Numerical solutions of the sediment conservation law: A review and improved formulation for coastal morphological modelling

Numerical solutions of the sediment conservation law are reviewed in terms of their application to bed update schemes in coastal morphological models. It is demonstrated that inadequately formulated numerical techniques lead to the introduction of diffusion, dispersion and the bed elevation oscillations previously reported in the literature. Four different bed update schemes are then reviewed and tested against benchmark analytical solutions. These include a first order upwind scheme, two Lax-Wendroff schemes and a non-oscillating centred scheme (NOCS) recently applied to morphological modelling by Saint-Cast [Saint-Cast, F., 2002. Modelisation de la morphodynamique des corps sableux en milieu littoral (Modelling of coastal sand banks morphodynamics), University Bordeaux 1, Bordeaux, 245 pp.]. It is shown that NOCS limits and controls numerical errors while including all the sediment flux gradients that control morphological change. Further, no post solution filtering is required, which avoids difficulties with selecting filter strength. Finally, NOCS is compared to a recent Lax-Wendroff scheme with post-solution filtering for a longer term simulation of the morphological evolution around a trained river entrance. (C) 2006 Elsevier B.V. All rights reserved.

Application of a coupled ground-surface water flow model to simulate periodic groundwater flow influenced by a sloping boundary, capillarity and vertical flows

Theoretical developments as well as field and laboratory data have shown the influence of the capillary fringe on water table fluctuations to increase with the fluctuation frequency. The numerical solution of a full, partially saturated flow equation can be computationally expensive. In this paper, the influence of the capillary fringe on water table fluctuations is simplified through its parameterisation into the storage coefficient of a fully-saturated groundwater flow model using the complex effective porosity concept [Nielsen, P., Perrochet, P., 2000. Water table dynamics under capillary fringes: experiments and modelling. Advances in Water Resources 23 (1), 503-515; Nielsen, P., Perrochet, P., 2000. ERRATA: water table dynamics under capillary fringes: experiments and modelling (Advances in Water Resources 23 (2000) 503-515). Advances in Water Resources 23, 907-908]. The model is applied to sand flume observations of periodic water table fluctuations induced by simple harmonic forcing across a sloping boundary, analogous to many beach groundwater systems. While not providing information on the moisture distribution within the aquifer, this approach can reasonably predict the water table fluctuations in response to periodic forcing across a sloping boundary. Furthermore, he coupled ground-surface water model accurately predicts the extent of the seepage face formed at the sloping boundary. (C) 2005 Elsevier Ltd. All rights reserved.

Sheet flow sediment transport under waves with acceleration skewness and boundary layer streaming

The effect of acceleration skewness on sheet flow sediment transport rates (q) over bar (s) is analysed using new data which have acceleration skewness and superimposed currents but no boundary layer streaming. Sediment mobilizing forces due to drag and to acceleration (similar to pressure gradients) are weighted by cosine and sine, respectively, of the angle phi(.)(tau)phi(tau) = 0 thus corresponds to drag dominated sediment transport, (q) over bar (s)similar to vertical bar u(infinity)vertical bar u(infinity), while phi(tau) = 90 degrees corresponds to total domination by the pressure gradients, (q) over bar similar to du(infinity)/dt. Using the optimal angle, phi = 51 degrees based on that data, good agreement is subsequently found with data that have strong influence from boundary layer streaming. Good agreement is also maintained with the large body of U-tube data simulating sine waves with superimposed currents and second-order Stokes waves, all of which have zero acceleration skewness. The recommended model can be applied to irregular waves with arbitrary shape as long as the assumption negligible time lag between forcing and sediment transport rate is valid. With respect to irregular waves, the model is much easier to apply than the competing wave-by-wave models. Issues for further model developments are identified through a comprehensive data review.

Large scale experiments on gravel and mixed beaches: Experimental procedure, data documentation and initial results

This paper provides information on the experimental set-up, data collection methods and results to date for the project Large scale modelling of coarse grained beaches, undertaken at the Large Wave Channel (GWK) of FZK in Hannover by an international group of researchers in Spring 2002. The main objective of the experiments was to provide full scale measurements of cross-shore processes on gravel and mixed beaches for the verification and further development of cross-shore numerical models of gravel and mixed sediment beaches. Identical random and regular wave tests were undertaken for a gravel beach and a mixed sand/gravel beach set up in the flume. Measurements included profile development, water surface elevation along the flume, internal pressures in the swash zone, piezometric head levels within the beach, run-up, flow velocities in the surf-zone and sediment size distributions. The purpose of the paper is to present to the scientific community the experimental procedure, a summary of the data collected, some initial results, as well as a brief outline of the on-going research being carried out with the data by different research groups. The experimental data is available to all the scientific community following submission of a statement of objectives, specification of data requirements and an agreement to abide with the GWK and EU protocols. (C) 2005 Elsevier B.V. All rights reserved.

Estimation of water retention curve from mercury intrusion porosimetry and van Genuchten model

The water retention curve (WRC) is a hydraulic characteristic of concrete required for advanced modeling of water (and thus solute) transport in variably saturated, heterogeneous concrete. Unfortunately, determination by a direct experimental method (for example, measuring equilibrium moisture levels of large samples stored in constant humidity cells) is a lengthy process, taking over 2 years for large samples. A surrogate approach is presented in which the WRC is conveniently estimated from mercury intrusion porosimetry (MIP) and validated by water sorption isotherms: The well-known Barrett, Joyner and Halenda (BJH) method of estimating the pore size distribution (PSD) from the water sorption isotherm is shown to complement the PSD derived from conventional MIP. This provides a basis for predicting the complete WRC from MIP data alone. The van Genuchten equation is used to model the combined water sorption and MIP results. It is a convenient tool for describing water retention characteristics over the full moisture content range. The van Genuchten parameter estimation based solely on MIP is shown to give a satisfactory approximation to the WRC, with a simple restriction on one. of the parameters.

Inhibitors of cyclo-oxygenase-2 and secretory phospholipase A2 preserve bone architecture following ovariectomy in adult rats

Epidemiological evidence and in vitro data suggest that COX-2 is a key regulator of accelerated remodeling. Accelerated states of osteoblast and osteoclast activity are regulated by prostaglandins in vitro, but experimental evidence for specific roles of cyclooxygenase-2 (COX-2) and secretory phospholipase A(2) (sPLA(2)) in activated states of remodeling in vivo is lacking. The aim of this study was to determine the effect of specific inhibitors of sPLA(2)-IIa and COX-2 on bone remodeling activated by estrogen deficiency in adult female rats. One hundred and twenty-four adult female Wistar rats were ovariectomized (OVX) or sham-operated. Rats commenced treatment 14 days after surgery with either vehicle, a COX-2 inhibitor (DFU at 0.02 mg/kg/day and 2.0 mg/kg/day) or a sPLA(2)-group-IIa inhibitor (KH064 at 0.4 mg/kg/day and 4.0 mg/kg/day). Treatment continued daily until rats were sacrificed at 70 days or 98 days post-OVX. The right tibiae were harvested, fixed and embedded in methylmethacrylate for structural histomorphometric bone analysis at the proximal tibial metaphysis. The specific COX-2 or sPLA(2) inhibitors prevented ovariectomy-induced (OVX-induced) decreases in trabecular connectivity (P < 0.05); suppressed the acceleration of bone resorption; and maintained bone turnover at SHAM levels following OVX in the rat. The sPLA2 inhibitor significantly suppressed increases in osteoclast surface induced by OVX (P < 0.05), while the effect of COX-2 inhibition was less marked. These findings demonstrate that inhibitors of COX-2 and sPLA(2)-IIa can effectively suppress OVX-induced bone loss in the adult rat by conserving trabecular bone mass and architecture through reduced bone remodeling and decreased resorptive activity. Moreover, we report an important role of sPLA(2)-IIa in osteoclastogenesis that may be independent of the COX-2 metabolic pathway in the OVX rat in vivo. (c) 2006 Elsevier Inc. All rights reserved.

Comparison of cellulose solubilisation rates in rumen and landfill leachate inoculated reactors

The aim of this study was to conduct a number of controlled digestions to obtain easily comparable cellulose solubilisation rates and to compare these rates to those found in the literature to see which operational differences were significant in affecting cellulose degradation during anaerobic digestion. The results suggested that differences in volumetric cellulose solubilisation rates were not indicative of the true performance of cellulose digestion systems. When cellulose solubilisation rates were normalised by the mass of cellulose in the reactor at each time step, the comparison of the rates became more meaningful. Cellulose solubilisation was surface area limited. Therefore, changes in the loading rate of cellulose to the reactor altered the volumetric solubilisation rate without changing the mass normalised rate. Comparison of mass normalised solubilisation rates from this study and the literature demonstrated that differences in reactor configuration and operational conditions did not significantly impact on the solubilisation rate whereas the difference in composition of the microbial communities showed a marked effect. This work highlights the importance of using appropriately normalised data when making comparisons between systems with differing operational conditions. (c) 2005 Elsevier Ltd. All rights reserved.

Field observations of instantaneous water slopes and horizontal pressure gradients in the swash-zone

Field observations of instantaneous water surface slopes in the swash zone are presented. For free-surface flows with a hydrostatic pressure distribution the surface slope is equivalent to the horizontal pressure gradient. Observations were made using a novel technique which in its simplest form consists of a horizontal stringline extending seaward from the beach face. Visual observation, still photography or video photography is then sufficient to determine the surface slope where the free-surface cuts the line or between reference points in the image. The method resolves the mean surface gradient over a cross-shore distance of 5 m or more to within +/- 0.001, or 1/20th -1/100th of typical beach gradients. In addition, at selected points and at any instant in time during the swash cycle, the water surface slope can be determined exactly to be dipping either seaward or landward. Close to the location of bore collapse landward dipping water surface slopes of order 0.05-0.1 occur over a very small region (order 0.5 m) at the blunt or convex leading edge of the swash. In the middle and upper swash the water surface slope at this leading edge is usually very close to horizontal or slightly seaward. Behind the leading edge, the water surface slope was observed to be very close to horizontal or dipping seaward at all times throughout the swash uprush. During the backwash the water surface slope was observed to be always dipping seaward, approaching the beach slope, and remained seaward until a new uprush edge or incident bore passed any particular cross-shore location of interest. The observations strongly Suggest that the swash boundary layer is subject to an adverse pressure gradient during uprush and a favourable pressure gradient during the backwash. Furthermore, assuming Euler's equations are a good approximation in the swash, the observations also show that the total fluid acceleration is negative (offshore) for almost the whole of the uprush and for the entire backwash. The observations are contrary to recent work suggesting significant shoreward directed accelerations and pressure gradients occur in the swash (i.e., delta u/delta t > 0 similar to delta p/delta x < 0), but consistent with analytical and numerical solutions for swash uprush and backwash. The results have important implications for sediment transport modelling in the swash zone.

Long wave generation by the shoaling and breaking of transient wave groups on a beach

This paper presents new laboratory data on the generation of long waves by the shoaling and breaking of transient-focused short-wave groups. Direct offshore radiation of long waves from the breakpoint is shown experimentally for the first time. High spatial resolution enables identification of the relationship between the spatial gradients of the short-wave envelope and the long-wave surface. This relationship is consistent with radiation stress theory even well inside the surf zone and appears as a result of the strong nonlinear forcing associated with the transient group. In shallow water, the change in depth across the group leads to asymmetry in the forcing which generates significant dynamic setup in front of the group during shoaling. Strong amplification of the incident dynamic setup occurs after short-wave breaking. The data show the radiation of a transient long wave dominated by a pulse of positive elevation, preceded and followed by weaker trailing waves with negative elevation. The instantaneous cross-shore structure of the long wave shows the mechanics of the reflection process and the formation of a transient node in the inner surf zone. The wave run-up and relative amplitude of the radiated and incident long waves suggests significant modification of the incident bound wave in the inner surf zone and, the dominance of long waves generated by the breaking process. It is proposed that these conditions occur when the primary short waves and bound wave are not shallow water waves at the breakpoint. A simple criterion is given to determine these conditions, which generally occur for the important case of storm waves.

Characterisation of sea-water intrusion in the Pioneer Valley, Australia using hydrochemistry and three-dimensional numerical modelling

Sea-water intrusion is actively contaminating fresh groundwater reserves in the coastal aquifers of the Pioneer Valley,north-eastern Australia. A three-dimensional sea-water intrusion model has been developed using the MODHMS code to explore regional-scale processes and to aid assessment of management strategies for the system. A sea-water intrusion potential map, produced through analyses of the hydrochemistry, hydrology and hydrogeology, offsets model limitations by providing an alternative appraisal of susceptibility. Sea-water intrusion in the Pioneer Valley is not in equilibrium, and a potential exists for further landward shifts in the extent of saline groundwater. The model required consideration of tidal over-height (the additional hydraulic head at the coast produced by the action of tides), with over-height values in the range 0.5-0.9 m giving improved water-table predictions. The effect of the initial water-table condition dominated the sensitivity of the model to changes in the coastal hydraulic boundary condition. Several salination processes are probably occurring in the Pioneer Valley, rather than just simple landward sea-water advancement from modern sources of marine salts. The method of vertical discretisation (i.e. model-layer subdivision) was shown to introduce some errors in the prediction of watertable behaviour.

Reply to comment by A. G. J. Hilberts and P. A. Troch on "Influence of capillarity on a simple harmonic oscillating water table: Sand column experiments and modeling"

We thank Hilberts and Troch [2006] for their comment on our paper [Cartwright et al, 2005]. Before proceeding with our specific replies to the comments we would first like to clarify the definitions and meanings of equations (1)-(3) as presented by Hilberts and Troch [2006]. First, equation (1) is the fundamental definition of the (complex) effective porosity as derived by Nielsen and Perrochet [2000]. Equations (2) and (3), however, represent the linear frequency response function of the water table in the sand column responding to simple harmonic forcing. This function, which was validated by Nielsen and Perrochet [2000], provides an alternative method for estimating the complex effective porosity from the experimental sand column data in the absence of direct measurements of h_(tot) (which are required if equation (1) is to be used).

Beach face and berm morphodynamics fronting a coastal lagoon

This study documents two different modes of berm development: (I) vertical growth at spring tides or following significant beach cut due to substantial swash overtopping, and (2) horizontal progradation at neap tides through the formation of a proto-berm located lower and further seaward of the principal berm. Concurrent high-frequency measurements of bed elevation and the associated wave runup distribution reveal the details of each of these berm growth modes. In mode I sediment is eroded from the inner surf and lower swash zone where swash interactions are prevalent. The net transport of this sediment is landward only, resulting in accretion onto the upper beach face and over the berm crest. The final outcome is a steepening of the beach face gradient, a change in the profile shape towards concave and rapid vertical and horizontal growth of the berm. In mode 2 sediment is eroded from the lower two-thirds of the active swash zone during the rising tide and is transported both landward and seaward. On the falling tide sediment is eroded from the inner surf and transported landward to backfill the zone eroded on the rising tide. The net result is relatively slow steepening of the beach face, a change of the profile shape towards convex, and horizontal progradation through the formation of a neap berm. The primary factor determining which mode of berm growth occurs is the presence or absence of swash overtopping at the time of sediment accumulation on the beach face. This depends on the current phase of the spring-neap tide cycle, the wave runup height (and indirectly offshore wave conditions) and the height of the pre-existing berm. A conceptual model for berm morphodynamics is presented, based on sediment transport shape functions measured during the two modes of berm growth. (c) 2006 Elsevier B.V. All rights reserved.

Effects of iron additions on filament growth and productivity of the cyanobacterium Lyngbya majuscula

The bioavailability of iron, in combination with essential macronutrients such as phosphorus, has been hypothesised to be linked to nuisance blooms of the toxic cyanobacterium Lyngbya majuscula. The present laboratory study used two biological assay techniques to test whether various concentrations of added iron (inorganic and organically chelated) enhanced L. majuscula filament growth and productivity (C-14-bicarbonate uptake rate). Organically chelated iron (FeEDTA) with adequate background concentrations of phosphorus and molybdenum caused the largest increases (up to 4.5 times the control) in L. majuscula productivity and filament growth. The addition of inorganic iron (without added phosphorus or molybdenum) also stimulated L. majuscula filament growth. However, overall the FeEDTA was substantially and significantly more effective in promoting L. majuscula growth than inorganic iron (FeCl3). The organic chelator (EDTA) alone and molybdenum alone also enhanced L. majuscula growth but to a lesser extent than the chelated iron. The results of the present laboratory study support the hypothesis that iron and chelating organic compounds may be important in promoting blooms of L. majuscula in coastal waters of Queensland, Australia.

Submerged and unsubmerged natural hydraulic jumps in a bedrock step-pool mountain channel (Fig. 1 Classical hydraulic jump with partially developed inflow conditions)

Fig. 1. Classical hydraulic jump with partially developed inflow conditions. F1 = 13.6, V1 = 4.7 m/s, B = 0.25 m, h = 0.020 mm, d1 = 0.012 mm, Q = 14 L/s. Photo courtesy of Dr. Hubert Chanson. published in: Geomorphology Volume 82, Issues 1-2, 6 December 2006, Pages 146-159 The Hydrology and Geomorphology of Bedrock Rivers doi:10.1016/j.geomorph.2005.09.024 Submerged and unsubmerged natural hydraulic jumps in a bedrock step-pool mountain channel Brett L. Vallé and Gregory B. Pasternacka

On the modelling of wave breaking and set-up on coral reefs

An extended refraction-diffraction equation [Massel, S.R., 1993. Extended refraction-diffraction equation for surface waves. Coastal Eng. 19, 97-126] has been applied to predict wave transformation and breaking as well as wave-induced set-up on two-dimensional reef profiles of various shapes. A free empirical coefficient alpha in a formula for the average rate of energy dissipation [epsilon(b)] = (alpha rho g omega/8 pi)(root gh/C)(H-3/h) in the modified periodic bore model was found to be a function of the dimensionless parameter F-c0 = (g(1.25)H(0)(0.5)T(2.5))/h(r)(1.75), proposed by Gourlay [Gourlayl M.R., 1994. Wave transformation on a coral reef. Coastal Eng. 23, 17-42]. The applicability of the developed model has been demonstrated for reefs of various shapes subjected to various incident wave conditions. Assuming proposed relationships of the coefficient alpha and F-c0, the model provides results on wave height attenuation and set-up elevation which compare well with experimental data. (C) 2000 Elsevier Science B.V. All rights reserved.