A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches

The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, epsilon(N) = alphaepsilon cot beta (in which beta is the beach slope, alpha is the amplitude parameter and epsilon is the shallow water parameter) and are limited to tan(-1) (alphaepsilon) much less than beta less than or equal to pi/2. In this paper, a new higher-order solution to the non-linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations. The relative difference between the linear solution and the present solution increases as 6 and a increase, and reaches 7% of the linear solution. (C) 2003 Elsevier Ltd. All rights reserved.

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.

Response of the salt-freshwater interface in a coastal aquifer to a wave-induced groundwater pulse: field observations and modelling

Field observations on an unconfined coastal aquifer showed that a groundwater pulse, generated by it moderate (significant wave height, H-sig similar to 4.5 m) wave/storm event, induced significant oscillations in the salt-freshwater interface of the order of several metres in the horizontal direction. A dynamic sharp-interface model is developed to quantify the mechanism of these interface oscillations. The model uses the 50% seawater salinity contour as the location of the equivalent sharp-interface. The model was calibrated against the observed groundwater table fluctuations. It predicted reasonably well the interface oscillations with a slight over-prediction of the oscillation magnitude and a steepening of the interface. The neglect of mixing in the salt-freshwater mixing zone by the sharp-interface model is suggested as a possible contributor to the discrepancies between the model predictions and observations. In contrast with the significant wave effects, there was no observable response of the interface to diurnal or semidiurnal tides. (C) 2004 Elsevier Ltd. All rights reserved.

Pumice rafting and faunal dispersion during 2001-2002 in the Southwest Pacific: record of a dacitic submarine explosive eruption from Tonga

A new influx of sea-rafted pumice reached the eastern coast of Australia in October 2002, approximately 1 year after a felsic, shallow-marine explosive eruption at a previously unknown volcano (0403-091) along the Tofua volcanic arc (Tonga). The eruption produced floating pumice rafts that first became stranded in Fiji in November 2001, approximately I month after the eruption. Strandings of sea-rafted pumice along shorelines have been the only record of products from this submarine explosive eruption at the remote, submerged volcano. Computed drift trajectories of the sea-rafted pumice using numerical models of southwest Pacific surface wind fields and ocean currents indicate two cyclonic systems disturbed the drift of pumice to eastern Australia, as well as the importance of the combined wave and direct wind effect on pumice trajectory. Pumice became stranded along at least two-thirds (>2000 km) of the coastline of eastern Australia, being deposited on beaches during a sustained period of fresh onshore winds. Typical amounts of pumice initially stranded on beaches were 500-4000 individual clasts per in, and a minimum volume estimate of pumice that arrived to eastern Australia is 1.25 x 10(5) m(3). Pumice was beached below maximum tidal/storm surge levels and was quickly reworked back into the ocean, such that the concentration of beached pumice rapidly dissipated within weeks of the initial stranding, and little record of this stranding event now exists. Most stranded pumice clasts ranged in size from 2 to 5 cm in diameter; the largest measured clasts were 10 cm in Australia and 20 cm in Fiji. The pumice has a low phenocryst content (3500 km) and period of pumice floatation (greater than or equal to1 year), confirm the importance of sea-rafted pumice as a long-distance dispersal mechanism for marine organisms including marine pests and harmful invasive species. Billions of individual rafting pumice clasts can be generated in a single small-volume eruption, such as observed here, and the geological implications for the transport of sessile taxa over large distances are significant. An avenue for future research is to examine whether speciation events and volcanicity are linked; the periodic development of globalism for some taxa (e.g., corals, gastropods, bryozoa) may correlate in time and/or space with voluminous silicic igneous events capable of producing >10(6) km(3) of silicic pumice-rich pyroclastic material and emplaced into ocean basins. (C) 2004 Elsevier B.V. All rights reserved.

Mine waste beach profile and flow resistance equations

Four mine waste beach longitudinal profile equations are compared theoretically and in statistical analyses of profile data from 64 field and laboratory beaches formed by mine tailings, co-disposed coal mine wastes, and sand. All four equations fit the profile data well. The best performing equation both accounts for particle sorting and satisfies hydraulic constraints, and the combination of assumptions underlying it is considered to best represent the processes occurring on mine waste beaches. Combining these assumptions with the Lacey normal equation leads to a variant of the Manning resistance equation. Features that it is desirable to incorporate in theoretical and numerical models of mine waste beaches are listed.

Response of coastal groundwater table to offshore storms

Large groundwater table fluctuations were observed in a coastal aquifer during an offshore storm. The storm induced significant changes of the mean shoreline elevation, characterized by a pulse-like oscillation. This pulse propagated in the aquifer, resulting in the water table fluctuations. A general analytical solution is derived to quantify this new mechanism of water table fluctuation. The solution is applied to field observations and is found to be able to predict reasonably well the observed storm-induced water table fluctuations. Based on the analytical solution, the damping characteristics and phase shift of the oscillation as it propagates inland are examined.

New approximation for free surface flow of groundwater: capillarity correction

An existing capillarity correction for free surface groundwater flow as modelled by the Boussinesq equation is re-investigated. Existing solutions, based on the shallow flow expansion, have considered only the zeroth-order approximation. Here, a second-order capillarity correction to tide-induced watertable fluctuations in a coastal aquifer adjacent to a sloping beach is derived. A new definition of the capillarity correction is proposed for small capillary fringes, and a simplified solution is derived. Comparisons of the two models show that the simplified model can be used in most cases. The significant effects of higher-order capillarity corrections on tidal fluctuations in a sloping beach are also demonstrated. (c) 2004 Elsevier Ltd. All rights reserved.

Coral mortality increases wave energy reaching shores protected by reef flats: Examples from the Seychelles

In the granitic Seychelles, many shores and beaches are fringed by coral reef flats which provide protection to shores from erosion by waves. The surfaces of these reef flats support a complex ecology. About 10 years ago their seaward zones were extensively covered by a rich coral growth, which reached approximately to mean low water level, but in 1998 this was largely killed by seawater warming. The resulting large expanses of dead coral skeletons in these locations are now disintegrating, and much of the subsequent modest recovery by new coral recruitment was set back by further mortalities. A mathematical model of wave energy reaching shorelines protected by coral reef flats has been applied to 14 Seychelles reefs. It is derived from equations which predict: (1) the raised water level, or wave set-up, on reef flats resulting from wave breaking, which depends upon offshore wave height and period, depth of still water over the reef flat and the reef crest profile, and (2) the decay of energy from reef edge to shoreline that is affected by width of reef flat, surface roughness, sea level rise and 'pseudo-sea level rise' created by increased depth resulting from disintegration of coral colonies. The model treats each reef as one entity, but because biota and zonation on reef flats are not homogenous, all reefs are divided into four zones. In each, cover by both living and dead biota was estimated for calculation of parameters, and then averaged to obtain input data for the model. All possible biological factors were taken into account, such as the ability of seagrass beds to grow upwards to match expected sea level rise, reduction in height of the reef flat in relation to sea level as zones of dead corals decay, and the observed 'rounding' of reef crests as erosion removes corals from those areas. Estimates were also made of all these factors for a time approximately a decade ago, representing a time before the mass coral mortality, and for approximately a decade in the future when the observed rapid state of dead coral colony disintegration is assumed to have reached an end point. Results of increased energy over the past decade explain observations of erosion in some sites in the Seychelles. Most importantly, it is estimated that the rise in energy reaching shores protected by fringing reefs will now accelerate more rapidly, such that the increase expected over the next decade will be approximately double than that seen over the past decade. (c) 2005 Elsevier Ltd. All rights reserved.

Steepness expansion for free surface flows in coastal aquifers

Free surface flow of groundwater in aquifers has been studied since the early 1960s. Previous investigations have been based on the Boussinesq equation, derived from the non-linear kinematic boundary condition. In fact, the Boussinesq equation is the zeroth-order equation in the shallow-water expansion. A key assumption in this expansion is that the mean thickness of the aquifer is small compared with a reference length, normally taken to be the linear decay length. In this study, we re-examine the expansion scheme for free surface groundwater flows, and propose a new expansion wherein the shallow-water assumption is replaced by a steepness assumption. A comparison with experimental data shows that the new model provides a better prediction of water table levels than the conventional shallow-water expansion. The applicable ranges of the two expansions are exhibited. (c) 2004 Elsevier B.V. All rights reserved.

Evaluating trends in abundance of immature green turtles, Chelonia mydas, in the Greater Caribbean

Many long-lived marine species exhibit life history traits. that make them more vulnerable to overexploitation. Accurate population trend analysis is essential for development and assessment of management plans for these species. However, because many of these species disperse over large geographic areas, have life stages inaccessible to human surveyors, and/or undergo complex developmental migrations, data on trends in abundance are often available for only one stage of the population, usually breeding adults. The green turtle (Chelonia mydas) is one of these long-lived species for which population trends are based almost exclusively on either numbers of females that emerge to nest or numbers of nests deposited each year on geographically restricted beaches. In this study, we generated estimates of annual abundance for juvenile green turtles at two foraging grounds in the Bahamas based on long-term capture-mark-recapture (CMR) studies at Union Creek (24 years) and Conception Creek (13 years), using a two-stage approach. First, we estimated recapture probabilities from CMR data using the Cormack-Jolly-Seber models in the software program MARK; second, we estimated annual abundance of green turtles. at both study sites using the recapture probabilities in a Horvitz-Thompson type estimation procedure. Green turtle abundance did not change significantly in Conception Creek, but, in Union Creek, green turtle abundance had successive phases of significant increase, significant decrease, and stability. These changes in abundance resulted from changes in immigration, not survival or emigration. The trends in abundance on the foraging grounds did not conform to the significantly increasing trend for the major nesting population at Tortuguero, Costa Rica. This disparity highlights the challenges of assessing population-wide trends of green turtles and other long-lived species. The best approach for monitoring population trends may be a combination of (1) extensive surveys to provide data for large-scale trends in relative population abundance, and (2) intensive surveys, using CMR techniques, to estimate absolute abundance and evaluate the demographic processes' driving the trends.