Finite Water Research Articles

Gravity wave interaction with an articulated submerged plate resting on a Winkler foundation

Surface gravity wave interaction with an articulated flexible submerged plate in the presence of lateral compressive force is investigated within the framework of blocking dynamics, assuming that the submerged plate is resting on a uniform Winkler foundation. The problem is studied considering small-amplitude plate response and linearised water wave theory in finite water depth. The loci of the dispersion relation reveal the occurrence of wave blocking in the submerged plate mode for a range of wave frequency and compressive force when the submerged plate is resting on a Winker foundation. However, in the absence of the Winkler foundation, no wave blocking occurs in the plate mode irrespective of the values of compressive force, and plane wave propagation in plate mode does not happen for particular values of compressive force. Four propagating wavenumbers exist within the blocking frequencies, of which one is in the surface mode, and others are in the submerged plate mode. Thus, to account for the four propagating wave modes, the existing solution approach for a pair of propagating wave modes is modified in an appropriate manner within the limit of blocking frequencies. Consequently, the energy relation is obtained using Green’s identity, in which the reflection and transmission coefficients are a combination of the amplitudes of different reflected and transmitted wave modes and the associated energy transfer rates. The reflection coefficient in the submerged plate mode jumps from one to zero for very small values of frequency due to the introduction of the Winkler foundation in the presence of compressive force. In addition, zero wave reflection occurs for a higher frequency range with an increase in the values of the Winkler constant. Removable discontinuities are observed at the blocking and saddle points, whilst jump discontinuities occur in the reflection and transmission coefficients due to the change of incident wave mode within the blocking frequencies. Linear time-dependent displacements in surface and submerged plate modes are presented prior to the blocking limit.

Hydroelastic Response to Oblique Wave Incidence on a Floating Plate with a Submerged Perforated Base

A hydroelastic model is developed of a floating flexible structure in the presence of a submerged perforated base connected with mooring lines under oblique wave action. Using the velocity decomposition method, the analytical solution of the referred model is obtained in finite water depth. The convergence of the analytical solution for different oblique wave incidences is examined, and the present results of deflection amplitude are compared with experimental datasets and the numerical results available in the literature. The effects of oblique wave incidence, along with various design parameters on the reflection, transmission, and dissipation coefficients, as well as structural displacements, are analysed through hydroelastic analysis. Further, the effect of oblique incidence angle on the free oscillation hydroelastic waves in two wave modes is investigated by deriving the free motion velocity potential in a wave basin.

Hydration effect of selected atmospheric gases with finite water clusters: A quantum chemical investigation towards atmospheric implications

Water vapor in atmosphere is ubiquitous, and it varies according to geographical locations. Various toxic and non-toxic gases co-exist with water vapor/moisture in the atmosphere. This computational study addresses the fact that how those gases interact with water vapor. We have done quantum chemical density functional theory calculations to probe the interaction of certain gases with a finite number of water molecules in gas phase with various functionals/basis sets. An ensemble of 14 gas molecules comprising various diatomic, triatomic, and polyatomic gases have been chosen for the investigations. The intermolecular interactions are understood from the interaction energy, electrostatic potential, frontier molecular orbitals, energy gap, and natural bond orbital analyses. Furthermore, quantum molecular descriptors such as electronegativity, chemical potential, chemical hardness and electrophilicity index are calculated to have deep insight on chemical nature of the gas molecules. Additionally, we have done implicit solvent modelling using PCM, and the corresponding solvation energies have been calculated. Interestingly, all the calculations and analyses have projected the similar results that Cl2, SO2, and NH3 have very high interaction with the water clusters. To mimic various altitudes (0 km, 5 km and 10 km) in the atmosphere, thermochemistry calculations have been carried out at different temperature and pressure values. The Gibbs free energies of formation suggest that the hydration of Cl2 is higher followed by O2, SO2 and NH3 at all altitudes. Remarkably, it is found that the formation of hydrated clusters of Cl2 and O2 with 4H2O are thermodynamically favourable. On the other hand, SO2 and NH3 requires 5H2O and 3H2O to form thermodynamically favourable clusters. In summary, it is anticipated that this kind of extensive computational studies facilitate to understand the structural, electronic, chemical and thermochemical properties of hydrated atmospheric gases that leads to the formation of prenucleation clusters followed by atmospheric aerosols.

No Pure Capillary Solitary Waves Exist in 2D Finite Depth

We prove that the 2D finite depth capillary water wave equations admit no solitary wave solutions. This closes the existence/non-existence problem for solitary water waves in 2D, under the classical assumptions of incompressibility and irrotationality, and with the physical parameters being gravity, surface tension and the fluid depth.

Ship’s Wake on a Finite Water Depth in the Presence of a Shear Flow

The ship’s wake in the presence of a shear flow of constant vorticity at a finite water depth is investigated by expanding the Whitham-Lighthill kinematic theory. It has been established that the structure of a wave ship wake radically depends on Froude number Fr (in terms of water depth) and especially on the critical Froude number Frcr, which depends on the magnitude and direction of the shear flow. At its subcritical values Fr<Frcr two types of waves are presented: long transverse and short divergent waves inside the wedge area with an angle depending on Fr For the supercritical range Fr>Frcr only divergent waves are presented inside the wake region. Critical Froude number Frcr is variable and mostly depends on collinear with the ship path component of the shear flow: it decreases with the unidirectional shear flow and increases on the counter shear current. The wedge angle of the ship wake expands with an increase in the unidirectional shear flow and narrows in the oncoming flow in the subcritical mode of the ship’s motion Fr<Frcr. Wake angle decreased with Froude number for Fr>Frcr and only divergent waves with the crests almost collinear with ship path are finally presented in the narrow ship wake. For a critical value of the Froude number Fr=Frcr, the ship’s wake has a total wedge angle of 180° with waves directed parallel to the ship’s motion. The presence of a shear flow crossing the path of the ship gives a strong asymmetry to the wake. An increase in the perpendicular shear flow leads to an increase in the difference between the angles of the wake arms.

Attenuation of wave force on a floating dock by multiple porous breakwaters

The impact of an array of porous breakwaters for reducing wave forces on a floating dock is studied based on the small-amplitude water wave theory in finite water depth. The breakwater is approximated by a porous bottom-standing rectangular structure and an impermeable floating rectangular structure is placed at a finite distance on the lee-side representing a dock. The physical problem is solved analytically using Eigenfunction expansion method and numerically using a hybrid element multi domain boundary element method. Two scenarios are considered: (i) wave scattering by N porous structures and the floating dock and (ii) wave reflection by a dock attached to the impermeable wall in presence of N porous structures. The reflection, transmission and dissipation coefficients are evaluated and analyzed for various structural and wave parameters. The study reveals that the Bragg reflection occurs in the case of wave scattering by an array of porous structures in the absence of floating dock. It is also found that in the absence of dock N−2 sub-harmonic peaks occurs whereas, in the presence of dock the effect of Bragg resonance is clearly evident on hydrodynamic coefficients. Also, the study concludes that for four structures with larger height, 100% of wave energy can be dissipated and thus mitigate the wave force on the floating rigid dock. Furthermore, the height and width of the porous structure and spacing between the structures play a vital role to protect the floating platform.

A framework for irrigation performance assessment using WaPOR data: the case of a sugarcane estate in Mozambique

Abstract. The growing competition for finite land and water resources and the need to feed an ever-growing population require new techniques to monitor the performance of irrigation schemes and improve land and water productivity. Datasets from FAO's portal to monitor Water Productivity through Open access Remotely sensed derived data (WaPOR) are increasingly applied as a cost-effective means to support irrigation performance assessment and identify possible pathways for improvement. This study presents a framework that applies WaPOR data to assess irrigation performance indicators, including uniformity, equity, adequacy, and land and water productivity differentiated by irrigation method (furrow, sprinkler, and centre pivot) at the Xinavane sugarcane estate, Mozambique. The WaPOR data on water, land, and climate are in near-real time and spatially distributed, with the finest spatial resolution in the area of 100 m. The WaPOR data were first validated agronomically by examining the biomass response to water, and then the data were used to systematically analyse seasonal indicators for the period 2015 to 2018 on ∼8000 ha. The WaPOR-based yield estimates were found to be comparable to the estate-measured yields with ±20 % difference, a root mean square error of 19±2.5 t ha−1 and a mean absolute error of 15±1.6 t ha−1. A climate normalization factor that enables the spatial and temporal comparison of performance indicators are applied. The assessment highlights that in Xinavane no single irrigation method performs the best across all performance indicators. Centre pivot compared to sprinkler and furrow irrigation shows higher adequacy, equity, and land productivity but lower water productivity. The three irrigation methods have excellent uniformity (∼94 %) in the four seasons and acceptable adequacy for most periods of the season except in 2016, when a drought was observed. While this study is done for sugarcane in one irrigation scheme, the approach can be broadened to compare other crops across fields or irrigation schemes across Africa with diverse management units in the different agroclimatic zones within FAO WaPOR coverage. We conclude that the framework is useful for assessing irrigation performance using the WaPOR dataset.

An Iterative Method for Interaction of Hydro-Elastic Waves with Several Vertical Cylinders of Circular Cross-Sections

The problem of ice loads acting on multiple vertical cylinders of circular cross-sections frozen in an ice cover of infinite extent is studied. The loads are caused by a flexural-gravity wave propagating in the ice cover towards the rigid bottom-mounted cylinders. This is a three-dimensional linearized problem of hydroelasticity with finite water depth. The flow under the ice is potential and incompressible. The problem is solved by the vertical mode method combined with an iterative method. The velocity potential is written with respect to each cylinder and is expanded into the Fourier series. The algorithm of the problem solving is reduced to calculations of the Fourier coefficients of the velocity potential. Numerical results for the forces acting on four circular cylinders are presented for different ice thicknesses, incident wave angles and cylinder spacing. The obtained wave forces are compared with the results by others. Good agreement is reported.

3D hydroelastic modelling of fluid–structure interactions of porous flexible structures

A 3D hydroelastic model subjected to linear wave interaction with horizontal flexible floating and submerged porous structures is developed. The dispersion relation of the aforesaid problem is derived based on Green’s functions approach in water of finite and infinite depths. Three-dimensional Fourier-type expansion formulae for the velocity potentials associated with orthogonal mode-coupling relations are derived in a channel of finite and infinite water depths of finite width. A real physical problem of surface gravity wave interaction with a moored floating and submerged porous plate in finite water depth is analysed by the expansion formula to validate the usefulness of the current method. The numerical accuracy of the present numerical results is checked via convergence test. Further, the effect of different design parameters on the hydroelastic response of floating and a submerged porous plate is studied by analysing the deflection amplitude and structural deformation. It is observed that the present analysis could be useful for a greater insight to design a multi-use flexible floating system.

The solitonic solutions of finite depth long water wave models

The nonlinear Fokas and breaking soliton equations are important modeling equations for coastal and ocean waves, such as long water waves and tsunami waves. Moreover, these models have effective applications for simulating surface and internal waves in oceans and rivers, wave packets in finite depth water, and Riemann wave propagation interactions. By exploiting the enhanced modified simple equation approach, in this article, we have established further generic, radical, and standard solitons to the erstwhile nonlinear framework with some parameters. The reputed schematic solitons, such as bell-shaped, periodic, cuspon, compacton, plane-shaped, singular soliton, kink, and other solitons, are devised for varied scores of parameters. The accomplished results might assist in better understanding the dynamics of coastal waves modulated by the formerly acknowledged couple of nonlinear models. We have studied the impacts of physical parameters and propagation rate on wave structure and affirmed their role in changing the waveform. Three- and two-dimensional diagrams are sketched to interpret the context profiles of the obtained solitary wave solutions. The established solutions demonstrate the applicability and competence of the approach to investigating nonlinear models.

Higher-order gap resonance between two identical fixed barges: A study on the effect of water depth

Nonlinear piston-mode fluid resonance in the gap formed by two identical fixed barges in close proximity is investigated using a two-dimensional (2D) fully nonlinear numerical wave tank. To delve into the effect of water depth on higher-order resonances in the gap, consistent models are employed to describe the incident waves and wave-structure interactions for finite and shallow water depths. In contrast to previous studies, strong fourth- and fifth-order nonlinear gap resonances are observed under the action of shallow-water waves, resulting in significant higher-harmonic responses that are comparable to the corresponding first and second harmonics. For a given wave height, those waves are found to be more critical than the finite-depth waves, which are capable of evoking second- or third-order gap resonance. Highly oscillatory behavior is observed at the trough under the action of shallow-water waves. This is ascribed to the higher-harmonic diffraction effects, breaking the “perfect cancellation” between the incident-wave harmonics, which should, otherwise, produce smooth and flatter wave trough. Unlike what a linear diffraction theory will predict, the gap response does not behave completely in a quasi-static manner under long cnoidal waves, and the higher harmonics generally show larger phase differences to the corresponding incident-wave components until the resonance occurs. The present study suggests that the water-depth effect and higher harmonics should be consistently accounted for in the design and analysis of side-by-side marine operations in coastal environments involving piston-mode gap responses.

Forest cover lessens the impact of drought on streamflow in Puerto Rico

AbstractTropical regions are experiencing high rates of forest cover loss coupled with changes in the volume and timing of rainfall. These shifts can compromise streamflow and water provision, highlighting the need to identify how forest cover influences streamflow generation under variable rainfall conditions. Although rainfall is the key driver of streamflow regimes, the role of forests is less clear, particularly in tropical regions where forest loss is an ongoing risk. Forest cover loss alters evapotranspiration, rainfall infiltration and storage, and may increase stream ecosystem vulnerability to rainfall extremes. Puerto Rico, an island with spatially heterogenous forest cover and a marked geographic rainfall gradient, is projected to experience more frequent droughts and flash flooding. Using 15‐min streamflow data collected between 2005 and 2016 from 20 US Geological Survey stream gages and 3‐hourly Multi‐Source Weighted‐Ensemble Precipitation rainfall estimates, we utilized flow‐duration curves and linear mixed regression models to examine the role of forest cover in regulating the timing and volume of streamflow. The mixed model approach helps to account for differences in watershed characteristics. We determined the effects of rainfall and forest cover on low and peak flows in Puerto Rican streams, then evaluated changes in these relationships under dry and wet antecedent rainfall conditions. Watersheds with high forest cover had consistently greater low and peak streamflow than deforested ones under all rainfall conditions, although the effect was more marked during wet antecedent conditions, suggesting that peak flow is largely the result of saturation excess overland flow. During dry antecedent rainfall conditions, highly forested watersheds had higher streamflow than deforested ones, suggesting greater hillslope storage and release may also be at play. Our results demonstrate that forest cover generated a net increase in hillslope infiltration and storage and may lessen drought impacts on streamflow in Puerto Rico. Resilience to prolonged drought may be limited by finite water storage potential in this steep, mountainous setting, highlighting maintenance of forest cover as an important water management strategy to increase infiltration.

Modified ECa – ECe protocols for mapping soil salinity under micro-irrigation

Climate change will increase the frequency and intensity of drought in water-scarce agricultural areas that rely on irrigation. The increased strain on finite water resources for irrigated agriculture will cause a shift from sprinkler and flood irrigation to micro-irrigation. Micro-irrigation results in complex 3-dimensional salinity patterns. Current field-scale apparent soil electrical conductivity (ECa) directed soil sampling protocols and guidelines are inadequate for mapping the complex local-scale 3-dimensional nature of salinity resulting from water applications by micro-irrigation systems (i.e., drip, buried drip, micro sprinklers, bubblers, etc.). A field study was conducted to develop additional ECa-directed soil sampling guidelines to map local- and field-scale variability in salinity under drip-irrigation systems within a commercial nut production orchard (i.e., pistachio orchard) using hard (i.e., salinity or ECe, electrical conductivity of the saturation extract) and soft data (i.e., geospatial ECa measurements), which required an accurate ECa – ECe calibration. The revised ECa-directed soil sampling guidelines for drip irrigation on a mature pistachio orchard indicate that a single soil core should be taken 0.9–1.2 m perpendicular to the drip line within the tree root system, rather than at the drip line, to improve the ECa – ECe calibration. Calibration of ECa to ECe, improved from R2 = 0.25 to R2 = 0.73 for site Flores D01, and from R2 = 0.17 to R2 = 0.72 for site Flores D05. The improved guidelines broaden the scope of application of ECa-directed soil sampling to map field-scale salinity on orchards under drip irrigation. The information presented is of value and benefit to producers, agriculture consultants, irrigation practitioners, cooperative extension specialists, Natural Resources Conservation Service field staff, and soil and water researchers.

Hydrodynamic analysis of ship manoeuvrability in shallow water using high-fidelity URANS computations

The manoeuvring performance of a ship in shallow water is substantially different from its performance in deep water, attributed to shallow water effects caused by the presence of a finite water depth. Without a doubt a ship will navigate in areas of shallow water at various times during its operational life (such as when approaching harbours or ports), which underscores the importance of understanding the shallow water effects on ship manoeuvrability. In the present paper, the manoeuvrability of the KRISO Container Ship (KCS) model in different shallow water conditions was comprehensively analysed by means of the unsteady Reynolds-Averaged Navier-Stokes (URANS) computations coupled with the equations of rigid body motion with full six degrees of freedom (6DOF). A dynamic overset grid approach was implemented to allow the ship hull to move in 6DOF in a computational domain and to enable the rudder to be deflected according to a rudder controller for free-running manoeuvres. A series of manoeuvring simulations were performed in shallow waters with water depth to draft ratios varying between 1.2 and 4.0, and partially validated with the available experimental data from a free running test. The numerical results revealed that the ship advance, transfer, and tactical diameter mainly increased with the decrease in the ratio of water depth to draft, closely associated with the complicated interactions between the hull wake, boundary layer, propeller, vortex, and sea floor.

The Radiation Problem of a Submerged Oblate Spheroid in Finite Water Depth Using the Method of the Image Singularities System

This study examines the hydrodynamic parameters of a unique geometry that could be used effectively for wave energy extraction applications. In particular, we are concerned with the oblate spheroidal geometry that provides the advantage of a wider impact area on waves, closer to the free surface where the hydrodynamic pressure is higher. In addition, the problem is formulated and solved analytically via a method that is robust and most importantly very fast. In particular, we develop an analytical formulation for the radiation problem of a fully submerged oblate spheroid in a liquid field of finite water depth. The axisymmetric configuration of the spheroid is considered, i.e., the axis of symmetry is perpendicular to the undisturbed free surface. In order to solve the problem, the method of the image singularities system is employed. This method allows for the expansion of the velocity potential in a series of oblate spheroidal harmonics and the derivation of analytical expressions for the hydrodynamic coefficients for the translational degrees of freedom of the body. Numerical simulations and validations are presented taking into account the slenderness ratio of the spheroid, the immersion below the free surface and the water depth. The validations ensure the correctness and the accuracy of the proposed method. Utilizing the same approach, the whole process is implemented for a disc as well, given that a disc is the limiting case of an oblate spheroid since its semi-minor axis approaches zero.

Scattering of Water Waves by Very Large Floating Structure in the Presence of a Porous Box

Abstract We investigate the effectiveness of a porous box in attenuating the structural response of a very large floating structure (VLFS). Assuming the water depth to be finite and small amplitude water wave theory, the physical problem is formulated by employing Darcy’s law for flow past a porous structure. The boundary value problem is reduced to a system of linear algebraic equations with the aid of matched eigenfunction expansion method. Further, these simultaneous equations are solved numerically to compute physical quantities. The mathematical model is validated through a comparison with the theoretical results available in the literature. The reflection, transmission, and dissipation coefficients, elastic plate deflection, forces acting on the box, and free-surface elevation are computed. The reflection, transmission, and dissipation coefficients exhibit an oscillatory pattern for large values of wavenumber irrespective of the structural parameters of the box. It is highlighted that a porous box with moderate values of the porous-effect parameter is effective in reducing strain and shear force on the VLFS. Further, the results on elevation and VLFS deflection depict that the suitable porous-effect parameter values for the box reduce the resultant wave amplitude of the elastic plate deflection as well as the amplitude in the lee side of the VLFS. The study reveals that the width and height of the porous box are critical toward the trapping of incident waves inside the box and dissipating the maximum amount of incident wave energy in reduction of wave transmission in the lee side of the structure and thereby attenuating the structural response of the VLFS.

A GPU-Accelerated and LTS-Based Finite Volume Shallow Water Model

This paper presents a GPU (Graphics Processing Unit)-accelerated and LTS (Local-time-Step)-based finite volume Shallow Water Model (SWM). The model performance is compared against the other five model versions (Single CPU versions with/without LTS, Multi-CPU versions with/without LTS, and a GPU version) by simulating three flow scenarios: an idealized dam-break flow; an experimental dam-break flow; a field-scale scenario of tidal flows. Satisfactory agreements between simulation results and the available measured data/reference solutions (water level, flow velocity) indicate that all the six SWM versions can well simulate these challenging shallow water flows. Inter-comparisons of the computational efficiency of the six SWM versions indicate the following. First, GPU acceleration is much more efficient than multi-core CPU parallel computing. Specifically, the speed increase in the GPU can be as high as a hundred, whereas those for multi-core CPU are only 2–3. Second, implementing the LTS can bring considerable reduction: the additional maximum speed-ups can be as high as 10 for the single-core CPU/multi-core CPU versions, and as high as five for the GPU versions. Third, the GPU + LTS version is computationally the most efficient in most cases; the multi-core CPU + LTS version may run as fast as a GPU version for scenarios over some intermediate number of cells.

Merging of the Case 2 Regional Coast Colour and Maximum-Peak Height chlorophyll-a algorithms: validation and demonstration of satellite-derived retrievals across US lakes

Water quality monitoring is relevant for protecting the designated, or beneficial uses, of water such as drinking, aquatic life, recreation, irrigation, and food supply that support the economy, human well-being, and aquatic ecosystem health. Managing finite water resources to support these designated uses requires information on water quality so that managers can make sustainable decisions. Chlorophyll-a (chl-a, µg L−1) concentration can serve as a proxy for phytoplankton biomass and may be used as an indicator of increased anthropogenic nutrient stress. Satellite remote sensing may present a complement to in situ measures for assessments of water quality through the retrieval of chl-a with in-water algorithms. Validation of chl-a algorithms across US lakes improves algorithm maturity relevant for monitoring applications. This study compares performance of the Case 2 Regional Coast Colour (C2RCC) chl-a retrieval algorithm, a revised version of the Maximum-Peak Height (MPH(P)) algorithm, and three scenarios merging these two approaches. Satellite data were retrieved from the MEdium Resolution Imaging Spectrometer (MERIS) and the Ocean and Land Colour Instrument (OLCI), while field observations were obtained from 181 lakes matched with U.S. Water Quality Portal chl-a data. The best performance based on mean absolute multiplicative error (MAEmult) was demonstrated by the merged algorithm referred to as C15−M10 (MAEmult = 1.8, biasmult = 0.97, n = 836). In the C15−M10 algorithm, the MPH(P) chl-a value was retained if it was > 10 µg L−1; if the MPH(P) value was ≤ 10 µg L−1, the C2RCC value was selected, as long as that value was < 15 µg L−1. Time-series and lake-wide gradients compared against independent assessments from Lake Champlain and long-term ecological research stations in Wisconsin were used as complementary examples supporting water quality reporting requirements. Trophic state assessments for Wisconsin lakes provided examples in support of inland water quality monitoring applications. This study presents and assesses merged adaptations of chl-a algorithms previously reported independently. Additionally, it contributes to the transition of chl-a algorithm maturity by quantifying error statistics for a number of locations and times.

Predicting the breaking onset of wave groups in finite water depths based on the Hilbert-Huang transform method

This experimental study focuses on the nonlinear characteristics and breaking onset of extreme waves. The critical value of the first-order instantaneous frequency f1 obtained by the Hilbert-Huang transform method is proposed to determine the wave breaking onset. Specifically, when the normalized instantaneous frequency f1/fp ≥ 2 (fp denotes the dominant frequency), the wave breaks; otherwise, it is less likely to break. For the wave groups considered in this study, the normalized maximum crest height shows an exponential growth as the normalized instantaneous frequency increases. Moreover, it was found that there is a close logarithmic growth relationship between the normalized instantaneous frequency and the local wave steepness. Thus, the instantaneous frequency can be an effective indicator for evaluating extreme wave nonlinearity.

Performance analysis of a coast – OWC wave energy converter integrated system

In this paper, a cylindrical dual-chamber oscillating water column (OWC) wave energy converter semi-embedded in a coastline or breakwater is proposed. A theoretical model based on linear potential flow theory is developed to evaluate the power absorption performance of the integrated system in the finite water depth. According to the matched eigenfunction expansions, the fluid domain is divided into five sub-domains and unknown coefficients in the diffraction and radiation problems are separately solved by matching the velocity and pressure between adjacent sub-domains. A linear power take-off system considering air compressibility is adopted to connect air volume flux with the chamber pressure. The reliability of this model is assessed by general identities (i.e., far-field relations). Then the model is performed to investigate the effects of wave conditions, draft, breadth and opening angle of the chambers on the wave power extraction. It is shown that the proposed integrated system can improve the total hydrodynamic efficiency in both regular and irregular waves.