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Shallow water bathymetric information is important for human life because it has a strong influence on phenomena and dynamics in coastal areas. Conventional bathymetric mapping methods are capable of obtaining high-precision accuracy, but require expensive and complex resources. Specifically, in shallow waters, survey instruments have difficulty obtaining adequate depth data due to the many obstacles that must be overcome. Remote sensing-based shallow water bathymetry called as Satellite-Derived Bathymetry (SDB) is a reasonable and efficient choice. Technological developments enable SDB data processing to be much more efficient in terms of time and storage by utilizing cloud-based platforms such as Google Earth Engine (GEE). Spatial and temporal resolution is still a challenge in SDB, so in this condition PlanetScope with daily temporal resolution capabilities is an optimistic choice. However, this image falls into a relatively new image category. In this study we tested the performance of Sentinel-2A imagery and new PlanetScope imagery bands. The existence of the new sensor owned by PlanetScope allows an increased choice of SDB data sources with high spatial and temporal resolution that is better than the general datasets currently available. There are four additional channels are Coastal Blue, Green I, Yellow, and Red Edge. Assessment is needed to test the capabilities of each new channel using empirical methods via the Stumpf algorithm. Based on accuracy assessment observations, the Sentinel-2A channel combination is still better in terms of accuracy and determination, because it is able to represent the depth in the study area up to 70%. The potential use of PlanetScope's new channels for SDB applications can still be seen in the combination of the Coastal Blue and Yellow channels. This channel combination is still able to represent 47% of the depth variations in the study area. [ABSTRACT FROM AUTHOR]

Low frequency acoustic methods are a common tool for seabed stratigraphy mapping. Due to the efficiency in seabed mapping compared to geotechnical methods, estimating geotechnical sediment properties from acoustic surveying is attractive for many applications. In this study, co-located geotechnical and geoacoustic measurements of different seabed sediment types in shallow water environments (<5 m of water depth) are analyzed. Acoustic impedance estimated from sediment properties based on laboratory testing of physical samples is compared to acoustic impedance deduced from CHIRP sonar measurements using an inversion approach. Portable free fall penetrometer measurements provided in situ sediment strength. The results show that acoustic impedance values deduced from acoustic data through inversion fall within a range of ±25% of acoustic impedance estimated from porosity and bulk density. The acoustic measurements reflect variations in shallow sediment properties such as porosity and bulk density (~10 cm below seabed surface), even for very soft sediments (su < 3 kPa) and loose sands (~20% relative density). This is a step towards validating the ability of acoustic methods to capture geotechnical properties in the topmost seabed layers. [ABSTRACT FROM AUTHOR]

Over the years, air lubrication technology has been widely applied to maritime vessels, demonstrating its significant energy-saving and emission-reducing effects. However, the application of this technology in inland waterway transportation faces unique challenges due to the shallower water depths, particularly during low water periods. Under such conditions, the formation of the air layer and its associated drag-reduction effects may undergo alterations. Conducting research on air lubrication technology in shallow water conditions holds great practical significance for promoting its application in inland waterway vessels. Therefore, a numerical study is undertaken to examine the impact of water depth on Air layer Drag Reduction (ALDR) to promote the use of ALDR technology on inland canal boats with shallow water depths. The object was a specific river-sea direct ship model, and a groove was created at the bottom of the model with air injection. At two distinct speeds, numerical simulations were run for four different depths: deep water, moderate water, shallow water, and ultra-shallow water. A comparative examination of the air layer morphology on the ship bottom and drag reduction was conducted to investigate the impact of water depth on ALDR and confirm the viability of using ALDR technology on shallow-water navigation boats. The results indicate that due to the change in the velocity and pressure fields at the bottom of the ship, the efficiency of drag reduction and the form of the air layer on the ship's bottom are significantly impacted by variations in water depth in restricted waters. However, the total resistance can still be significantly reduced by setting grooves on the hull with air injected in shallow waterways. Reduced frictional resistance no longer predominates the overall resistance reduction in shallow water; the proportion of the decrease in viscous pressure resistance rises and can reach up to 4.8 times the decrease in frictional resistance. The research confirms the application prospects of this technology on inland waterway transport ships. [ABSTRACT FROM AUTHOR]

In this work, we investigate a partial differential equation (PDE) derived from a Boussinesq system of two equations that describe the wave motion in shallow water when the wavelength is small compared to wave amplitude. The Lie point symmetries of the PDE are utilized to reduce it to an ordinary differential equation (ODE) the travelling wave solutions of which are obtained. These solutions are of trigonometric, hyperbolic and exponential types. Graphical representation of some solutions exhibiting solitary and cnoidal wave phenomena are presented.

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.

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.

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.

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.

ABSTRACTSporadic salinity caused by seawater intrusion is a serious concern for rice (Oryza sativa L.) production in the Red River Delta (RRD) of Vietnam, and guidance for on-farm agronomic management is needed. Three sets of on-farm experiments – namely, trials of (1) nitrogen (N) fertilizer use (replicated trials and surveys of farmer fields, including plots receiving zero N), (2) resistant varieties, and (3) shallow irrigation management – were conducted from 2015 to 2017 in three communes in Nam Dinh province in the RRD, to assess technologies adaptable by farmers. Yield response to N fertilizer in the farmer fields was generally low and greatly variable, associated with variable N recovery efficiency and internal efficiency, particularly in fields at risk of high salinity in one commune during summer 2015. In the replicated trials, N fertilizer applied at 120–180 kg N ha−1 in spring and 100–150 kg N ha−1 in summer generally produced better yields with higher N use efficiencies than the current high N application rates (219 and 189 kg N ha−1, respectively). Recently developed salinity-resistant varieties M2 and M14 produced almost 50% higher yield than the conventional varieties in very saline at-risk fields. Shallow water-depth management (

In this study, Particulate Image Velocimetry (PIV) was utilized to determine the flow characteristics of three side-by-side circular cylinders with a base bleed. The height of the water was set as hW=20 mm which has characteristics of shallow water and flow images were captured from an elevation of hL/hW= 0.5 (mid-plane of water height). The freestream velocity of water and circular cylinder diameters were chosen as U∞=0.125 m/sec and D=40 mm, respectively which are the corresponding Reynolds number of ReD=5000. Three different gap/diameter ratios between the cylinders were tested as G/D=1.0, 1.25, and 1.5 throughout the experiments. As a passive flow control technique, base bleed slots located through the cylinders were used with the dimensionless width ratio of B/D= 0.05 to 0.25 with 0.05 increment. As a result of the study, the base bleed was found out an effective way to control unsteady wake. Besides, whereas the increasing height of VSP results in further decrement turbulence statistics, Increasing the width of base bleed leads to a reduction of maximum Reynolds shear stress concentration. Nevertheless, jet deflection flow cannot be avoided for the G/D=1.25 while, flow deflection is avoided with all base bleed case the gap ratio increases to G/D=1.5. The wake size of each cylinder is almost the same for G/D=1.5.

ABSTRACTAccurate bathymetric information is an important foundation for marine resource development and nearshore ecological protection. Existing empirical algorithms can estimate water depth from high resolution images with the aid of ground truth bathymetry data. However, empirical models are not applicable in areas without measured bathymetric data. To overcome the difficulty of estimating bathymetry in areas without measured data, we developed a dual-time phase bispectrum optimization algorithm (DPBOA) that combines the empirical data for estimating bathymetry in Case-I water using the blue-green bands of dual-temporal multispectral imagery. The hyperspectral optimization process exemplar is first transformed into a dual-band model applicable to multi-band images, and the model is then applied separately to the same locations of different time-phase images, using least squares optimization to derive all unknown model parameters. The depth was estimated by the dual-band model after the unknown parameters were determined. To assess the performance of the algorithm, bathymetric estimation was performed using dual-time images from Sentinel-2, Gaofen-2, Gaofen-6, and Worldview-2 in Ganquan Island and Qilianyu Island, respectively. Validation was performed with the data from airborne LiDAR bathymetry (ALB) and ICESat-2. The results indicate that for the Ganquan Islands, the coefficient of determination ([Formula: see text]) was 0.92, and the root mean square deviation (RMSE) was 1.26 m; for the Qilianyu Islands, the [Formula: see text] was 0.94 and the RMSE was 1.00 m. The developed model obtains better results compared with the Lyzenga empirical model and the dual-band bathymetry estimation algorithm in terms of bathymetry estimation without measured data. Additionally, the impacts of the time interval between images on bathymetry estimation are analyzed.

This paper describes a 2D‐3D hybrid model for tsunami simulations that uses an overlapping method based on an arbitrary grid. A 2D model is used to simulate wave propagation from the source area to the offshore area, and a 3D model is then used to simulate the free surface flow around structures in coastal areas. An overlapping method that satisfies the conservation and compatibility conditions is developed to couple the two models. The shallow water equations are applied for the 2D model, and the Navier‐Stokes equations and continuity equations are applied for the flow field of the 3D model. The Allen‐Cahn equation is applied for the interface‐capturing method of the 3D model. The stabilized finite element method is applied for the spatial discretization and the Crank‐Nicolson method is used for the temporal discretization of the governing equations. The model is verified and validated through several numerical analysis examples. [ABSTRACT FROM AUTHOR]

Due to the blockage of seawater, seafloor displacement cannot be directly measured by space geodesy. The combination of Global Navigation Satellite Systems‐acoustic ranging (GNSS‐A) has been used to overcome the electromagnetic barrier, so that a GNSS‐determined sea surface vessel's coordinates can be transformed to seafloor benchmarks in a global reference frame. Due to the high cost and science priorities, previous GNSS‐A studies mainly targeted relatively deep water and a minimum of three transponders were used to form an array, equivalent to a precision geodetic station. With recent developments in unmanned autonomous surface vessels, low cost GNSS‐A surveys are poised to become practical. Here we demonstrate that with a carefully designed surveying trajectory, Wave Glider‐based GNSS‐A surveying of a single transponder in shallow water can provide centimeter‐level accuracy on horizontal seafloor positioning, even if the sound speed model deviates from the actual value by a few meters per second. Results from a nine‐month experiment conducted at ∼54 m water depth show that the repeatability of the seafloor horizontal positioning is better than 2 cm. When conditions allow, the acoustic observations should be collected symmetrically about the transponder and data redundancies are recommended to reduce the error associated with time‐dependent variations in sound speed. Plain Language Summary: Seafloor geodesy is important for monitoring offshore strain processes. Global Navigation Satellite Systems‐acoustic ranging (GNSS‐A) uses sound signals traveling in water as rulers to measure the distances between the sea surface vessel and the seafloor sensor (transponder), so that the GNSS‐determined sea surface vessel's coordinates can be transformed to the seafloor through triangulation. Multiple transponders deployed on the seafloor are often needed to form an array so that noise caused by irregular variations in the sound signals can be reduced. In shallow water, due to the relatively short distance, the range distortion caused by a sound signal's refraction is smaller, and the time it takes to conduct each complete cycle of survey is shorter. These conditions allow the seafloor displacements to be measured with centimeter‐level accuracy using only one transponder. Key Points: For single transponder Global Navigation Satellite Systems‐acoustic ranging in shallow water, seafloor vertical position estimation is sensitive to sound speed error and variationA geometrically symmetric surveying trajectory is preferable for error reduction in horizontal seafloor positioningSeafloor horizontal positions were measured with <2 cm repeatability at ∼54 m water depth over five repeat surveys with Wave Gliders [ABSTRACT FROM AUTHOR]

In this paper, we study the variations of holograms of a moving source in an inhomogeneous ocean waveguide. It is assumed that intense internal waves (internal solitons) are the reason for the inhomogeneities of the shallow water waveguide. The results of 3D modeling of the sound field considering horizontal refraction by internal waves are presented. In the context of 3D modeling, the interferogram (sound intensity distributions in frequency–time coordinates) and hologram (2D Fourier transform of the interferogram) of moving sources are analyzed. The hologram consists of two disjoint regions corresponding to the unperturbed field and the field perturbed by internal waves. This structure of the hologram allows for the reconstruction of the interferogram of the unperturbed field in a waveguide in the absence of intense internal waves. The error in the reconstruction of the unperturbed interferogram is estimated. [ABSTRACT FROM AUTHOR]

A data-driven method, the truncated LS-SVM, is proposed for estimating the nondimensional hydrodynamic coefficients of a nonlinear manoeuvring model. Experimental data collected in a shallow water towing tank are utilized in this study. To assess the accuracy and robustness of the truncated LS-SVM method, different test data sizes are selected as the training set. The identified nondimensional hydrodynamic coefficients are presented, as well as the corresponding parameter uncertainty and confidence intervals. The validation is carried out using the reference data, and statistical measures, such as the correlation coefficient, centred RMS difference, and standard deviation are employed to quantify the similarity. The results demonstrate that the truncated LS-SVM method effectively models the hydrodynamic force prediction problems with a large training set, reducing parameter uncertainty and yielding more convincing results. [ABSTRACT FROM AUTHOR]

The maximum range of detection of an autonomous underwater vehicle (AUV) in the high-frequency region has been estimated range applying holographic processing. The estimation is performed based on numerical simulation of the sound field attenuation with distance and the experimental spectral characteristics of the underwater vehicle noise emission and the background noise of the water area. [ABSTRACT FROM AUTHOR]

The robustness of the holographic processing of hydroacoustic broadband signals with respect to the spatial and temporal inhomogeneities of the ocean medium has been experimentally studied. The experiment was performed in shallow water against the background of intense internal waves (IIWs). The sound source was a towed pneumatic emitter; a single hydrophone played the role of a receiver. The interference patterns and holograms of sound pressure for different instants, when a perturbation of the medium caused horizontal refraction or coupling of acoustic field modes, are presented. It is shown that, in the presence of IIWs (which perturb the source field), holographic processing makes it possible to separate the spectral densities of unperturbed and perturbed fields. This circumstance allows one to reconstruct the hologram and interference pattern of unperturbed source field, thus demonstrating the robustness of holographic processing of hydroacoustic signals in the presence of hydrodynamic perturbations. [ABSTRACT FROM AUTHOR]

The rising sea levels caused by the climate crisis are causing significant changes in the coastal environment of the Korean Peninsula, leading to increased demand for coastal erosion protection. Accurate bathymetric information is crucial for implementing effective prevention measures. However, existing methods such as the airborne light detection and ranging (LiDAR) bathymetry (ALB) and multibeam echo sounder (MBES) are not cost-effective for small-scale regions, and the single-beam echo sounder (SBES) method using manned survey vessels is challenging to use in low-water-depth areas. In this study, we aimed to develop an autonomous surface vehicle (ASV) to conduct bathymetric surveying at a very small water depth of less than 2.0 m. The survey was conducted by connecting SBES and network real-time kinematic (N-RTK) positioning data to a small, self-developed ASV. The vessel was autonomously navigated using N-RTK positioning data during most measurement operations, allowing for precise sounding intervals using a simple waypoint setting for each planned sidetrack without direct steering. The bathymetric measurements of exposed or partially exposed rocks at average water depths of 2.0 m or less could be obtained from the bathymetric surveying using the unmanned vessel and devices applied in this study. [ABSTRACT FROM AUTHOR]

In this paper, a numerical assessment of the effect of shallow water on the total resistance of the solar catamaran SolarCat is carried out using computational fluid dynamics within the software package STAR–CCM+. The unsteady viscous fluid flow was modelled based on the Reynolds-averaged Navier–Stokes (RANS) equations with the application of the k − ω SST ( k − ω Shear Stress Transport) turbulence model. The RANS equations were discretized by the finite volume method, and the position of the free surface is determined by the volume of fluid method. In shallow water conditions, a mesh morphing algorithm is applied. Numerical simulations were carried out for the deep water and limited depths corresponding to h / T = 7. 6 , h / T = 4 , and h / T = 2 at two speeds. The verification study was carried out and the total numerical uncertainty was calculated for the total resistance and sinkage of the catamaran. A detailed analysis of the flow around the catamaran was carried out. [ABSTRACT FROM AUTHOR]

When designing coastal protection measures, special attention is paid to the creation and expansion of a natural beach slope on the coast of a water body. To assign geometric dimensions to relatively stable beach slopes, it is necessary to evaluate the relationship of waves, taking into account the level regime characteristic of a given section of the coast. The aim of the research is to explore the features of the transformation of the wave profile in shallow water and to conduct a comparative analysis of theory and experiment. The studies were carried out in a wave tray, where the waves were reproduced by a swinging shield. The features of the transformation of the wave profile at decreasing depths of the shallow water of a large water body are considered. An assessment is given of the change in the kinematic characteristics of a wave incident in a shallow water zone on an unfortified beach slope with a depth of 10, 20 and 30. The results of experimental studies are presented and analyzed, as a result of which the influence of the wave steepness on the kinematic characteristics and features of wave transformation in shallow water is revealed. A comparative analysis of theoretical solutions and experimental data with an assessment of the area of their applicability is carried out. On the whole, the wave profile and the horizontal component of the orbital velocity during the passage of the wave crest are in satisfactory agreement with the calculations according to the Stokes theory at relative depths of more than 0.07. It has been established that for shallow water conditions the relative height of the wave crest affecting the beach slope of the near-shore zone of the coast of a large water body is most noticeably affected by the slope, with an increase from 10 to 30 the magnitude of the wave steepness can increase by 1.2 times.

Seabed logging (SBL) is a direct and remote application of controlled source electromagnetic (CSEM) method to detect hydrocarbon resources beneath the seafloor in offshore conditions. In this method, electromagnetic waves are used to detect the resistivity contrast between various sediment layers. The current source of electromagnetic waves is a horizontal electric dipole (HED) antenna. The antenna design represents a challenge in shallow waters (less than500 m seawater depth) due to the presence of airwaves that lead to a low signal-to-noise ratio, hence hindering the detection of a hydrocarbon reservoir. A horizontal circular electric half-wave dipole will be used in this work as the source of electromagnetic waves. The numerical solution for the electric field response will be developed based on solving the Maxwell equations in two modes: the poloidal and toroidal modes. Simulation results have shown that the new antenna is able to detect the presence of deep hydrocarbon reservoirs (up to 5000 m) in shallow-water environment. Comparison of the average percentage difference in delineation between the circular and the HED was carried out. The new antenna results in 61 % delineation compared to 15 % for the HED at 5000 m hydrocarbon depth and 200 m seawater depth, indicating the ability of the antenna to disperse the airwaves. The results also show that the airwaves are significantly reduced from nearly 15000 m (for the HED) to 10000 m offset for the proposed antenna, hence increasing the signal-to-noise ratio. These results seem to indicate the potential for the new antenna to be used as an EM source for SBL in shallow-water environment.

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.

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 VX and VY 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.

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.

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.

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 Due to the blockage of seawater, seafloor displacement cannot be directly measured by space geodesy. The combination of Global Navigation Satellite Systems‐acoustic ranging (GNSS‐A) has been used to overcome the electromagnetic barrier, so that a GNSS‐determined sea surface vessel's coordinates can be transformed to seafloor benchmarks in a global reference frame. Due to the high cost and science priorities, previous GNSS‐A studies mainly targeted relatively deep water and a minimum of three transponders were used to form an array, equivalent to a precision geodetic station. With recent developments in unmanned autonomous surface vessels, low cost GNSS‐A surveys are poised to become practical. Here we demonstrate that with a carefully designed surveying trajectory, Wave Glider‐based GNSS‐A surveying of a single transponder in shallow water can provide centimeter‐level accuracy on horizontal seafloor positioning, even if the sound speed model deviates from the actual value by a few meters per second. Results from a nine‐month experiment conducted at ∼54 m water depth show that the repeatability of the seafloor horizontal positioning is better than 2 cm. When conditions allow, the acoustic observations should be collected symmetrically about the transponder and data redundancies are recommended to reduce the error associated with time‐dependent variations in sound speed.

Numerical simulation is used to study the possibility of remote acoustic monitoring of underwater keels in ice-covered shallow-water waveguides. A statistically average hummock for the Arctic region is considered, with a keel draft of 8 m, located in a waveguide with a depth of 40 m. It is assumed that the ridge of the hummock is perpendicular to the acoustic track, the length of which is 10 km. A point broadband source and a vertical receiving array are used, which are necessary for extracting the mode amplitudes. It is shown that mode coupling due to the keel manifests itself quite distinctly in modulation of the mode amplitudes in a broad frequency band. A methodology for analyzing this modulation by constructing cepstrograms (spectrograms from the spectrum) is proposed. The cepstrograms reveal dispersion curves corresponding to pairs of coupled modes. Then, from the location of the dispersion curves on the cepstrogram, it is possible to estimate the location of the keel on the track. [ABSTRACT FROM AUTHOR]

This study presents a comprehensive analysis of the second-order perturbation theory applied to the Navier–Stokes equations governing free surface flows. We focus on gravity–capillary surface waves in incompressible viscous fluids of finite depth over a flat bottom. The amplitude of these waves is regarded as the perturbation parameter. A systematic derivation of a nonlinear-surface-wave equation is presented that fully takes into account dispersion, while nonlinearity is included in the leading order. However, the presence of infinitely many over-damped modes has been neglected and only the two least-damped modes are considered. The new surface-wave equation is formulated in wave-number space rather than real space and nonlinear terms contain convolutions making the equation an integro-differential equation. Some preliminary numerical results are compared with computational-modelling data obtained via open source CFD software OpenFOAM. [ABSTRACT FROM AUTHOR]

In the context of preserving stationary states, e.g. lake at rest and moving equilibria, a new formulation of the shallow water system, called flux globalization has been introduced by Cheng et al. (J Sci Comput 80(1):538–554, 2019). This approach consists in including the integral of the source term in the global flux and reconstructing the new global flux rather than the conservative variables. The resulting scheme is able to preserve a large family of smooth and discontinuous steady state moving equilibria. In this work, we focus on an arbitrary high order WENO finite volume (FV) generalization of the global flux approach. The most delicate aspect of the algorithm is the appropriate definition of the source flux (integral of the source term) and the quadrature strategy used to match it with the WENO reconstruction of the hyperbolic flux. When this construction is correctly done, one can show that the resulting WENO FV scheme admits exact discrete steady states characterized by constant global fluxes. We also show that, by an appropriate quadrature strategy for the source, we can embed exactly some particular steady states, e.g. the lake at rest for the shallow water equations. It can be shown that an exact approximation of global fluxes leads to a scheme with better convergence properties and improved solutions. The novel method has been tested and validated on classical cases: subcritical, supercritical and transcritical flows. [ABSTRACT FROM AUTHOR]

Sporadic salinity caused by seawater intrusion is a serious concern for rice (Oryza sativa L.) production in the Red River Delta (RRD) of Vietnam, and guidance for on-farm agronomic management is needed. Three sets of on-farm experiments – namely, trials of (1) nitrogen (N) fertilizer use (replicated trials and surveys of farmer fields, including plots receiving zero N), (2) resistant varieties, and (3) shallow irrigation management – were conducted from 2015 to 2017 in three communes in Nam Dinh province in the RRD, to assess technologies adaptable by farmers. Yield response to N fertilizer in the farmer fields was generally low and greatly variable, associated with variable N recovery efficiency and internal efficiency, particularly in fields at risk of high salinity in one commune during summer 2015. In the replicated trials, N fertilizer applied at 120–180 kg N ha−1 in spring and 100–150 kg N ha−1 in summer generally produced better yields with higher N use efficiencies than the current high N application rates (219 and 189 kg N ha−1, respectively). Recently developed salinity-resistant varieties M2 and M14 produced almost 50% higher yield than the conventional varieties in very saline at-risk fields. Shallow water-depth management (<5 cm) resulted in grain yields similar to the higher conventional-depth management in the less saline fields, but significantly reduced yields in the more saline fields. These results indicate potential resource-use efficiencies in rice production to better cope with coastal salinity in the RRD. [ABSTRACT FROM AUTHOR]

Shallow landslides pose a significant threat to people and infrastructure. Despite significant progress in the understanding of such phenomena, the evaluation of the size of the landslide release zone, a crucial input for risk assessment, still remains a challenge. While often modeled based on limit equilibrium analysis, finite or discrete elements, continuum particle‐based approaches like the Material Point Method (MPM) have more recently been successful in modeling their full 3D elasto‐plastic behavior. In this paper, we develop a depth‐averaged Material Point Method (DAMPM) to efficiently simulate shallow landslides over complex topography based on both material properties and terrain characteristics. DAMPM is a rigorous mechanical framework which is an adaptation of MPM with classical shallow water assumptions, thus enabling large‐deformation elasto‐plastic modeling of landslides in a computationally efficient manner. The model is here demonstrated on the release of snow slab avalanches, a specific type of shallow landslides which release due to crack propagation within a weak layer buried below a cohesive slab. Here, the weak layer is considered as an external shear force acting at the base of an elastic‐brittle slab. We verify our model against previous analytical calculations and numerical simulations of the classical snow fracture experiment known as Propagation Saw Test. Furthermore, large scale simulations are conducted to investigate cross‐slope crack propagation and the complex interplay between weak layer dynamic failure and slab fracture. In addition, these simulations allow us to evaluate and discuss the shape and size of avalanche release zones over different topographies. Given the low computational cost compared to 3D MPM, we expect our work to have important operational applications in hazard assessment, in particular for the evaluation of release areas, a crucial input for geophysical mass flow models. Our approach can be easily adapted to simulate both the initiation and dynamics of various shallow landslides, debris and lava flows, glacier creep and calving. Plain Language Summary: Shallow landslides represent a significant threat to people and infrastructure. In mountainous regions, snow slab avalanches are a particular type of shallow landslide responsible for numerous casualties and important damage. Such an avalanche releases due to the failure of a weak layer buried below a cohesive slab. Despite significant progress in the understanding and modeling of such phenomena, the evaluation of the avalanche release size still remains a difficult task. This quantity is important for avalanche forecasting and is also a crucial input for hazard mapping model chains. To tackle this challenge, we develop a numerical method based on shallow water equations that simulates efficiently the release of slab avalanches over complex topography based on snow properties and terrain characteristics. The model is verified based on theoretical and numerical analysis of a state‐of‐the‐art snow fracture experiment. Then, large scale simulations are conducted to evaluate the shape and size of avalanche release zones over different topographies. Given its low computational cost, we expect our model to have operational applications in hazard assessment, especially for the evaluation of the avalanche release size which is an important quantity for avalanche forecasting and management. The model can be easily adapted to simulate the initiation and dynamics of other processes such as debris and lava flows, glacier creep and calving. Key Points: Development of a depth‐averaged Material Point Method for shallow landslidesVerification of the method based on analytical solutionsApplication to snow slab avalanche release [ABSTRACT FROM AUTHOR]

Despite the high accuracy of conventional acoustic hydrographic systems, measurement of the seabed along coastal belts is still a complex problem due to the limitations arising from shallow water. In addition to traditional echo sounders, airborne LiDAR also suffers from high application costs, low efficiency, and limited coverage. On the other hand, remote sensing offers a practical alternative for the extraction of depth information, providing fast, reproducible, low-cost mapping over large areas to optimize and minimize fieldwork. Satellite-derived bathymetry (SDB) techniques have proven to be a promising alternative to supply shallow-water bathymetry data. However, this methodology is still limited since it usually requires in situ observations as control points for multispectral imagery calibration and bathymetric validation. In this context, this paper illustrates the potential for bathymetric derivation conducted entirely from open satellite data, without relying on in situ data collected using traditional methods. The SDB was performed using multispectral images from Sentinel-2 and bathymetric data collected by NASA's ICESat-2 on two areas of relevant interest. To assess outcomes' reliability, bathymetries extracted from ICESat-2 and derived from Sentinel-2 were compared with the updated and reliable data from the BathyDataBase of the Italian Hydrographic Institute. [ABSTRACT FROM AUTHOR]

To describe demographic findings, typical injuries and functional neurological outcomes in patients with cervical trauma and tetraplegia sustained after diving into shallow water. A retrospective study was performed including all patients treated in BG Klinikum Hamburg suffering from tetraplegia after jumping into shallow water between 1st June 1980 and 31st July 2018. One hundred and sixty patients with cervical spinal injuries and tetraplegia following a dive into shallow water were evaluated. Of these, 156 patients (97.5%) were male. The mean age was 24.3 years ± 8.1 and the accidents occurred most often in inland waters (56.2%) and mostly between May and August (90.6%). In all cases there was one vertebra fractured, whereas in 48.1% of cases, two vertebrae were severed. In the majority of cases (n = 146), a surgical procedure was performed. Overall, the mean hospital stay was 202 days (±72, range: 31–403) and one patient died. On admission, 106 patients (66.2%) showed a complete lesion according to AIS A, with incomplete lesions in the remaining 54 patients (AIS B: n = 25 [15.6%], AIS C: n = 26 [16.3%], AIS D: n = 3 [1.9%]). In two thirds of the patients, the level of paralysis on admission was at the level of segments C4 (31.9%) or C5 (33.7%). Seventeen patients (10.6%) needed prehospital resuscitation. In 55 patients (34.4%), the neurological findings improved during the course of inpatient treatment and rehabilitation. Sixty-eight patients (42.5%) developed pneumonia, of which 52 patients (76.5%) were ventilated. In addition, 56.5% of patients with paralysis levels C0–C3 required ventilation, whereas only 6.3% of patients with paralysis levels C6–C7 were affected. Three patients (1.9%) were discharged from hospital with continuous ventilation. Overall, 27.4% of all AIS A patients, 56% of all AIS B patients and 46.2% of all AIS C patients improved neurologically, with 17% of all patients being able to walk. The consequences of a cervical spine injury after diving into shallow water are severe and lifelong. Functionally, patients may benefit from care in a specialised centre, both in the acute phase and during rehabilitation. The more incomplete the primary paralysis, the greater the possibility of neurological recovery. [ABSTRACT FROM AUTHOR]

The Lie symmetry analysis is applied for the study of a modified one-dimensional Saint–Venant system in which the density depends on the average temperature of the fluid. The geometry of the bottom we assume that is a plane, while the viscosity term is considered to be nonzero, as the gravitational force is included. The modified shallow water system is consisted by three hyperbolic first-order partial differential equations. The admitted Lie symmetries form a four-dimensional Lie algebra, the A3,3 ⊕ A1. However, for the viscosity free model, the admitted Lie symmetries are six and form the A5,19 ⊕ A1 Lie algebra. For each Lie algebra we determine the one-dimensional optimal system and we present all the possible independent reductions provided by the similarity transformations. New exact and analytic solutions are calculated for the modified Saint–Venant system. [ABSTRACT FROM AUTHOR]

Viscous linear surface waves are studied at arbitrary wavelength, layer thickness, viscosity, and surface tension. We find that in shallow enough fluids no surface waves can propagate. This layer thickness is determined for some fluids, water, glycerin, and mercury. Even in any thicker fluid layers, propagation of very short and very long waves is forbidden. When wave propagation is possible, only a single propagating mode exists for a given horizontal wave number. In contrast, there are two types of non-propagating modes. One kind of them exists at all wavelength and material parameters, and there are infinitely many such modes for a given wave number, distinguished by their decay rates. The other kind of non-propagating mode that is less attenuated may appear in zero, one, or two specimens. We notice the presence of two length scales as material parameters, one related to viscosity and the other to surface tension. We consider possible modes for a given material on the parameter plane layer thickness versus wave number and discuss bifurcations among different mode types. Motion of surface particles and time evolution of surface elevation is also studied at various parameters in glycerin, and a great variety of behaviour is found, including counterclockwise surface particle motion and negative group velocity in wave propagation. [ABSTRACT FROM AUTHOR]

This work presents an investigation of ice shelf vibration using a model based on shallow water approximation. The study focused on the effect of changes in the draft on the vibration of the ice shelf and presents both time-domain and frequency-domain results. The model used a radiation condition for energy propagation into the ice shelf. Furthermore, an energy balance relation was derived to investigate the energy flow within the system. Results show that changes in the draft can significantly impact the ice shelf's vibration and that the energy flow within the system is affected by the geometry of the ice shelf. Results are presented for the interaction of wave packets in the time domain with the ice shelf. These show that energy is reflected and transmitted by the ice shelf and that the motion of the wave packets is very different in the ice shelf than in the open water. Overall, this study provides insight into the dynamics of ice shelf vibration and highlights the importance of considering changes in the draft and using the time domain when modelling these phenomena. [ABSTRACT FROM AUTHOR]

A few scholars have developed the models for retrieval of water depth from subsurface reflectance of multispectral images to avoid the influences of sun glitter. However, the models are only suitable for case I water. For this reason, this study proposes a bathymetry retrieval model using subsurface reflectance for both case I and case II water. The model first corrects the water surface reflectance image and then converts it into a subsurface reflectance image, and the subsurface reflectance image is used as the water depth retrieval image. Landsat 8 images were taken for experiments in case 1 water and case 2 water, and two water areas, Weizhou Island, Guangxi, China, and Molokai Island, Hawaii, USA, were used to verify the proposed model. The experimental results showed that the proposed model reduced the root-mean-squared error of the retrieved water depth in the Weizhou and Molokai areas from 3.113 to 2.903 m and 4.239 to 3.653 m, respectively, i.e., improve accuracy of water depth at 6.75% and 13.82% for Weizhou and Molokai areas, respectively. Therefore, the results demonstrate that the proposed model using subsurface reflectance can significantly improve the accuracy of bathymetry retrieval via spaceborne multispectral images.

Inland transport plays a significant role in the lives of the peoples of many countries since it offers many environmental, economic, and social benefits over other modes of transportation. Therefore, many studies have recently been carried out with the purpose of improving the infrastructure of the River Nile in order to increase the annual volume of transported cargoes over a huge network of inland waterways that connect most Egyptian cities. However, further research is required to select a suitable transport system capable of transporting the greatest amount of cargoes through River Nile's very shallow waterways. Thus, in this article, the distinctive characteristics of all river transportation modes employed in Egypt is analyzed and the pusher train barge system has been found to be the most appropriate method of transporting cargoes along waterways with limited water depth. Based on a technical and operational criterion termed transport efficiency, six possible configurations of a proposed pusher train barge system are compared in order to select the most economically feasible configuration to operate along the Cairo-Aswan waterway. For three different loading conditions, this study is carried out with the use of a computational fluid dynamics software package (CFD-FLUENT) and the results are validated.

In this paper, a 2D numerical modeling of sound wave propagation in a shallow water medium that acts as a waveguide, are presented. This modeling is based on the method of characteristic which is not constrained by the Courant–Friedrichs–Lewy (CFL) condition. Using this method, the Euler time-dependent equations have been solved under adiabatic conditions inside of a shallow water waveguide which is consists of one homogeneous environment of water over a rigid bed. In this work, the stability and precision of the method of characteristics (MOC) technique for sound wave propagation in a waveguide were illustrated when it was applied with the semi-Lagrange method. The results show a significant advantage of the method of characteristics over the finite difference time domain (FDTD) method.

Describing the long waves in shallow water, a generalized Broer-Kaup-Kupershmidt system is investigated in this paper. With respect to the horizontal velocity of the water wave and the height of the water surface, we use symbolic computation to build up (A) a scaling transformation, (B) a set of the hetero-Bäcklund transformations, from that generalized system to a known linear partial differential equation, as well as (C) two sets of the similarity reductions, each of which from that generalized system to a known ordinary differential equation. Our results depend on all the shallow-water coefficients for that generalized system. [ABSTRACT FROM AUTHOR]

The measurements of airborne and underwater noise radiated by a Griffon BHT130 hovercraft were conducted in the Ural-Caspian Channel and in the North Caspian Sea. This type of hovercraft is being used for all-season cargo and crew transportation to oil and gas platforms within the environmentally sensitive area of the Ural River estuary known for its abundant bird and fish fauna. Several field campaigns were organized from 2017 to 2022 to measure and analyze acoustic noise levels simultaneously in the air and underwater at various sites and hovercraft speeds. Airborne noise levels were estimated according to ISO 2922:2020, 2021. Underwater noise study included not only acoustic pressure recordings but also particle velocity measurements with a self-designed pressure gradient sensor (PGS), which is important since the hearing of the majority of fish perceives the sound in terms of particle motion. This study is the first to report the particle velocity levels formed underwater during hovercraft passages. The minimum levels of underwater noise, 100 dB re 1 µPa (pressure), 45 dB re 1 nm/s (particle velocity), and airborne noise, 93 dBA re 20 µPa (pressure), normalized to a distance of 25 m were observed for the hovercraft passages at a cruising speed of 7–15 m/s. Thus, this speed interval can be recommended as an optimum to minimize an acoustic impact on ornitho- and fish fauna. The directivity of the hovercraft noise was estimated for the first time and utilized for noise mapping of the Ural-Caspian Channel. The possible hydrodynamic effect of a passing hovercraft is discussed. [ABSTRACT FROM AUTHOR]