Two sets of higher-order Boussinesq-type equations for water waves

Based on the classical Boussinesq model by Peregrine [Peregrine, D.H., 1967. Long waves on a beach. J. Fluid Mech. 27 (4), 815–827], two parameters are introduced to improve dispersion and linear shoaling characteristics. The higher order non-linear terms are added to the modified Boussinesq equations. The non-linearity of the Boussinesq model is analyzed. A parameter related to h/L₀ is used to improve the quadratic transfer function in relatively deep water. Since the dispersion characteristic of the modified Boussinesq equations with two parameters is only equal to the second-order Padé expansion of the linear dispersion relation, further improvement is done by introducing a new velocity vector to replace the depth-averaged one in the modified Boussinesq equations. The dispersion characteristic of the further modified Boussinesq equations is accurate to the fourth-order Padé approximation of the linear dispersion relation. Compared to the modified Boussinesq equations, the accuracy of quadratic transfer functions is improved and the shoaling characteristic of the equations has higher accuracy from shallow water to deep water.     

A coupled numerical model for simulation of wave breaking and hydraulic performances of a composite seawall

A numerical model is developed by combining a porous flow model and a two-phase flow model to simulate wave transformation in porous structure and hydraulic performances of a composite type low-crest seawall. The structure consists of a wide submerged reef, a porous terrace at the top and an impermeable rear wall. The porous flow model is based on the extended Navier-Stokes equations for wave motion in porous media and k−ε turbulence equations. The two-phase flow model combines the water domain with the air zone of finite thickness above water surface. A unique solution domain is established by satisfying kinematic boundary condition at the interface of air and water. The free surface advection of water wave is modeled by the volume of fluid method with newly developed fluid advection algorithm. Comparison of computed and measured wave properties shows reasonably good agreement. The influence of terrace width and structure porosity is investigated based on numerical results. It is concluded that there exist optimum value of terrace width and porosity that can maximize hydraulic performances. The velocity distributions inside and in front of the structure are also investigated.     

Simplified higher-order Boussinesq equations: I. Linear simplifications

In this paper, we derive and test simplified higher-order Boussinesq equations, i.e., higher-order Boussinesq equations which only show lower-order terms. Simplifications are performed linearly for flat beds and slopes of O(∇h). With proper coefficient choice, dispersion and shoaling properties are found to be good, while interior fluid velocities show relatively greater error at high wavenumbers.The resulting sets of equations are found to be variants of already-existing equations, which may be easily modified to improve performance. The new equations have dispersion identical to previous results but significantly improved shoaling.     

Observation and measurement of the bottom boundary layer flow in the prebreaking zone of shoaling waves

In this paper, the characteristics of the bottom boundary layer flow induced by nonlinear, asymmetric shoaling waves, propagating over a smooth bed of 1/15 uniform slope, is experimentally investigated. Flow visualization technique with thin-layered fluorescent dye was first used to observe the variation of the flow structure, and a laser Doppler velocimeter was then employed to measure the horizontal velocity, U.The bottom boundary layer flow is found to be laminar except within a small region near the breaking point. The vertical distribution of the phase-averaged velocity U at each phase is non-uniform, which is directly affected by the mean velocity, . The magnitude of increases from zero at the bottom to a local positive maximum at about z/δ2.02.5 (where z is the height above the sloping bottom and δ is the Stokes layer thickness), then decreases gradually to zero at z/δ6.07.0 approximately, and finally becomes negative as z/δ increases further. Moreover, as waves propagate towards shallower water, the rate of increase in the maximum onshore oscillating velocity component is greater than that of the offshore counterpart except near the breaking point. The free stream velocities in the profiles of the maximum onshore and offshore oscillating velocity components, and are found to appear at z/δ≥6.0. This implies that, if the Stokes layer thickness is used as a length scale, the non-dimensionalized boundary layer thickness remains constant in the pre-breaking zone. Although is greater than and the asymmetry of the maximum free stream velocities (i.e. ) increases with decrease of water depth, a universal similar profile can be established by plotting z/δ versus ( ) or ( ). The final non-dimensional profile is symmetric and unique for the distributions of the maximum onshore and offshore oscillating velocity components within the bottom boundary layer, which are induced by nonlinear, asymmetric shoaling waves crossing the pre-breaking zone.     

A new form of higher order Boussinesq equations

On the basis of the higher order Boussinesq equations derived by the author (1999), a new form of higher order Boussinesq equations is developed through replacing the depth-averaged velocity vector by a new velocity vector in the equations in order to increase the accuracy of the linear dispersion, shoaling property and nonlinear characteristics of the equations. The dispersion of the new equations is accurate to a [4/4] Pade expansion in kh. Compared to the previous higher order Boussinesq equations, the accuracy of quadratic transfer functions is improved and the shoaling property of the equations have higher accuracy from shallow water to deep water.     

Boussinesq–Green–Naghdi rotational water wave theory

Using Boussinesq scaling for water waves while imposing no constraints on rotationality, we derive and test model equations for nonlinear water wave transformation over varying depth. These use polynomial basis functions to create velocity profiles which are inserted into the basic equations of motion keeping terms up to the desired Boussinesq scaling order, and solved in a weighted residual sense. The models show rapid convergence to exact solutions for linear dispersion, shoaling, and orbital velocities; however, properties may be substantially improved for a given order of approximation using asymptotic rearrangements. This improvement is accomplished using the large numbers of degrees of freedom inherent in the definitions of the polynomial basis functions either to match additional terms in a Taylor series, or to minimize errors over a range. Explicit coefficients are given at O(μ²) and O(μ⁴), while more generalized basis functions are given at higher order. Nonlinear performance is somewhat more limited as, for reasons of complexity, we only provide explicitly lower order nonlinear terms. Still, second order harmonics may remain good to kh ≈ 10 for O(μ⁴) equations. Numerical tests for wave transformation over a shoal show good agreement with experiments. Future work will harness the full rotational performance of these systems by incorporating turbulent and viscous stresses into the equations, making them into surf zone models.     

Settleable and Non-Settleable Suspended Sediments in the Ogeechee River Estuary, Georgia, U.S.A.

Suspended particle dynamics were investigated in the Ogeechee River Estuary during neap tide in July 1996. Samples were operationally separated into ‘ truly suspended ’ (settling velocity <0·006 cm s⁻¹) and ‘ settleable ’ (settling velocity >0·006 cm s⁻¹) fractions over the course of a tidal cycle to determine whether these two fractions were comprised of particles with differing biological and chemical characteristics. Total suspended sediment, organic carbon and nitrogen, chlorophyll a and phaeopigment concentrations were measured in each fraction, as well as rates of bacterial hydrolytic enzyme activity [β-1,4-glucosidase (βGase) and β-xylosidase (βXase)]. The majority of the suspended sediment (by weight) was in the truly suspended fraction; all measured parameters were largely associated with this fraction as well. When compared to the settleable material, the truly suspended material was significantly higher in % POC (5·7±0·6 vs. 3·9±1·8), % chlorophyll (0·07±0·02 vs. 0·03±0·01), % phaeopigment (0·030±0·006 vs. 0·018±0·012), and weight-specific maximal uptake rates (V_maxper mg suspended sediment) of both enzymes (1·8±0·4 vs. 0·7± 0·2 nmol mg⁻¹ h⁻¹βGase and 1·1±0·3vs . 0·3±0·2 nmol mg⁻¹ h⁻¹βXase), providing clear evidence for a qualitative distinction between the two fractions. These results are interpreted to mean that the more organic-rich, biologically active material associated with the suspended fraction is likely to have a different fate in this Estuary, as ‘ truly suspended ’ sediments will be readily transported whereas ‘ settleable ’ sediments will settle and be resuspended with each tide. These types of qualitative differences should be incorporated into models of particle dynamics in estuaries.     

Prediction of wave pressures on smooth impermeable seawalls

Simple prediction methods are proposed to estimate the wave induced pressures on smooth impermeable seawalls. Based on the physics of the wave structure interaction, the sloped seawall is divided into a total of five zones (zones 1, 2 and 3 during run-up (corresponding pressures are called as positive pressures) and zones 4 and 5 during run-down (corresponding pressures are called negative pressures)) (Fig. 1). Zone 1 (0<z<d−H_i/2), where the wave pressure is governed by the partial reflection and phase shift; Zone 2 (d−H_i/2<z<d), where the effect of wave breaking and turbulence is significant; Zone 3 (d<z<Run-up height), where the pressure is induced by the run-up water; Zone 4 (Run-down<z<d), where the wave pressure is caused by the run-down effect and Zone 5 (0<z<d-Run down), where the negative wave pressures are due to partial reflection and phase shift effects. Here d is the water depth at the toe of the seawall, H_i is the incident wave height and z is the vertical elevation with toe of the seawall as origin and z is positive upward. For wave pressure prediction in zones 1 and 5, the empirical formula proposed by Ahrens et al. (1993) to estimate the wave reflection and Sutherland and Donoghue's recommendations (1998) for the estimation of phase shift of the waves caused by the sloped structures are used. Multiple regression analysis is carried out on the measured pressure data and empirical formulas are proposed for zones 2, 3 and 4. The recommendations of Van der Meer and Breteler (1990) and Schüttrumpf et al. (1994) for the prediction of wave run-down are used for pressure prediction at zone 4. Comparison of the proposed prediction formulas with the experimental results reveal that the prediction methods are good enough for practical purposes. The present study also shows a strong relation between wave reflection, wave run-up, wave run-down and phase shift of waves on wave pressures on the seawalls.     

Sediment–water interactions of natural oestrogens under estuarine conditions

The natural human female hormones oestrone and 17β-oestradiol have been implicated in the disruption of endocrine systems in some wildlife adjacent to sewage effluents. The sorption behaviour of these two compounds under estuarine conditions was studied by spiking either 2.55 μg of oestrone or 2.65 μg of 17β-oestradiol in kinetic experiments. In equilibrium experiments, 3 ng of oestrone or 3.2 ng of 17β-oestradiol was added in each of the centrifuge tubes. Sorption onto sediment particles was relatively slow, with sorption equilibrium being reached in about 70 and 170 h for oestrone and 17β-oestradiol, respectively. The effects of a variety of environmental parameters on sorption were studied including salinity, sediment concentration (SC), the presence of a third phase, particle size and, also, surfactant concentrations. Results show that although salinity did not induce any statistically significant effect on the sorption of 17β-oestradiol, it did statistically enhance the sorption of oestrone, and a salting constant of 0.3 l mol⁻¹ was derived. The partition coefficient for both compounds decreased with increasing sediment concentration, a phenomenon that has been widely reported and attributed to the presence of colloids (which could enhance dissolved concentrations). In this paper, the true partition coefficients for sediment particles (K_p^true) and colloidal particles (K_c^true) have been calculated, and a K_p^true value of 141 and 102 ml g⁻¹ was obtained for oestrone and 17β-oestradiol, respectively. In addition, K_c^true values for oestrone (222×10² ml g⁻¹) and 17β-oestradiol (135×10² ml g⁻¹) were two orders of magnitude higher than their respective K_p^true values, suggesting that the colloidal particles are significantly stronger sorbents for natural oestrogens than sediment particles. Particles of different sizes were found to have different partition coefficients due to the strong relationships between partition coefficients for the two compounds and particulate organic carbon (POC) contents and specific surface areas (SSAs). The presence of a surfactant was shown to reduce the partition coefficients for the two compounds, although its concentrations being used were higher than those normally found in the natural environment.     

Determination of Henry's law constants for hexachlorocyclohexanes in distilled water and artificial seawater as a function of temperature

Henry's law constants were determined for α- and γ-hexachlorocyclohexane (HCH) as a function of temperature (0.5–45°C) in artificial seawater (SW; 30‰) and distilled water (DW) using the gas stripping method. Water samples (1–5 ml) were withdrawn from the stripping vessel during the stripping process (30–360 h), solvent extracted and analyzed by gas chromatography—electron-capture detection. The effect of bubbling depth was checked to ensure that bubbles leaving the system were at equilibrium with HCHs in the aqueous phase. Henry's law constants determined at 35 and 45°C in SW were significantly higher (P≤ 0.05) than in DW for both α- and γ-HCH, but not at lower temperatures. The slopes (m) and intercepts (b) of log H vs. 1 / T plots were: α-HCH (DW, 0.5–45°C); m = −2810 ± 110, B = 9.31 ± 0.38; α-HCH (SW, 0.5–23°C); M = −2969 ± 218, B = 9.88 ± 0.76; γ-HCH (DW, 0.5–45°C); M = −2382 ± 160, B = 7.54 ± 0.54; γ-HCH (SW, 0.5–23°C); M = −2703 ± 276, B = 8.68 ± 0.96. Henry's law constants determined in this study compared well with those calculated from reported vapor pressure and solubility data.     

A phase-averaged Boussinesq model with effective description of carrier wave group and associated long wave evolution

From the phase-resolving improved Boussinesq equations (Beji and Nadaoka, Ocean Engineering 23 (1996) 691), a phase-averaged Boussinesq model for water waves is derived by more effectively describing carrier wave groups and accompanying long wave evolution with less CPU time. Linear shoaling characteristics of carrier wave equations are investigated and found to agree exactly with the analytical expression obtained from the constancy of energy flux for the improved Boussinesq equations themselves, showing that the present model equations are the results of a consistent derivation procedure regarding energy considerations. Numerical simulations of the derived equations for the single wave group and narrow-banded random waves show the validity of the present model and its high performance, especially on the CPU time.     

Spectral characteristics of high shallow water waves

The spectral characteristics of shallow water waves with significant wave height more than 2 m based on the data collected along the Indian coast is examined. It was found that the value of Joint North Sea Wave Project (JONSWAP) parameters (α and γ) increases with significant wave height and mean wave period and decreases with spectral peak period. The estimated average value (0.0027 and 1.63) of the JONSWAP parameters, α and γ were less than the generally recommended values of 0.0081 and 3.3, respectively. By carrying out a multi-regression analysis, an empirical equation is arrived relating the JONSWAP parameters with significant wave height, peak wave period and mean wave period. It was found that the Scott spectra underestimate the maximum spectral energy of high waves. The study shows that the measured wave spectra can be represented by JONSWAP spectra with the JONSWAP parameters estimated based on the equation proposed in this paper.     

An investigation on internal solitary waves in a two-layer fluid: Propagation and reflection from steep slopes

Experimental investigations on internal solitary wave (ISW) propagation and their reflection from a smooth uniform slope were conducted in a two-layered fluid system with a free surface. A 12-meter-long wave flume was in use which incorporated with: (1) a movable vertical gate for generating ISW; (2) six ultrasonic probes for measuring the fluctuation of an ISW; and (3) a steep uniform slope (from one of θ=30°, 50°, 60°, 90°, 120° and 130°) much greater than those ever published in the literature. This paper presents the wave profile properties of the ISW recorded in the flume and their nonlinear features in comparison with the existing Korteweg de Vries (KdV) and modified Korteweg-de Vries (MKdV) theories. Experimental results show that the KdV theory is suitable for most small-amplituded ISWs and MKdV theory is appropriate for the reflected ISWs from various uniform slopes. In addition, both the amplitude-based reflection coefficient and reflected energy approach a constant value asymptotically when plotted against the slope and the characteristic length ratio, respectively. The reflected wave amplitudes calculated from experimental data agree well with those reported elsewhere. The optimum reflection coefficient is found within the limit of 0.85 for wave amplitude, among the test runs from steep normal slope of 30° to inverse angle of 130°, and around 0.75 for the reflected wave energy, produced by an ISW on a vertical wall.     

The solubility of CaCO3 in seawater at 2°C based upon in-situ sampled pore water composition

Analyses of the concentration product (Ca²⁺) × (CO₃²⁻) in the pore waters of marine sediments have been used to estimate the apparent solubility products of sedimentary calcite (K′_SPc) and aragonite (K′_SPa) in seawater. Regression of the data gives the relation In K′^P_SPc = 1.94 × 10⁻³ δP − 14.59 The 2°C, 1 atm value of K′_SPc is, then, 4.61 × 10⁻⁷ mol² l⁻². The pressure coefficient yields a at 2°C of −43.8 cm³ atm⁻¹. A single station where aragonite is present in the sediments gives a value of K′_SPa = 9.2 × 10⁻⁷ (4°C, 81 atm). The calcite data are very similar to those determined experimentally by Ingle et al. (1973) for K′_SPc at 2°C and 1 atm. The calculated is also indistinguishable from the experimental results of Ingle (1975) if is assumed to be independent of pressure.     

Nitrogen dynamics within a wind-driven eddy

Wind-driven cyclonic eddies are hypothesized to relieve nutrient stress and enhance primary production by the upward displacement of nutrient-rich deep waters into the euphotic zone. In this study, we measured nitrate (NO₃⁻), particulate carbon (PC), particulate nitrogen (PN), their stable isotope compositions (δ¹⁵N-NO₃⁻, δ¹³C-PC and δ¹⁵N-PN, respectively), and dissolved organic nitrogen (DON) within Cyclone Opal, a mature wind-driven eddy generated in the lee of the Hawaiian Islands. Sampling occurred in March 2005 as part of the multi-disciplinary E-Flux study, approximately 4–6 weeks after eddy formation. Integrated NO₃⁻ concentrations above 110 m were 4.8 times greater inside the eddy (85.8±6.4 mmol N m⁻²) compared to the surrounding water column (17.8±7.8 mmol N m⁻²). Using N-isotope derived estimates of NO₃⁻ assimilation, we estimated that 213±59 mmol m⁻² of NO₃⁻ was initially injected into the upper 110 m Cyclone Opal formation, implying that NO₃⁻ was assimilated at a rate of 3.75±0.5 mmol N m⁻² d⁻¹. This injected NO₃⁻ supported 68±19% and 66±9% of the phytoplankton N demand and export production, respectively. N isotope data suggest that 32±6% of the initial NO₃⁻ remained unassimilated. Self-shading, inefficiency in the transfer of N from dissolved to particulate export, or depletion of a specific nutrient other than N may have led to a lack of complete NO₃⁻ assimilation. Using a salt budget approach, we estimate that dissolved organic nitrogen (DON) concentrations increased from eddy formation (3.8±0.4 mmol N m⁻²) to the time of sampling (4.0±0.09 mmol N m⁻²), implying that DON accumulated at rate of 0.83±1.3 mmol N m⁻² d⁻¹, and accounted for 22±15% of the injected NO₃⁻. Interestingly, no significant increase in suspended PN and PC, or export production was observed inside Cyclone Opal relative to the surrounding water column. A simple N budget shows that if 22±15% of the injected NO₃⁻ was shunted into the DON pool, and 32±6% is unassimilated, then 46±16% of the injected NO₃⁻ remains undocumented. Alternative loss processes within the eddy include lateral exchange of injected NO₃⁻ along isopycnal surfaces, remineralization of PN at depth, as well as microzooplankton grazing. A 9-day time series within Cyclone Opal revealed a temporal depletion in δ¹⁵N-PN, implying a rapid change in the N source. A change in NO₃⁻ assimilation, or a shift from NO₃⁻ fueled growth to assimilation of a ¹⁵N-deplete N source, may be responsible for such observations.     

The speciation of Fe(II) and Fe(III) in natural waters

The interactions of Fe(II) and Fe(III) with the inorganic anions of natural waters have been examined using the specific interaction and ion pairing models. The specific interaction model as formulated by Pitzer is used to examine the interactions of the major components (Na⁺, Mg²⁺, Ca²⁺, K⁺, Sr²⁺, Cl⁻, SO₄⁻, HCO₃⁻, Br⁻, CO₃²⁻, B(OH)₄⁻, B(OH)₃ and CO₂) of seawater and the ion pairing model is used to account for the strong interaction of Fe(II) and Fe(III) with major and minor ligands (Cl⁻, SO₄²⁻, OH⁻, HCO₃⁻, CO₃²⁻ and HS⁻) in the waters. The model can be used to estimate the activity and speciation of iron in natural waters as a function of composition (major sea salts) and ionic strength (0 to 3 M). The measured stability constants (K_FeX^*) of Fe(II) and Fe(III) have been used to estimate the thermodynamic constants (K_FeX) and the activity coefficient of iron complexes (γ_FeX) with a number of inorganic ligands in NaClO₄ medium at various ionic strengths: In(K_FeX/γ_Feγ_X) = InK_FeX − In(γ_FeX) The activity coefficients for free ions (γ_Fe, γ_x) needed for this extrapolation have been estimated from the Pitzer equations. The activity coefficients of the ion pairs have been used to determine Pitzer parameters (B_FeX, B_FeX⁰, C_FeX^φ) for the iron complexes. These results make it possible to estimate the stability constants for the formation of Fe(II) and Fe(III) complexes over a wide range of ionic strengths and in different media. The model has been used to determine the solubility of Fe(III) in seawater as a function of pH. The results are in good agreement with the measurements of Byrne and Kester and Kuma et al. When the formation of Fe organic complexes is considered, the solubility of Fe(III) in seawater is increased by about 25%.     

Does transported seagrass provide an important trophic link in unvegetated, nearshore areas?

The contribution of detritus from seagrass and other primary producers to faunal production in unvegetated nearshore areas was examined primarily using stable isotopes. Fish, macroinvertebrates, meiofauna and primary producers (seagrasses, macroalgae, seston and benthic microalgae) were sampled from sites in south-western Australia. All samples were analysed for δ¹³C and δ¹⁵N values and fish gut contents were determined. δ¹³C values for seagrasses in the region were high compared to other macrophytes, ranging from 49.9 to −8.2‰ compared to −19.8 to −12.6‰ for macroalgae. The δ¹⁵N values ranged between 4.0 and 7.7‰ for the red, brown and green algae, and between 3.2 and 5.9‰ for seagrasses. Seston and benthic microalgae samples had a mean δ¹³C value of −12.8 and −14.0‰, respectively, and their δ¹⁵N values were comparable to the macroalgae. All invertebrate fauna had mean δ¹³C values considerably lower than seagrasses. However, individual samples harpacticoid copepods and polychaetes had a value as high as −11.7‰. δ¹⁵N values for consumers were higher than those of the primary producers, except for copepods and amphipods. The δ¹³C values for fish had a relatively small range, between −16.6 and −13.1‰, and the δ¹⁵N values of fish were elevated compared to the invertebrates and primary producers, ranging mostly between 10.0 and 12.6‰. Mixing model analysis based on δ¹³C values indicated that seagrass ranked low as a likely carbon source for all invertebrates other than harpacticoid copepods at a single site and some samples of polychaetes. The δ¹³C values for fish were similar to those of a combination of harpacticoid and calanoid copepods, amphipods and polychaetes. The consumption of harpacticoid copepods by some fish species indicates that Amphibolis and Posidonia species in south-western Australia can contribute to the food web of unvegetated nearshore areas as detritus, but brown algae is likely to make a greater contribution. At least for the time of year that was sampled, the flow of detrital seagrass material into the foodweb may be mediated by specific detrivores, in this case harpactacoid copepods, rather than by all detritivores.     

The distribution and δC of dissolved organic carbon and its humic fraction in estuaries of southeastern USA

In this study, we examine the distribution and carbon stable isotope signature of dissolved organic carbon (DOC) and humic substances (HS) along a salinity gradient in the Altamaha and Satilla River estuaries. The maximum DOC concentrations in the Altamaha and Satilla were 10 and 29 mg C l⁻¹, respectively, though concentrations were similar at the mouth of both estuaries. There was a decrease in HS content of DOC from 50 to 80% at the head of the estuaries to 10% at salinities higher than 30‰. The δ¹³C DOC varied between −25.5 and −19‰ and between −27 and −21‰ in the Altamaha and Satilla estuaries, respectively. The tendency towards more depleted δ¹³C DOC in the Satilla, especially in the lower salinity portion of this estuary, suggests greater terrestrial inputs in the Satilla than in the Altamaha. Seasonal fluctuations were observed in the form of increased (two to three times) range in DOC concentration, heavier δ¹³C DOC and increased proportion of estuarine–marine-derived DOC (average enrichment of δ¹³C DOC from +1 to +2) during low river flow (July–October). The δ¹³C HS in both rivers showed a similar trend, but was consistently more depleted than DOC, with an average range from −28 to −24.5‰. This suggests that HS have larger proportions of terrestrial components (a maximum of >60% at the mouth of the estuary) than DOC. The less depleted δ¹³C values of DOC in comparison with HS indicate a different source for the non-humic (non-HS) component of DOC (range in δ¹³C non-HS, −22 to −16‰). That source could either be the decomposition of detrital material derived from saltmarsh environments or microalgal-derived DOC of estuarine or marine origins.     

Food web structure in a near-pristine mangrove area of the Australian Wet Tropics

Carbon and nitrogen isotopic composition was used to identify the main sources of carbon and describe the main trophic pathways in Deluge Inlet, a near-pristine mangrove estuary in tropical north Queensland, Australia. Producers' δ¹³C varied from −28.9‰ for mangroves to −18.6‰ for seagrass. Animals were also well separated in δ¹³C (−25.4‰ to −16.3‰ for invertebrates and −25.2‰ to −17.2‰ for fish), suggesting considerable differences in ultimate sources of carbon, from a substantial reliance on mangrove carbon to an almost exclusive reliance on seagrass. In general, invertebrates had lower δ¹⁵N than fish, indicating lower trophic levels. Among fish, δ¹⁵N values reflected well the assumed trophic levels, as species from lower trophic levels had lower δ¹⁵N than species from higher trophic levels. Trophic levels and trophic length were estimated based on δ¹⁵N of invertebrate primary consumers (6.1‰), with results suggesting a food web with four trophic levels. There was also evidence of a high level of diet overlap between fish species, as indicated by similarities in δ¹³C for fish species of higher trophic levels. Stable isotope data was also useful to construct a general model for this food web, where five main trophic pathways were identified: one based on both mangrove and microphytobenthos, one on plankton, two on both microphytobenthos and seagrass, and one based mainly on seagrass. This model again suggested the presence of four trophic levels, in agreement with the value calculated based on the difference in δ¹⁵N between invertebrate primary consumers and top piscivores.