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A large Courant–Friedrichs–Lewy (CFL) algorithm is presented for the explicit, finite volume solution of hyperbolic systems of conservation laws, with a focus on the shallow water equations. The Riemann problems used in the flux computation are determined using averaging kernels that extend over several computational cells. The usual CFL stability constraint is replaced with a constraint involving the kernel support size. This makes the method unconditionally stable with respect to the size of the computational cells, allowing the computational mesh to be refined locally to an arbitrary degree without altering solution stability. The practical implementation of the method is detailed for the shallow water equations with topographical source term. Computational examples report applications of the method to the linear advection, Burgers and shallow water equations. In the case of sharp bottom discontinuities, the need for improved, well‐balanced discretisations of the geometric source term is acknowledged. [ABSTRACT FROM AUTHOR]

We perform the so‐called rigid lid limit on different shallow water models such as the abcd Bousssinesq systems or the Green–Naghdi equations. To do so, we consider an appropriate nondimensionalization of these models where two small parameters are involved: the shallowness parameter μ$\mu$ and a parameter ε$\epsilon$ which can be interpreted as a Froude number. When the parameter ε$\epsilon$ tends to zero, the surface deformation formally goes to the rest state, hence the name rigid lid limit. We carefully study this limit for different topologies. We also provide rates of convergence with respect to ε$\epsilon$ and careful attention is given to the dependence on the shallowness parameter μ$\mu$. [ABSTRACT FROM AUTHOR]

In the present paper, a new model equation with the Coriolis effect is derived from the incompressible and irrotational two-dimensional shallow water in the equatorial region according to the formal asymptotic procedures. This new model equation is called the rotational b -family of equations, which generalize the rotational Camassa-Holm equation. Subsequently, the local well-posedness and the blow-up criteria for the rotational b -family of equations on the Sobolev space H s , for s > 3 / 2 , are presented. Additionally, we study the effects of the Coriolis force and nonlocal higher nonlinearities on wave-breaking phenomena for both the rotational b -family of equations and the rotational Camassa-Holm equation. [ABSTRACT FROM AUTHOR]

The coast of Bahia state is the longest along the Brazilian coastline, and there are significant knowledge gaps concerning its estuarine fish fauna. Thus, there is a need to provide extensive coverage of the estuarine ichthyofauna of Bahia to provide an updated checklist of its fishes, which could function as a database for the management of such biodiversity. Therefore, this study aimed to characterize three different important estuarine systems (Camamu, Todos os Santos Bay, and Caravelas) in Bahia to contribute information on the ichthyofauna in shallow areas of the state. We recorded 29 orders, 54 families, 101 genera, and 147 species of fish. The families with the highest number of species were Sciaenidae and Carangidae, with twelve and nine species, respectively, followed by Gobiidae and Engraulidae, each with eight species. In terms of abundance in the northern region, the orders Atheriniformes (28.80%), Pleuronectiformes (15.92%), Clupeiformes (14.20%), and Gerreiformes (13.91%) predominated. In the Central region, Gerreiformes (21.55%), Tetraodontiformes (17.94%), Gobiiformes (12.83%), and Clupeiformes (8.94%) were the most representative. In the southern region, the orders Clupeiformes (57.48%), Mugiliformes (14.09%), Atheriniformes (4.10%), Lutjaniformes (3.97%), Gerreiformes (3.60%), and Carangiformes (2.23%) predominated. The region was characterized by a high representation of guilds of marine migrant species, followed by marine, estuarine, and freshwater visitors. [ABSTRACT FROM AUTHOR]

This paper introduces a unified model for layered rotating shallow‐water (RSW) and quasi‐geostrophic (QG) equations, based on the intrinsic relationship between these two sets of equations. We propose a novel formulation of the QG equations as a projection of the RSW equations. This formulation uses the same prognostic variables as RSW, namely velocity and layer thickness, thereby restoring the proximity of these two sets of equations. It provides direct access to the ageostrophic velocities embedded within the geostrophic velocities resolved by the QG equations. This approach facilitates the study of differences between QG and RSW using a consistent numerical discretization. We demonstrate the effectiveness of this formulation through examples including vortex shear instability, double‐gyre circulation, and a simplified North Atlantic configuration. Plain Language Summary: In this paper, we present a straightforward way to connect two important sets of ocean equations: the layered rotating shallow‐water (RSW) equations and the quasi‐geostrophic (QG) equations. We consider a unified method to formulate the QG equations as a projection of the RSW equations. This method uses the same variables as the RSW equations, making it easier to understand how these two sets of equations relate to each other. Our approach also provides direct access to important velocity information that is usually hidden in the QG equations. This allows us to study the differences between the QG and RSW equations using the same numerical techniques. We show the benefits of our model with two examples: a vortex shear instability and a double‐gyre configuration. This work provides a useful tool for the understanding of ocean dynamics. Developing a unified numerical framework for nested models can greatly simplify oceanographic modeling and enhance accuracy. Key Points: Introduces QG equations as a projection of rotating shallow‐water (RSW) equations using the same prognostic variablesAllows consistent nested numerical methods for both QG and RSW equationsSuccessfully tested on vortex shear instability, double‐gyre circulation, and a simplified North Atlantic configuration [ABSTRACT FROM AUTHOR]

In order to study the supercritical flow in a curved channel of a rectangular cross section, the classical shallow water equations in a cylindrical coordinate system based on the mass and momentum laws that take into account the friction and bottom slope are used. The obtained mathematical model forms nonlinear partial differential equations of first-order. For simplification, a linearization of the partial differential equations (PDEs) set is performed using small perturbation approach valid for weak bends (axial curvature radius extremely larger than the channel width). The governing equations with well-posed initial and boundary conditions were solved for a rectangular bend channel flow by applying the method of characteristics that is capable of transforming the hyperbolic partial differential equations to a system of ordinary differential equations (ODEs). The proposed model is tested and validated by comparing the results with broad available experimental data reported in the literature, and particular attention was paid to the wave maximum and its location. Comparisons indicate a reasonable agreement between the results obtained for the maximum flow depth along the outer channel wall. However, the model prediction is only reliable for a small relative curvature. Despite the model limitations, the results show the reliability and accuracy of the proposed approach for practical design purposes. [ABSTRACT FROM AUTHOR]

A combined method of wave superposition and finite element is proposed to solve the radiation noise of targets in shallow sea. Taking the sound propagation of spherical sound source in shallow sea as an example, the radiation sound field of the spherical sound source is equivalent to the linear superposition of the radiation sound field of several internal point sound sources, and then the radiated noise induced by spherical sound source can be predicted quickly. The accuracy and efficiency of the method are verified by comparing with the numerical results of finite element method, and the rapid prediction of underwater radiated noise of cylindrical shell is carried out based on the method. The results show that compared with the finite element method, the relative error of the calculation results under different simulation conditions does not exceed 0.1%, and the calculation time is about 1/10 of the finite element method, so this method can be used to solve the radiated noise of shallow underwater targets. [ABSTRACT FROM AUTHOR]

Shallow-water mooring chains of floating offshore wind turbines pose challenges such as nonlinear tension characteristics, high cost and prominent fatigue issues, which seriously hinder the large-scale use of floating wind power. Based on the hydrological and meteorological data of an offshore wind farm in the South China Sea, a sensitivity analysis of the mooring chain fatigue of a semi-submersible floating offshore wind turbine in shallow water was conducted with different environmental loads and mooring chain design parameters. It was found that mooring fatigue is mainly caused by the wave condition within diagonal distribution of the wave dispersion diagram. The mooring chain fatigue calculated using the main monochromatic wave was more conservative than that calculated using the wave scatter diagram with a difference of about 28%. The mooring fatigue calculated using turbulent wind spectrum was greater than that calculated using steady wind. In contrast, waves are the main source of mooring fatigue, and the second-order wave force has an undeniable impact on the mooring fatigue of a semi-submersible floating offshore wind turbine, which accounts for approximately 26% of wave-induced mooring fatigue. In addition, the current-induced mooring fatigue should not be neglected, although its effect is not as large as that caused by the wave or wind loads. An increase in the cross-sectional diameter and the length of a mooring chain, as well as a reasonable clump weight arranged, all contribute to improving the fatigue life of mooring chains in shallow water, which provide useful technical references for the optimization of mooring lines fatigue in shallow-water areas. [ABSTRACT FROM AUTHOR]

Fish habitats and reproduction can be significantly altered downstream of hydroelectric power plants operated by hydropeaking and resulting in rapid and frequent changes in river hydrodynamic conditions. To mitigate the impacts, it is necessary to maintain the habitat quality through operational measures. The microhabitat method, coupling 1 D or 2 D hydraulic simulations to biological models, is a useful tool to assess the evolution of hydromorphological parameters and fish habitats and define these mitigation measures. Calibration of the hydraulic model must be carried out carefully because the model must accurately reproduce hydraulic conditions from low to high flows. The objective is therefore to evaluate the sensitivity of the habitat value as a function of the type of calibration and the friction law for shallow habitats. The analysis is performed by estimating the uncertainty in fish habitat values resulting from Strickler's law or Nikuradse's law. The study is carried out on a river in the French Pyrenees based on the modeling of 2 stations with different cross-sectional shapes, one with progressive overflow and the other without these phenomena. Thanks to field measurements at low and high flowrates, the calibration process showed that the friction coefficient can be multiplied by 2. Two dimensionnal simulations give similar results to those obtained with 1 D when the flow remains unidirectional but differ for areas with high overflows. Calibration and models can lead to different conclusions regarding the estimation of habitat modifications due to hydropeaking operation and the definition of base flow and maximum turbine discharge. [ABSTRACT FROM AUTHOR]

Coastal lagoons are important wetland sites for migratory species and the local flora and fauna population. The Stagnone Lagoon is a coastal lagoon located on the west edge of Sicily between the towns of Marsala and Trapani. The area is characterized by salt-harvesting plants and several archaeological sites and is affected by microtidal excursion. Two mouths allow exchange with the open sea: one smaller and shallower in the north and one larger and deeper in the south. This study aims to understand the lagoon's hydrodynamics, in terms of circulation and involved forces. The circulation process appears to be dominated mainly by tide excursions and wind forces. Wind velocity, water levels, and water velocity were recorded during different field campaigns in order to obtain a benchmark value. The hydrodynamic circulation has been studied with a 2DH (two-dimensional in the horizontal plane) unstructured mesh model, calibrated with data collected during the 2006 field campaign and validated with the data of the 2007 campaign. Rapid changes in averaged velocity have been found both in Vx and Vy components, showing the strong dependence on seiches. This study tries to identify the main factor that domains the evolution of the water circulation. Sensitivity analyses were conducted to estimate the correct energy transfer between the forcing factors and dissipating ones. A Gauckler–Strickler roughness coefficient between 20 and 25 m1/3/s is found to be the most representative in the lagoon. To enhance the knowledge of this peculiar lagoon, the MIKE 21 model has been used, reproducing all the external factors involved in the circulation process. Nash–Sutcliffe coefficient of efficiency (NSE) values up to 0.92 and 0.79 are reached with a Gauckler–Strickler coefficient equal to 20 m1/3/s related to water depth and the Vy velocity component. The Vx velocity component NSE has never been satisfying, showing the limits of the 2D approach in reproducing the currents induced by local morphological peculiarities. Comparing the NSE value of water depth, there is a loss of up to 70% in model predictivity capability between the southern and the northern lagoon areas. This study aims to support the local decision-makers to improve the management of the lagoon itself. [ABSTRACT FROM AUTHOR]

The high spatial resolution and wide applicability of multi-spectral remote sensing make it significant for estimating shallow water depth. In areas with mixed substrates, determining the contribution of substrate reflection to the sensor's received signal can effectively enhance the precision of multi-spectral remote sensing bathymetry. Therefore, this paper proposes a Two Factors constrained Quasi-Analytical Algorithm (TF-QAA). Firstly, the algorithm considers the spectral variation of the mixed substrates. Secondly, a robust correlation between inherent optical parameters and water depth is established in this study, which is used to enforce a linear relationship constraint on the initially estimated water depth. Sentinel-2 image data was used to verify the algorithm in the Antelope Reef area of the South China Sea. The best result from images taken at different times indicates that the TF-QAA method has the average absolute error (MAE) of 0.92 m, the root mean square error (RMSE) of 1.20 m, the average relative error (MRE) of 10.6%, and the correlation coefficient (R2) of 0.97. The results suggest that the algorithm is effective for Case 1 water, providing a novel approach for extensive bathymetric mapping in shallow water areas of islands, with or without LiDAR-measured depth data. [ABSTRACT FROM AUTHOR]

A set of planar motion mechanism experiments of the Duisburg Test Case Post-Panamax container model executed in a towing tank with shallow depth is applied to train a neural network to analyse the ability of the proposed model to learn the effects of different depth conditions on ship's manoeuvring capabilities. The motivation of the work presented in this paper is to contribute an alternative and effective approach to model non-linear systems through artificial neural networks that address the manoeuvring simulation of ships in shallow water. The system is developed using the Levenberg–Marquardt backpropagation training algorithm and the resilient backpropagation scheme to demonstrate the correlation between the vessel forces and the respective trajectories and velocities. Sensitivity analyses were performed to identify the number of layers necessary for the proposed model to predict the vessel manoeuvring characteristics in two different depths. The outcomes achieved with the proposed system have shown excellent accuracy and ability in predicting ship manoeuvring with varying depths of shallow water. [ABSTRACT FROM AUTHOR]

This study aims to employ the extended direct algebraic method (EDAM) to generate and evaluate soliton solutions to the nonlinear, space-time conformable Estevez Mansfield-Clarkson equation (CEMCE), which is utilized to simulate shallow water waves. The proposed method entails transforming nonlinear fractional partial differential equations (NFPDEs) into nonlinear ordinary differential equations (NODEs) under the assumption of a finite series solution by utilizing Riccati ordinary differential equations. Various mathematical structures/solutions for the current model are derived in the form of rational, exponential, trigonometric, and hyperbolic functions. The wide range of obtained solutions allows for a thorough analysis of their actual wave characteristics. The 3D and 2D graphs are used to illustrate that these behaviors consistently manifest as periodic, dark, and bright kink solitons. Notably, the produced soliton solutions offer new and critical insights into the intricate behaviors of the CEMCE by illuminating the basic mechanics of the wave's interaction and propagation. By analyzing these solutions, academics can better understand the model's behavior in various settings. These solutions shed light on complicated issues such as configuration dispersion in liquid drops and wave behavior in shallow water.

Abstract This study retrieves some novel exact solutions to the family of 3D space–time fractional Wazwaz–Benjamin–Bona–Mahony (WBBM) equations in the context of diverse nonlinear physical phenomena resulting from water wave mechanics. The family of WBBM equations is transformed for this purpose using a space and time fractional transformation into an ordinary differential equation (ODE). The ODE then uses a strong method, namely the Unified Method. Consequently, lump solutions, dark-bright soliton, singular and multiple soliton solutions, and periodic solutions are investigated. The disparities between the current study's conclusions and previously acquired solutions via other approaches are examined. All wave solutions produced are determined to be novel in terms of fractionality, unrestricted parameters, and implemented technique sense. The impact of unrestricted parameters and fractionality on the obtained solutions are visually presented, along with physical explanations. It is observed that the wave portents are varied with the increase of unrestricted parameters as well as fractionality. We dynamically showed that the appropriate transformation and the applied Unified approach more proficient in the study of water wave dynamics and might be used in future researches to clarify the many physical phenomena. The novelty of this work validate that the proposed method seem simple and useful tools for obtaining the solutions in PDEs and it is expected to use in mathematical physics and optical engineering.

In this paper, the dynamic behavior of floating double-plate structures under a moving load is investigated in great detail with different factors utilizing the moving element method (MEM). The structures in this study are very large floating structures (VLFSs). The Kirchhoff–Love theory is used to model two floating plates connected by a Winkler-type elastic core, whilst the water surrounding the structure is simulated by the shallow linear water wave theory. In order to improve the computational efficiency of moving load problems, the MEM is adopted. Since the MEM uses fewer discrete elements than those of the traditional finite element method (FEM), the computational cost is reduced. The proposed two-plate model helps to reduce the influence of the surrounding water on the upper plate. Several numerical results are presented to investigate the influence of the ratio of thickness between layers as well as core stiffness on the displacements with different water depths, and load speeds. [ABSTRACT FROM AUTHOR]

Of current interest, there have recently appeared a series of the shallow-water papers in Mod. Phys. Lett. B. Illuminated by those papers and to make the story more complete, for the nonlinear long waves in the shallow water, this paper is scheduled to investigate a (2+1)-dimensional generalized Broer-Kaup system. As for the wave height and wave horizontal velocity, we employ symbolic computation, with the view of constructing out two groups of the similarity reductions. [ABSTRACT FROM AUTHOR]

Concentric water waves are ubiquitous in nature and, under certain conditions, may exhibit azimuthal instabilities. Whereas transverse instability of their plane counterparts, governed by nearly plane Korteweg–de Vries and nonlinear Schrödinger equations in the shallow and deep water limits, respectively, have been extensively studied as enabled by the existence of localized solitons, in the cylindrical case stability analysis is impeded by the corresponding finite-amplitude waves being non-localized. The equations, governing such waves, emerge from a balance between dispersive and nonlinear effects and, in particular, admit non-localized solutions of self-similar form. It is the goal of the present work to study transverse stability of such solutions, in both the shallow and deep water limits, as a function of surface tension (a Weber We number). Whereas in the shallow water case, a nearly concentric Korteweg–de Vries equation has been previous deduced, a deep water weakly nonlinear model has not been established yet. With a systematic derivation in cylindrical coordinates, we demonstrate that the appropriate envelope equation becomes of the nearly concentric nonlinear Schrödinger type with time-dependent coefficients. Transverse stability analyses of the concentric self-similar solutions to these models indicate crucial differences from the plane configurations revealing the effects of cylindrical geometry, direction of the base-state wave propagation, and its amplitude variation. In particular, the azimuthal perturbations do not admit, in general, a regular periodic structure, except for the short-wavelength perturbations on deep water which are either stretched or compressed with time as τ 1 / 2 depending on whether the base state concentric wave is traveling outward or inward. In the shallow-water case, transient azimuthal growth of outgoing finite-amplitude concentric waves is observed for all We in contrast to the plane solitons case, in which there exists a nonzero critical We; also, inward-traveling cylindrical waves are unstable for all values of We. In the deep-water case, azimuthal perturbations of outward-traveling cylindrical wave are stable in the long-time limit, but experience transient growth for short times when W e < 1 2 . As for inward-traveling waves, transverse perturbations grow for all We. These observations are at variance with the plane deep water geometry, in which transverse instability is observed for all We. [ABSTRACT FROM AUTHOR]

This work investigates the interaction between water waves and multiple ice shelf fragments in front of a semi-infinite ice sheet. The hydrodynamics are modelled using shallow water wave theory and the ice shelf vibration is modelled using Euler–Bernoulli beam theory. The ensuing multiple scattering problem is solved in the frequency domain using the transfer matrix method. The appropriate conservation of energy identity is derived in order to validate our numerical calculations. The transient scattering problem for incident wave packets is constructed from the frequency domain solutions. By incorporating multiple scattering, this paper extends previous models that have only considered a continuous semi-infinite ice shelf. This paper serves as a fundamental step towards developing a comprehensive model to simulate the breakup of ice shelves. [ABSTRACT FROM AUTHOR]

The maneuverability of ships is influenced by several factors, including ship design, size, propulsion system, hull shape, and external conditions such as wind, waves, and currents. The size, shape, and arrangement of the hull, rudder, and propeller are decisive for maneuverability. Hydrodynamic forces such as bank effect and squat significantly impact the maneuverability of large ships in narrow channels. With the increasing trend of building ever-larger ships, the demand to evaluate the maneuvering performance of the ship at the design stage has become more critical than ever. Both experimental and computational methods are used to obtain accurate maneuvering characteristics of vessels. In this study, the methods for predicting ship maneuvering characteristics are analyzed using a systematic review based on the preferred reporting items for systematic reviews and meta-analyses (PRISMA). This article contributes to a deeper understanding of the hydrodynamic capabilities of ships and identifies possible future challenges in the field of ship hydrodynamics. The findings inform educators and the shipping industry about the importance of predicting the maneuvering performance of ships, with an emphasis on the education and training of seafarers needed to make timely decisions in critical situations. [ABSTRACT FROM AUTHOR]

This study aims to employ the extended direct algebraic method (EDAM) to generate and evaluate soliton solutions to the nonlinear, space-time conformable Estevez Mansfield-Clarkson equation (CEMCE), which is utilized to simulate shallow water waves. The proposed method entails transforming nonlinear fractional partial differential equations (NFPDEs) into nonlinear ordinary differential equations (NODEs) under the assumption of a finite series solution by utilizing Riccati ordinary differential equations. Various mathematical structures/solutions for the current model are derived in the form of rational, exponential, trigonometric, and hyperbolic functions. The wide range of obtained solutions allows for a thorough analysis of their actual wave characteristics. The 3D and 2D graphs are used to illustrate that these behaviors consistently manifest as periodic, dark, and bright kink solitons. Notably, the produced soliton solutions offer new and critical insights into the intricate behaviors of the CEMCE by illuminating the basic mechanics of the wave's interaction and propagation. By analyzing these solutions, academics can better understand the model's behavior in various settings. These solutions shed light on complicated issues such as configuration dispersion in liquid drops and wave behavior in shallow water. [ABSTRACT FROM AUTHOR]

One of the promising strategies for the improvement of the resistance characteristics and energy efficiency of a ship is trim optimization. Most of the studies conducted so far regarding trim optimization deal with unrestricted water. The effect of trim on the total resistance and its components for the KRISO Container Ship model in confined and shallow water is investigated using computational fluid dynamics. Numerical simulations of resistance tests with and without the free surface effects using two turbulence models are carried out for even keel and four trims in restricted water. A verification study is conducted for the total resistance, sinkage, and trim in terms of grid resolutions and time steps to assess the numerical uncertainty. The numerical results are validated against the experimental ones available in the literature. Performing the double body simulations enabled the analysis of the effect of trim on the resistance components. The numerical results pointed out that by adjusting the trim a reduction in the total resistance in confined and shallow water can be obtained. [ABSTRACT FROM AUTHOR]

This study retrieves some novel exact solutions to the family of 3D space–time fractional Wazwaz–Benjamin–Bona–Mahony (WBBM) equations in the context of diverse nonlinear physical phenomena resulting from water wave mechanics. The family of WBBM equations is transformed for this purpose using a space and time fractional transformation into an ordinary differential equation (ODE). The ODE then uses a strong method, namely the Unified Method. Consequently, lump solutions, dark-bright soliton, singular and multiple soliton solutions, and periodic solutions are investigated. The disparities between the current study's conclusions and previously acquired solutions via other approaches are examined. All wave solutions produced are determined to be novel in terms of fractionality, unrestricted parameters, and implemented technique sense. The impact of unrestricted parameters and fractionality on the obtained solutions are visually presented, along with physical explanations. It is observed that the wave portents are varied with the increase of unrestricted parameters as well as fractionality. We dynamically showed that the appropriate transformation and the applied Unified approach more proficient in the study of water wave dynamics and might be used in future researches to clarify the many physical phenomena. The novelty of this work validate that the proposed method seem simple and useful tools for obtaining the solutions in PDEs and it is expected to use in mathematical physics and optical engineering. [ABSTRACT FROM AUTHOR]

This article focuses on the design of semi-implicit schemes that are fully well-balanced for the one-dimensional shallow water equations, that is, schemes that preserve all smooth steady states of the system and not just water-at-rest equilibria. The proposed methods outperform standard explicit schemes in the low-Froude regime, where the celerity is much larger than the fluid velocity, eliminating the need for a large number of iterations on large time intervals. In this work, splitting and relaxation techniques are combined in order to obtain fully well-balanced semi-implicit first and second order schemes. In contrast to recent Lagrangian-based approaches, this one allows the preservation of all the steady states while avoiding the complexities associated with Lagrangian formalism. [ABSTRACT FROM AUTHOR]

Methods for stabilising the turbulent cascade of potential enstrophy are analysed and compared for a compatible finite element discretisation of the rotating shallow water equations. These different approaches to upwinding the potential vorticity include the well-known anticipated potential vorticity method (APVM), streamwise upwind Petrov-Galerkin (SUPG) method, and a more recent method where the trial functions are evaluated downstream within the reference element. In all cases the upwinding scheme conserves both potential vorticity and energy, since the antisymmetric structure of the equations is preserved. The APVM leads to a symmetric definite correction to the potential enstrophy that is dissipative and inconsistent. The SUPG scheme introduces a consistent correction to the APVM scheme that acts as a backscatter term ensuring a richer depiction of turbulent dynamics. The downwinded trial function formulation results in the advection of downwind corrections, which analysis and numerical experiments show to be quantitatively similar to the SUPG scheme for a turbulent shear flow. The main difference between the SUPG and downwinded trial function schemes is in the energy conservation and residual errors. If just two nonlinear iterations are applied then the energy conservation errors are improved for the downwinded trial function formulation, reflecting a smaller residual error than for the SUPG scheme. We also present new temporal formulations by which potential enstrophy is exactly integrated across each time level. Results using these formulations are observed to be stable in the absence of any dissipation, despite the aliasing of grid scale turbulence. Using such a formulation and the APVM with a coefficient O (100) times smaller that its regular value leads to turbulent spectra that are greatly improved at the grid scale over the SUPG and downwinded trial function formulations with unstable potential enstrophy errors. [ABSTRACT FROM AUTHOR]

It is necessary to maintain maneuverability for ship navigation in shallow water, such as channels, ports and other confined waters. In this study, a turning circle maneuver with 35° rudder deflection and a 20/5 zigzag maneuver for KVLCC2 in shallow waters are tested numerically to directly predict the maneuverability of the ship in shallow water. A viscous in-house CFD solver is applied with the dynamic overset grid approach. The impacts of the water depth on the ship's maneuverability in terms of turning and zigzag competence are evaluated, and the underlying mechanism is analyzed. The numerical method is validated by comparing it with experimental data on the turning indices, which shows good agreement. It is demonstrated that the turning capability become worse with a smaller depth–draft ratio, thus resulting in a lower yaw rate and a greater steady turning diameter. However, the drift angle and lateral speed are reduced with a smaller depth–draft ratio for zigzag maneuvers, but the overshoot angle and turn lag vary with the water depth non-monotonically. [ABSTRACT FROM AUTHOR]

This study evaluates the viability of WindPACT-1.5 MW Horizontal Axis Wind Turbine (HAWT) for offshore wind development in the shallow waters of Nigeria. With the imperative need to address escalating energy consumption and mitigate climate change impacts, offshore wind power holds promise, offering opportunities for substantial electricity generation and economic growth. In this study, key metrics were examined for three potential offshore electricity projects: Asabo, Forcados, and Bonny Offshores. Asabo Offshore demonstrated superior potential, projecting the highest electricity generation at 21,167,296.08 kWh, resulting in substantial revenue of ₦1,319,357,564.67 per annum. Moreover, its Levelized Cost of Electricity (LCOE) of ₦60.8184/kWh underscores its cost efficiency compared to Forcados and Bonny Offshore projects. Net profit analysis further revealed Asabo's positive financial returns, is very low and there are net losses for the other two sites. Notably, Asabo Offshore showcased a 2.49% Return on Investment (ROI), indicative of a very low profitability, while Forcados and Bonny Offshore indicated negative ROIs of -46.74% and -48.39%, signaling potential financial setbacks. This comprehensive evaluation demonstrates that the WindPACT-1.5 MW HAWT, does not hold significant promise for offshore wind development in Nigeria's shallow waters. [ABSTRACT FROM AUTHOR]

A high-speed advancing ship will cause significant squats in shallow water, which could increase the risk of grounding. To this end, a program based on the Rankine higher-order boundary element method (HOBEM) is developed to investigate a high-speed displacement ship with a transom stern moving in shallow water. The nonlinear free surface condition is satisfied by adopting an iterative algorithm on the real free surface. The transom condition is considered by implementing a modified transom condition. Computations of wave-making resistance, sinkage and trim in deep water are first performed, and satisfactory agreement is achieved by comparing with the experimental results; the simulations are then extended to the shallow water case. It indicates that the present method can provide a suitable balance of practicability and robustness, which can be considered as an efficient tool for the guidance in ship design stage. [ABSTRACT FROM AUTHOR]

The attenuation of vortex motion on the surface of shallow and deep water is investigated. The vortex flow is formed by two mutually perpendicular waves excited by plungers at a frequency of 6 Hz (wavelength λ = 5.6 cm) on the surface of water measuring 70 × 70 cm and depth h. After reaching a stationary state in the vortex system, the wave pumping is switched off and the attenuation of the surface flow is recorded. On the surface of shallow water, λ/2π ≈ h, when the characteristic size of vortices L exceeds the depth of the liquid, L h, the time dependence of the energy of the vortex flow Е(t) is described by an exponential function at all pumping levels while the dependence of enstrophy Ф(t) = Ω2(t) is exponential only in the range of wave vectors 0–0.3 cm–1. On the surface of deep water, λ/2π < h, L ≈ h the dependences Е(t) and Ф(t) are far from exponential in all wavenumber ranges. At high pumping wave amplitudes, the dependences Е(t) and Ф(t) are nonmonotonic, which can be attributed to the influence of volumetric flows. [ABSTRACT FROM AUTHOR]

Abstract This paper introduces a unified model for layered rotating shallow‐water (RSW) and quasi‐geostrophic (QG) equations, based on the intrinsic relationship between these two sets of equations. We propose a novel formulation of the QG equations as a projection of the RSW equations. This formulation uses the same prognostic variables as RSW, namely velocity and layer thickness, thereby restoring the proximity of these two sets of equations. It provides direct access to the ageostrophic velocities embedded within the geostrophic velocities resolved by the QG equations. This approach facilitates the study of differences between QG and RSW using a consistent numerical discretization. We demonstrate the effectiveness of this formulation through examples including vortex shear instability, double‐gyre circulation, and a simplified North Atlantic configuration.

In the realm of shallow water acoustics, reverberation poses a critical challenge to active sonar systems, yet it also serves as a valuable conduit for environmental information. This study presents the findings from a 48-hour experimental investigation of reverberation and clutter in the northern Yellow China Sea, conducted in July 2014. Utilizing temperature and depth sensor arrays, we captured multiple instances of nonlinear internal waves (NIWs). Notably, the reverberation data collected by a vertical array of hydrophones revealed peculiar intensity fluctuations, which were exclusively detected by hydrophones located below the thermocline as NIWs traversed the measurement vessel. To elucidate this phenomenon, we introduce a novel coupled-mode reverberation–clutter theory. Through numerical computations, we determined both the coherent and incoherent components of the reverberation intensities, effectively accounting for the observed target-like intensity variations. The model developed herein was further employed to successfully estimate the velocity of NIWs. These anomalous reverberation characteristics could potentially pave the way for innovative methods of NIW parameter detection in shallow water environments.

The low-power underwater acoustic modem is usually an important component of the Underwater Wireless Sensor Network (UWSN). Network nodes have predetermined energy resources that will not be replenished during the life of the node. In shallow waters, multipath propagation is constantly occurring and for the modem to work effectively, solutions to overcome them must be used, which will also meet the important criterion of energy efficiency. The article presents the concept of a low-power underwater modem using Multiple Frequency-Shift Keying (MFSK) modulation and the fast frequency- hopping spread spectrum technique. In order to determine the performance of the modem, simulation tests were carried out using the Watermark simulator using the measured impulse responses of channels in shallow waters. [ABSTRACT FROM AUTHOR]

The holographic signal-processing method for a single vector scalar receiver (VSR) in the high-frequency band in shallow water is developed in the paper. The aim of this paper is to present the results of the theoretical analysis, numerical modeling, and experimental verification of holographic signal processing for a noise source by the VSR. The developed method is based on the formation of the 2D interferogram and 2D hologram of a noise source in a shallow-water waveguide. The 2D interferograms and 2D holograms for different channels of the VSR (P sound pressure and V X and V Y vibration velocity components) are considered. It is shown that the 2D interferogram consists of parallel interference fingers in the presence of a moving noise source. As a result, the 2D hologram contains focal points located on a straight line, and the angular distribution of the holograms has the main extreme value. It is shown in the paper that the holographic signal-processing method allows detecting the source, estimating the source bearing, and filtering the useful signal from the noise. The results of the source detection, source bearing estimation, and noise filtering are presented within the framework of experimental data processing and numerical modeling. [ABSTRACT FROM AUTHOR]

Shallow water passive source localization is an essential problem in underwater detection and localization. Traditional matched-field processing (MFP) methods are sensitive to environment mismatches. Many neural network localization methods still have room for improvement in accuracy if they are further adjusted to underwater acoustic characteristics. To address these problems, we propose a deep learning localization method via improved input features and network structure, which can effectively estimate the depth and the closest point of approach (CPA) range of the acoustic source. Firstly, we put forward a feature preprocessing scheme to enhance the localization accuracy and robustness. Secondly, we design a deep learning network structure to improve the localization accuracy further. Finally, we propose a method of visualizing the network to optimize the estimated localization results. Simulations show that the accuracy of the proposed method is better than other compared features and network structures, and the robustness is significantly better than that of the MFP methods. Experimental results further prove the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The influence of developed wind waves on the gain of a vertical array in shallow ocean waveguides is studied analytically and numerically. An algorithm is proposed for calculating the model correlation matrix of the signal at the aperture of the vertical array, taking into account the interference structure of the acoustic field in the sound channel. The antenna gain is analyzed for three spatial processing methods: standard phased array, optimal linear processing method, and optimal quadratic processing. The numerical simulation results for winter hydrological conditions in the Barents Sea are presented. The main focus is the dependence of the antenna gain values, "smoothed" on the scale of the interference structure of the acoustic field in the waveguide, the wind speed, and seabed sediment characteristics. The influence of intermode correlations on the results of gain simulation for various signal processing methods is analyzed in detail. It is shown that ignoring intermode correlations in the case of a vertical array leads to fundamentally erroneous results with optimal processing methods. [ABSTRACT FROM AUTHOR]

In shallow-water ocean-bottom cable (OBC) seismic data, the ineffectiveness of conventional surface-related multiple elimination (SRME) methods due to poor seabed records is addressed. This research utilizes the seismic wavefield received by multiple cables from a single shot gather to predict shallow water multiple models for that shot gather. Initially, the seismic data within a finite aperture around a seismic trace in the time domain shot gather is treated as the known seismic wavefield. This seismic wavefield is then extrapolated along the water layer to this seismic trace, following the Fresnel diffraction principle. The extrapolated data becomes the shallow water multiple model for this seismic trace. This process is repeated for each trace in the shot gather to obtain the shallow water multiple model of the entire shot gather. Forward modeling tests have shown that smaller data apertures can effectively avoid the impact of spatial aliasing on multiple model prediction. To address the overlap of primary waves and shallow water multiples in deep seismic data, which have lower dominant frequencies, the multiple model data is used as a known seismic wavefield and extrapolated along the water layer again. This produces second-order and higher-order multiple models. Applying this model to suppress multiple waves can minimize primary waves loss. This entirely data-driven approach necessitates solely water depth information, imposing no additional conditions. Both forward modeling and real seismic data testing validate the efficacy of this method in shallow water. [ABSTRACT FROM AUTHOR]

This paper introduces a model-independent passive source localization method, employing asynchronous distributed hydrophones in shallow water. Based on the frequency invariability of the acoustic field, assuming the correct source range information, the warped spectra of received signals at distributed hydrophones exhibit identical shapes. Subsequently, a cost function is formulated to mutually align the warped spectra, with its maximum point indicating the source location. The proposed method can locate the source in two-dimensional horizontal space without requiring either angle- or time-synchronization information. Numerical simulations are conducted to demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

This study aims to develop a practical path following controller and examine its control effects for large-sized ships in shallow water. First, a new controller is designed and implemented in a ship manoeuvring simulator, and the controller's tracking capacity is evaluated via controlling a 6 DOF math model following a prescribed path at various speeds and water depths. Then, towing tank tests are conducted with the corresponding physical model to validate the simulation results. Based on experimental results, comparisons are executed between the proposed controller and the traditional controllers (e.g. fuzzy controller). Finally, the applicability of the controller is investigated through simulations of the ship transiting the Panama Canal, meanwhile, the bank effects on the controller's performance are discussed. The results show that the designed controller offers satisfactory tracking performance. Simulation results match well with the experimental results despite slight discrepancies. Additionally, satisfactory path following performance is obtained by the simulations in the canal. To conclude, the proposed controller is able to fulfill path following missions in shallow water with high precision and can be applied in the manoeuvring simulator. [ABSTRACT FROM AUTHOR]

A method is presented to calculate the vibrations of an ice shelf floating in shallow water under different boundary conditions. One condition is that there is no flux, which reduces all calculations and the other is that there is no pressure at the seaward end of the ice shelf. The effect of these boundary conditions is investigated in detail, and the modes of vibration are also determined. Motion simulations of the system are presented for the potential velocity of the water and the vertical displacement of the ice shelf. These are found through a numerical method, which reduces all calculations to matrix multiplication. The underlying motion is shown to be very complex and difficult to interpret from single-point response measurements. The motion of more realistic ice shelves can be expected to be even more complicated. [ABSTRACT FROM AUTHOR]

For the axial flow pumps water-jet propulsion system of undersea vehicles, the high specific speed axial flow pump designed by the lift method fails to work under shallow water and high-speed conditions at present. Therefore, this study put forward a method to design a low specific speed axial flow pump. By considering the blade grid characteristics of the NACA66a=0.8 airfoil, the design relationship among the angle of attack, lift coefficient, and other parameters was changed to establish an axial flow pump model suitable for high-speed conditions, and SST k-ω turbulence model and multi-reference frame model were used to simulate the flow field motion of the designed pump. The results show that under the design conditions, for the head and hydraulic efficiency of the designed pump, the error between the design value and the emulation value is controlled within 8%. At the same time, the cavitation resistance of the designed pump at different depths is tested to explore the minimum depth where the designed pump can work.

When using underwater optical wireless communication in areas close to human habitats— such as shallow sea areas—specifications for highly-secure, large-capacity optical transceivers are required. Real-time transmission of 850 nm, direct-current optical orthogonal frequency division multiplexing signals for full-duplex underwater invisible light communication has been achieved. We experimentally confirmed that subcarrier adaptive modulation could transmit at maximum capacity depending on the transmission distance, while changing the transmission distance in shallow seawater channels. We confirmed that there was no disturbing influence due to sunlight by using a honeycomb structure for sunlight shielding. Moreover, we found that the effect of disruption caused by the sea surface vibrating due to the 3 m/s wind speed did not affect the signal quality. 4K video streaming is also done on a 1.2 m underwater channel transmission. To the best of our knowledge, this is the first report of full-duplex transmission of invisible-band underwater optical wireless communication for shallow waters.

Satellite technology is an efficient tool, which can provide valuable observations for coastal areas from space. Compared with conventional bathymetric surveying approaches, remote sensing-based shallow water bathymetry retrieval methods have been widely used in recent years. Various empirical models have been proposed for deriving bathymetry of coastal shallow water, and prior topographic information is required to construct models. Traditional studies tend to select a cloud-free remote sensing image to map the coastal shallow water topography. As a result, in addition to the selection of empirical models, the high-quality remote sensing image and accurate prior topographic data are also of importance. This study aims to propose a method for mapping coastal shallow water bathymetry from multitemporal remote sensing imagery. Here, Sentinel-2 imagery time series are composited to produce a clear image, which can effectively avoid the contamination of clouds, water turbidity and other noises. ICESat-2 lidar altimeter data that contain accurate underwater elevations are used to provide topographic information. Moreover, Sentinel-2-based multispectral information and ICESat-2-based topographic information are combined for the coastal bathymetry retrieval by five empirical models (i.e., linear band model, ratio band model, support vector machine, neural network, and random forest). This proposed method is tested in Dongsha Atoll in South China Sea, and achieve a good performance [training: root mean square error (RMSE): 0.97 m ± 0.76 m, mean absolute percentage error (MAPE): 4.07% ± 0.046%, R-square (R2): 0.90 ± 0.14; validation: RMSE: 1.22 m ± 0.43 m, MAPE: 5.43% ± 0.035%, R2: 0.86 ± 0.089]. The comparison confirms that machine learning methods perform better than traditional methods, and the deep learning techniques can be further introduced in estimating shallow water bathymetry in the future, which is expected to achieve an excellent accuracy in bathymetry inversion.

Shallow-water mooring chains of floating offshore wind turbines pose challenges such as nonlinear tension characteristics, high cost and prominent fatigue issues, which seriously hinder the large-scale use of floating wind power. Based on the hydrological and meteorological data of an offshore wind farm in the South China Sea, a sensitivity analysis of the mooring chain fatigue of a semi-submersible floating offshore wind turbine in shallow water was conducted with different environmental loads and mooring chain design parameters. It was found that mooring fatigue is mainly caused by the wave condition within diagonal distribution of the wave dispersion diagram. The mooring chain fatigue calculated using the main monochromatic wave was more conservative than that calculated using the wave scatter diagram with a difference of about 28%. The mooring fatigue calculated using turbulent wind spectrum was greater than that calculated using steady wind. In contrast, waves are the main source of mooring fatigue, and the second-order wave force has an undeniable impact on the mooring fatigue of a semi-submersible floating offshore wind turbine, which accounts for approximately 26% of wave-induced mooring fatigue. In addition, the current-induced mooring fatigue should not be neglected, although its effect is not as large as that caused by the wave or wind loads. An increase in the cross-sectional diameter and the length of a mooring chain, as well as a reasonable clump weight arranged, all contribute to improving the fatigue life of mooring chains in shallow water, which provide useful technical references for the optimization of mooring lines fatigue in shallow-water areas.

Coastal lagoons are important wetland sites for migratory species and the local flora and fauna population. The Stagnone Lagoon is a coastal lagoon located on the west edge of Sicily between the towns of Marsala and Trapani. The area is characterized by salt-harvesting plants and several archaeological sites and is affected by microtidal excursion. Two mouths allow exchange with the open sea: one smaller and shallower in the north and one larger and deeper in the south. This study aims to understand the lagoon’s hydrodynamics, in terms of circulation and involved forces. The circulation process appears to be dominated mainly by tide excursions and wind forces. Wind velocity, water levels, and water velocity were recorded during different field campaigns in order to obtain a benchmark value. The hydrodynamic circulation has been studied with a 2DH (two-dimensional in the horizontal plane) unstructured mesh model, calibrated with data collected during the 2006 field campaign and validated with the data of the 2007 campaign. Rapid changes in averaged velocity have been found both in Vx and Vy components, showing the strong dependence on seiches. This study tries to identify the main factor that domains the evolution of the water circulation. Sensitivity analyses were conducted to estimate the correct energy transfer between the forcing factors and dissipating ones. A Gauckler–Strickler roughness coefficient between 20 and 25 m1/3/s is found to be the most representative in the lagoon. To enhance the knowledge of this peculiar lagoon, the MIKE 21 model has been used, reproducing all the external factors involved in the circulation process. Nash–Sutcliffe coefficient of efficiency (NSE) values up to 0.92 and 0.79 are reached with a Gauckler–Strickler coefficient equal to 20 m1/3/s related to water depth and the Vy velocity component. The Vx velocity component NSE has never been satisfying, showing the limits of the 2D approach in reproducing the currents induced by local morphological peculiarities. Comparing the NSE value of water depth, there is a loss of up to 70% in model predictivity capability between the southern and the northern lagoon areas. This study aims to support the local decision-makers to improve the management of the lagoon itself.

A set of planar motion mechanism experiments of the Duisburg Test Case Post-Panamax container model executed in a towing tank with shallow depth is applied to train a neural network to analyse the ability of the proposed model to learn the effects of different depth conditions on ship’s manoeuvring capabilities. The motivation of the work presented in this paper is to contribute an alternative and effective approach to model non-linear systems through artificial neural networks that address the manoeuvring simulation of ships in shallow water. The system is developed using the Levenberg–Marquardt backpropagation training algorithm and the resilient backpropagation scheme to demonstrate the correlation between the vessel forces and the respective trajectories and velocities. Sensitivity analyses were performed to identify the number of layers necessary for the proposed model to predict the vessel manoeuvring characteristics in two different depths. The outcomes achieved with the proposed system have shown excellent accuracy and ability in predicting ship manoeuvring with varying depths of shallow water.

The current time-domain solution methods for the wavefield equations of a single medium do not apply to the wavefield equations of shallow water seismic with a fluid–elastomer coupling. To solve this problem, based on the explicit central difference method and implicit Newmark method, the explicit–explicit method, implicit–implicit method, and explicit–implicit method time-domain expressions for the local solution are derived, and the time-domain expressions for the explicit and implicit methods in the global solution are derived.The stability and computational efficiency of different time-domain solving methods for the shallow water seismic wavefield equations are theoretically analyzed. The numerical results are compared with the simulation data from the multiphysics field simulation software COMSOL 6.0, and the numerical stability, computational efficiency and accuracy of the different solving methods are also analyzed theoretically. The results show that the implicit method in the global solution is relatively optimal among the methods proposed in this paper, which ensures numerical stability at the larger step size for improving the computational efficiency and considers the higher computational efficiency and accuracy. [ABSTRACT FROM AUTHOR]