment oscillatory sheet flow. Since the concentration of sediment particles is high in such flows, the kinematics of the fluid and sediment phases are strongly coupled. This model includes interaction forces, intergranular stresses and turbulent stress closure. Each phase was modeled via the Reynolds-Averaged Navier–Stokes equations, with interphase momentum conservation accounting for the interaction between the phases. The generation and transformation of turbulence was modeled using the two-equation k–ε$k''–''\epsilon$ turbulence model. Concentration and sediment flux profiles were compared with experimental data for sheet flow conditions considering both symmetric and asymmetric oscillatory flows. Sediment and fluid velocity variations, concentration profiles, sediment flux and turbulence parameters of wave-generated sheet flow were studied numerically with a focus on sediment transport characteristics. In all applications, the model predictions compared well with the experimental data. Unlike previous investigations in which the flow is driven by a horizontal pressure gradient, the present model solves the Navier–Stokes equations under propagating waves. The model’s ability to predict sediment transport under oscillatory sheet flow conditions underscores its potential for understanding the evolution of beach morphology.     

Numerical simulation of surf–swash zone motions and turbulent flow

A two-dimensional numerical model was presented for the simulation of wave breaking, runup and turbulence in the surf and swash zones. The main components of the model are the Reynolds-Averaged Navier–Stokes equations describing the average motion of a turbulent flow, a k–ε turbulence closure model describing the transformation and dissipation processes of turbulence and a volume of fluid technique for tracking the free surface motion. Nearshore wave evolution on a sloping bed, the velocity field and other wave characteristics were investigated. First, the results of the model were compared with experimental results for different surf zone hydrodynamic conditions. Spilling and plunging breakers were simulated and the numerical model investigated for different wave parameters. The turbulence field was also considered and the spatial and time-dependent variations of turbulence parameters were discussed. In the next stage of the study, numerical results were compared with two sets of experimental data in the swash zone. Generally, there is good agreement except for turbulence predictions near the breaking point where the model does not represent well the physical processes. On the other hand, turbulence predictions were found to be excellent for the swash zone. The model provides a precise and efficient tool for the simulation of the flow field and wave transformations in the nearshore, especially in the swash zone. The numerical model can simulate the surface elevation of the vertical shoreline excursion on sloping beaches, while swash–swash interactions within the swash zone are accounted for.     

Air–water two-phase flow modeling of turbulent surf and swash zone wave motions

Wave breaking and wave runup/rundown have a major influence on nearshore hydrodynamics, morphodynamics and beach evolution. In the case of wave breaking, there is significant mixing of air and water at the wave crest, along with relatively high kinetic energy, so prediction of the free surface is complicated. Most hydrodynamic studies of surf and swash zone are derived from single-phase flow, in which the role of air is ignored. Two-phase flow modeling, consisting of both phases of water and air, may be a good alternative numerical modeling approach for simulating nearshore hydrodynamics and, consequently, sediment transport. A two-phase flow tool can compute more realistically the shape of the free surface, while the effects of air are accounted for. This paper used models based on two-dimensional, two-phase Reynolds-averaged Navier–Stokes equations, the volume-of-fluid surface capturing technique and different turbulence closure models, i.e., k–ε, k–ω and re-normalized group (RNG). Our numerical results were compared with the available experimental data. Comparison of the employed method with a model not utilizing a two-phase flow modeling demonstrates that including the air phase leads to improvement in simulation of wave characteristics, especially in the vicinity of the breaking point. The numerical results revealed that the RNG turbulence model yielded better predictions of nearshore zone hydrodynamics, although the k–ε model also gave satisfactory predictions. The model provides new insights for the wave, turbulence and means flow structure in the surf and swash zones.     

A new epsilon-dominance hierarchical Bayesian optimization algorithm for large multiobjective monitoring network design problems

This study focuses on the development of a next generation multiobjective evolutionary algorithm (MOEA) that can learn and exploit complex interdependencies and/or correlations between decision variables in monitoring design applications to provide more robust performance for large problems (defined in terms of both the number of objectives and decision variables). The proposed MOEA is termed the epsilon-dominance hierarchical Bayesian optimization algorithm (ε$\epsilon$-hBOA), which is representative of a new class of probabilistic model building evolutionary algorithms. The ε$\epsilon$-hBOA has been tested relative to a top-performing traditional MOEA, the epsilon-dominance nondominated sorted genetic algorithm II (ε$\epsilon$-NSGAII) for solving a four-objective LTM design problem. A comprehensive performance assessment of the ε$\epsilon$-NSGAII and various configurations of the ε$\epsilon$-hBOA have been performed for both a 25 well LTM design test case (representing a relatively small problem with over 33 million possible designs), and a 58 point LTM design test case (with over 2.88×10¹⁷$2.88\times {10}^{17}$ possible designs). The results from this comparison indicate that the model building capability of the ε$\epsilon$-hBOA greatly enhances its performance relative to the ε$\epsilon$-NSGAII, especially for large monitoring design problems. This work also indicates that decision variable interdependencies appear to have a significant impact on the overall mathematical difficulty of the monitoring network design problem.     

Microwave link rainfall estimation: Effects of link length and frequency,temporal sampling,power resolution,and wet antenna attenuation

Issues associated with microwave link rainfall estimation such as the effects of spatial and temporal variation in rain, the nonlinearity of R–k$R''–''k$ relations, temporal sampling, power resolution, and wet antenna attenuation are investigated using more than 1.5 years of data from a high-resolution X-band weather radar. Microwave link signals are generated for different link frequencies and lengths from these radar data, so that retrieved path-averaged rainfall intensities can be compared to true path-averaged values. Results of these simulations can be linked to the space–time structure of rain. A frequency-dependent relation between the rainfall intensity at an antenna and the attenuation caused by its wetting is derived using microwave link and rain gauge data. It is shown that if the correct temporal sampling strategy is chosen, the effects of the degradation of power resolution and of wet antenna attenuation (if a correction is applied) are minor (i.e., MBE and bias-corrected RMSE are >−20% and <20% of the mean rainfall intensity, respectively) for link frequencies and lengths above ∼20 GHz and ∼2 km, respectively.     

Concentration profiles for fine and coarse sediments suspended by waves over ripples: An analytical study with the 1-DV gradient diffusion model

Field and laboratory measurements of suspended sediments over wave ripples show, for time-averaged concentration profiles in semi-log plots, a contrast between upward convex profiles for fine sand and upward concave profiles for coarse sand. Careful examination of experimental data for coarse sand shows a near-bed upward convex profile beneath the main upward concave profile. Available models fail to predict these two profiles for coarse sediments. The 1-DV gradient diffusion model predicts the main upward concave profile for coarse sediments thanks to a suitable β(y)$\beta (y)$-function (where β$\beta$ is the inverse of the turbulent Schmidt number and y   is the distance from the bed). In order to predict the near-bed upward convex profile, an additional parameter α$\alpha$ is needed. This parameter could be related to settling velocity (α$\alpha$ equal to inverse of dimensionless settling velocity) or to convective sediment entrainment process. The profiles are interpreted by a relation between second derivative of the logarithm of concentration and derivative of the product between sediment diffusivity and α$\alpha$.     

A cross-shore suspended sediment transport shape function parameterisation for natural beaches

A new field-based parameterisation (‘shape function’) describing the distribution of cross-shore suspended sediment transport across a beach profile is presented. Time-averaged and depth-integrated suspended sediment fluxes were measured over 39 tides at Sennen Cove, Cornwall, UK, for a range of wave conditions (offshore significant wave heights 0.1–2.5 m). The suspended sediment flux data were heuristically separated into four transport components: (1) mean flux in the surf/shoaling zone; (2) oscillatory flux in the surf/shoaling zone; (3) onshore flux in the swash/inner surf zone and (4) offshore flux in the swash/inner surf zone. Each of these transport components was related to the local water depth (h) normalised by the breakpoint depth (h_b) and the four resulting suspended transport shape functions were combined to form a total suspended load shape function. Each shape function component is scaled independently by the wave energy level through h_b. The total suspended load shape function predicts onshore sediment transport under low-energy conditions, with peaks at the breakpoint and in the swash zone, in agreement with the field observations. Under high-energy conditions the total suspended load shape function predicts onshore transport in the shoaling zone, offshore transport in the surf zone and onshore transport in the inner swash zone.     

Simulation of sediment motions using a discrete particle model in the inner surf and swash-zones

A volume-of-fluid Navier–Stokes solver (RIPPLE) was used to simulate inner surf and swash zone flow with a 3 s wave period and wave height of 0.14 m on a planar, 1:10 sloping beach (Iribarren number of 1.0). In addition to other hydrodynamic information, RIPPLE was used to provide high-resolution predictions of the pressure gradient and fluid velocity in the horizontal and vertical dimensions that served as forcing to a discrete particle model (DPM). Sediment transport processes in the inner surf and swash zones were simulated for a thin veneer of sediment particles over a 5 m test section in the DPM. Coupling between RIPPLE and the DPM was one-way such that particle–particle and fluid–particle interactions in the DPM did not provide feedback to alter the flow predicted by RIPPLE. The numerical simulation showed strong sediment suspension localized under vortices that reach the bed. Interestingly, the bulk of the sediment located in the small-scale vortex originated from locations nearly 0.2 m landward. These findings suggest that (1) sediment motion for a single swash event can be significant, (2) that sediment measured in suspension likely originates from locations other than the bed directly below the suspension plume suggesting the importance of sediment advection and (3) that sparse cross-shore measurements in the field will only sporadically capture localized suspension events.     

An efficient,high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media

In this study, a probabilistic collocation method (PCM) on sparse grids is used to solve stochastic equations describing flow and transport in three-dimensional, saturated, randomly heterogeneous porous media. The Karhunen–Loève decomposition is used to represent log hydraulic conductivity Y=ln_Ks$Y=\ln K_s$. The hydraulic head h   and average pore-velocity v$\mathbf{v}$ are obtained by solving the continuity equation coupled with Darcy’s law with random hydraulic conductivity field. The concentration is computed by solving a stochastic advection–dispersion equation with stochastic average pore-velocity v$\mathbf{v}$ computed from Darcy’s law. The PCM approach is an extension of the generalized polynomial chaos (gPC) that couples gPC with probabilistic collocation. By using sparse grid points in sample space rather than standard grids based on full tensor products, the PCM approach becomes much more efficient when applied to random processes with a large number of random dimensions. Monte Carlo (MC) simulations have also been conducted to verify accuracy of the PCM approach and to demonstrate that the PCM approach is computationally more efficient than MC simulations. The numerical examples demonstrate that the PCM approach on sparse grids can efficiently simulate solute transport in randomly heterogeneous porous media with large variances.     

Wave-forced dynamics in the nearshore river mouths,and swash zones

The role of wave forcing on the main hydro-morphological dynamics evolving in the shallow waters of the nearshore and at river mouths is analyzed. Focus is mainly on the cross-shore dynamics that evolve over mildly sloping barred, dissipative sandy beaches from the storm up to the yearly timescale, at most. Local and non-local mechanisms as well as connections across three main inter-related subsystems of the nearshore – the region of generation and evolution of nearshore bars, river mouths and the swash zone – are analyzed. The beach slope is a major controlling parameter for all nearshore dynamics. A local mechanism that must be properly described for a suitable representation of wave-forced dynamics of all such three subsystems is the proper correlation between orbital velocity and sediment concentration in the bottom boundary layer; while specific dynamics are the wave–current interaction and bar generation at river mouths and the sediment presuspension at the swash zone. Fundamental non-local mechanisms are both infragravity (IG) waves and large-scale horizontal vortices (i.e. with vertical axes), both influencing the hydrodynamics, the sediment transport and the seabed morphology across the whole nearshore. Major connections across the three subsystems are the upriver propagation of IG waves generated by breaking sea waves and swash–swash interactions, the interplay between the swash zone and along-river-flank sediment transport and the evolution of nearshore sandbars. © 2019 John Wiley & Sons, Ltd.     

Using dispersivity values to quantify the effects of pore-scale flow focusing on enhanced reaction along a transverse mixing zone

A key challenge for predictive modeling of transverse mixing and reaction of solutes in groundwater is to determine values of transverse dispersivity (_αT)$({\alpha }_T)$ in heterogeneous flow fields that accurately describe mixing and reaction at the pore scale. We evaluated the effects of flow focusing in high permeability zones on mixing enhancement using experimental micromodel flow cells and pore-scale lattice-Boltzmann-finite-volume model (LB-FVM) simulations. Micromodel results were directly compared to LB-FVM simulations using two different pore structures, and excellent agreement was obtained. Six different flow focusing pore structures were then systematically tested using LB-FVM, and both analytical solutions and a two-dimensional (2D) continuum-scale model were used to fit _αT${\alpha }_T$ values to pore-scale results. Pore-scale results indicate that the overall rate of mixing-limited reaction increased by up to 40% when flow focusing occurred, and it was greater in pore structures with longer flow focusing regions and greater porosity contrast. For each pore structure, _αT${\alpha }_T$ values from analytical solutions of transverse concentration profiles or total product at a given longitudinal location showed good agreement for nonreactive and reactive solutes, and values determined in flow focusing zones were always smaller than those downgradient after the flow focusing zone. Transverse dispersivity values from the 2D continuum model were between values within and downgradient from the flow focusing zone determined from analytical solutions. Also, total product and transverse concentration profiles along the entire pore structure from the 2D continuum model matched pore scale results. These results indicate that accurate quantification of pore-scale flow focusing with transverse dispersion coefficients is possible only when the entire flow and concentration fields are considered.     

Measurements and modelling of beach groundwater flow in the swash-zone: a review

This paper reviews research on beach groundwater dynamics and identifies research questions which will need to be answered before swash zone sediment transport and beach profile evolution can be successfully modelled. Beach groundwater hydrodynamics are a result of combined forcing from the tide and waves at a range of frequencies, and a large number of observations exist which describe the shape and elevation of the beach watertable in response to tidal forcing at diurnal, semi-diurnal and spring-neap tidal frequencies. Models of beach watertable response to tidal forcing have been successfully validated; however, models of watertable response to wave forcing are less well developed and require verification. Improved predictions of swash zone sediment transport and beach profile evolution cannot be achieved unless the complex fluid and sediment interactions between the surface flow and the beach groundwater are better understood, particularly the sensitivity of sediment transport processes to flow perpendicular to the permeable bed.The presence of a capillary fringe, particularly when it lies just below the sand surface, has influences on beach groundwater dynamics. The presence of a capillary fringe can have a significant effect on the exchange of water between the ocean and the coastal aquifer, particularly in terms of the storage capacity of the aquifer. Field and laboratory observations have also shown that natural groundwater waves usually propagate faster and decay more slowly in aquifers with a capillary fringe, and observations which suggest that horizontal flows may also occur in the capillary zone have been reported. The effects of infiltration and exfiltration are generally invoked to explain why beaches with a low watertable tend to accrete and beaches with a high watertable tend to erode. However, the relative importance of processes such as infiltration losses in the swash, changes in the effective weight of the sediment, and modified shear stress due to boundary layer thinning, are not yet clear. Experimental work on the influence of seepage flows within sediment beds provides conflicting results concerning the effect on bed stability. Both modelling and experimental work indicates that the hydraulic conductivity of the beach is a critical parameter. However, hydraulic conductivity varies both spatially and temporally on beaches, particularly on gravel and mixed sand and gravel beaches. Another important, but poorly understood, consideration in beach groundwater studies is the role of air encapsulation during the wetting of beach sand.     

Decadal‐scale gravel beach evolution on a tectonically‐uplifting coast: Wellington,New Zealand

Uplift of the shoreline in tectonically‐active areas can have a profound influence on geomorphology changing the entire process dynamics of the coast as the landforms are removed from the influence of the sea. Over decadal timescales it is possible for the landforms to return to their pre‐earthquake condition and this paper examines the re‐establishment of mixed sand and gravel beaches on the coast of Wellington, New Zealand, subsequent to an uplift event in 1855. Over 60 topographic profiles were surveyed, seven sets of aerial photographs from a 67 year period were mapped and sediment size analyses conducted in order to quantify the nature of beach change following uplift, and associated relative sea level fall. These data were supported by surveys using ground penetrating radar. It is found that uplift raised the gravel beaches out of the swash zone thereby removing them from the littoral zone. Intertidal rocky reefs which occur between each embayment were also uplifted during the same event and completely interrupted the longshore transport system. Continued input of gravel material to the littoral zone allowed beaches to re‐establish sequentially along the coast as each embayment was infilled with sediment. This reconnection of the embayments with the longshore drift system is associated with the beach planform being initially drift dominated during infill but then switching to swash alignment once the embayment becomes infilled. This has resulted in shoreline accretion of over 100 m in some places, at rates of up to 4 m/yr, covering shore protection works built in the past few decades. The ability of the shore to adjust back to its pre‐uplift condition appears to be a function of the accommodation space created during uplift and the rate of sediment supply. Copyright © 2012 John Wiley & Sons, Ltd.     

Sunlight and tidal interaction as a mechanism of carbon transport in an ice-covered region: Results of a coupled ice–ocean ecosystem model

In order to clarify the mechanism of carbon transport in an ice-covered ecosystem in Lake Saroma (44^°N${44}^{°}\mathrm{N}$, 143^°E${143}^{°}\mathrm{E}$, Hokkaido, Japan), a three-dimensional numerical calculation using a coupled ice–ocean ecosystem model was conducted. This model comprises an ocean ecosystem model, an ice ecosystem model, and equations for the coupling between ice and ocean. Comparisons of calculated results with observational data confirm that the calculation well reproduced the in situ phenomena with respect to tides, tidal currents, concentrations of POC and chlorophyll a in ice and in water, and sinking fluxes beneath the ice. The analysis of the organic carbon budget based on the calculation reveals that tide-induced transport, the enhancement of biological production in a pelagic system, and the physical release of organic matter from ice associated with ice-melting are important factors affecting the carbon transport during the ice-melting season. The carbon transport has a one-day time cycle. This is because principal driving forces are sunlight, and diurnal tides. The described mechanism of “sunlight and tidal pumping” is one of the most important features of carbon transport in a coupled ice–water ecosystem.