Shallow-water Cases Research Articles

Numerical Investigation on a High-Speed Transom Stern Ship Advancing in Shallow Water

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.

Increasing P-Wave and S-Wave Velocity Resolution with FWI — a North Sea Shallow Water Case Study

Increasing P-Wave and S-Wave Velocity Resolution with FWI — a North Sea Shallow Water Case Study

Shallow water memory: Stokes and Darwin drifts

It has been shown in [SciPost Phys. 14, 102 (2023)] that shallow water in the Euler description admits a dual gauge theory formulation. We show in the Lagrange description this gauge symmetry is a manifestation of the 2 dimensional area-preserving diffeomorphisms. We find surface charges associated with the gauge symmetry and their algebra, and study their physics in the shallow water system. In particular, we provide a reinterpretation of the Kelvin circulation theorem in terms of conserved charges. In the linear shallow water case, the charges form a u(1) current algebra with level proportional to the Coriolis parameter over the height of the fluid. We also study memory effect for the gauge theory description of the linearized shallow water and show Euler, Stokes and Darwin drifts can be understood as a memory effect and/or change of the surface charges in the gauge theory description.

Solving a Seismic Mystery With the Audio From a Diver's Camera: A Case of Shallow Water T‐Waves in the Persian Gulf

AbstractSparse offshore coverage of seismic networks has hindered detailed studies of submarine earthquakes and their associated seismic hazard. We present results of our analysis of a diver's recording of acoustic signals from an ML = 5.6 earthquake in the Persian Gulf. We model the signals as a set of several shallow water T phases the frequency and group velocity of which are determined by bathymetry. We show that the audio track from this recording can provide reliable estimates of earthquake location and seismic moment. We also show that the reported shaking in the southern Persian Gulf, >170 km from the source of this small earthquake could result from T waves traveling through the entire width of the basin. Our results point to rudimentary and affordable underwater microphones similar to those used in the divers' cameras as tools to build efficient, low‐cost networks for the study of offshore events and early warning.

Dispersive solitary wave structures with MI Analysis to the unidirectional DGH equation via the unified method

This article discusses the dynamical structures of unique traveling wave solutions to the unidirectional time-fractional Dullin–Gottwald–Holm equation, as well as the modulation instability analysis of solitary wave prorogations in shallow water mechanics. Different sorts of explicit solutions are obtained which are expressed as the kink, singular kink, singular soliton, multiple solitons and other forms of soliton with specified parameters by utilizing the unified method. Three-dimensional plots, density plots, and their two-dimensional combined line plots of the obtained novel solutions satisfying the corresponding equation of interest are given to comprehend the underlying mechanisms of the identified family.The obtained novel wave solutions can motivate applied scientists to refine their theories to the best of their abilities and can be utilized to verify the outcomes of numerical simulations for wave propagation in shallow water and other nonlinear cases. The implemented methods are shown to be straightforward and effective for approximating the considered equation, and it may be utilized to resolve numerous classes of nonlinear partial differential equations that arise in engineering and mathematical physics.

Simulations of nonlinear waves generated by an air-cushion vehicle

One major area of interest in air-cushion vehicle (ACV) hydrodynamics is ACV-generated waves. However, the nonlinear effects of varying cushion pressures on the wake system remain unclear. This study presents a fast time-domain method that simulates nonlinear waves. The paper uses a pressure distribution to represent the ACV, models the nonlinear waves by the high-order spectral method, and saves computational effort with damping and domain reconstruction techniques. We simulate the nonlinear waves generated by a constant-speed/accelerating ACV in calm water and by ACV in regular waves, and compare our time-domain results with experimental, CFD, and perturbation theoretical ones. The results show that the nonlinear effects are more pronounced in shallow water and low-speed cases. In the constant-speed case, the maximum wave drag predicted by the nonlinear method is lower than the linear prediction; in the accelerating case, the nonlinear method shows a slight decrease in the Froude number when the resistance reaches the maximum during acceleration. For ACV in waves, nonlinear simulations show a second-order wave component resulting from the interaction between the air cushion and incident waves. This component has little effect on wave force but does contribute to the near-field wave pattern.

An automatically well-balanced formulation of pressure forcing for discontinuous Galerkin methods for the shallow water equations

This paper begins a development of methods for addressing variable bottom topography in discontinuous Galerkin numerical methods for multi-layer, variable-density models of ocean circulation. For numerical models of ocean circulation, it is a widespread practice to split the fast (external) and slow (internal) dynamics into separate subsystems that are solved by different techniques. The fast dynamics are modeled by a vertically-integrated system that is very similar to the shallow water equations for a hydrostatic fluid of constant density. As a first step, the present paper focuses on variable bottom topography for the shallow water equations; extensions to the multi-layer case will be reported elsewhere.A central point of this work, for both the shallow water and the multi-layer cases, is the representation of the pressure forcing in the momentum equations. For the shallow water case, the present work does not use the standard representation of the pressure forcing that is widely used for the shallow water system. Instead, it begins with a more basic form of the momentum equations for a fluid flow, and it proceeds directly to a weak Galerkin form via integration over a suitable fluid region. The resulting formulation of the momentum equations is automatically well-balanced, subject to an assumption that the algorithms used to compute quantities at cell edges reproduce the continuous values in the case where all functions involved are continuous. In addition, this formulation has a structure that is analogous to that of the momentum equations in the individual layers of a multi-layer fluid, and this facilitates consistency between the two subsystems that are used to model such a fluid.The numerical computations described here include tests of well-balancing and tests of wave propagation over variable topography.

SHIP-SHIP HYDRODYNAMIC INTERACTION IN CONFINED WATERS WITH COMPLEX BOUNDARIES BY A PANELLED MOVING PATCH METHOD

This paper presents a potential flow solution for online estimation of hydrodynamic interaction between ships moving in restricted waters with complex boundaries. Each ship in concern is linked with a moving patch representing the arbitrary bathymetry beneath it. The wetted surfaces of ship hulls are meshed and loaded prior to the simulation, while the moving patches are dynamically discretized by a fast and robust mesh generator. The proposed method is validated for the ship- ship interaction case in the shallow water case with a flat and horizontal seabed where the mirror image technique is applicable, and satisfactory agreement is obtained. The method is further applied to simulate two interaction scenarios involving arbitrary seabed topography, and the numerical results are obtained and discussed.

A variety of novel closed‐form soliton solutions to the family of Boussinesq‐like equations with different types

This paper deals with the closed-form solutions to the family of Boussinesq-like equations with the effect of spatio-temporal dispersion. The sine-Gordon expansion and the hyperbolic function approaches are efficiently applied to the family of Boussinesq-like equations to explore novel solitary, kink, anti-kink, combo, and singular-periodic wave solutions. The attained solutions are expressed by the trigonometric and hyperbolic functions including tan, sec, cot, csc, tanh, sech, coth, csch, and of their combination. In addition, the mentioned two approaches are applied to the aforesaid models in the sense of Atangana conformable derivative or Beta derivative to attain new wave solutions. Three-dimensional and two-dimensional graphs of some of the obtained novel solutions satisfying the corresponding equations of interest are provided to understand the underlying mechanisms of the stated family. For the bright wave solutions in terms of Atangana’s conformable derivative, the amplitudes of the bright wave gradually decrease, but the smoothness increases when the fractional parameters α and β increase. On the other hand, the periodicities of periodic waves increase. The attained new wave solutions can motivate applied scientists for engineering their ideas to an optimal level and they can be used for the validation of numerical simulation results in the propagation of waves in shallow water and other nonlinear cases. The performed approaches are found to be simple and efficient enough to estimate the solutions attained in the study and can be used to solve various classes of nonlinear partial differential equations arising in mathematical physics and engineering.

Training deep networks with only synthetic data: Deep-learning-based near-offset reconstruction for (closed-loop) surface-related multiple estimation on shallow-water field data

Accurate removal of surface-related multiples remains a challenge in shallow-water cases. One reason is that the success of surface-related multiple estimation (SRME)-related algorithms is sensitive to the quality of the near-offset reconstruction. When it comes to a larger missing gap and a shallower water bottom, the state-of-the-art near-offset gap construction method — the parabolic Radon transform — fails to provide reliable recovery of the shallow reflections due to the limited information from the data and highly curved events at near offsets with strong lateral amplitude variations. Therefore, we have developed a novel workflow that first deploys a deep-learning-based reconstruction of the shallow reflections and then uses the reconstructed data as the input for the subsequent surface multiple removal. In particular, we use a convolutional neural network architecture — U-net that was developed from convolutional autoencoders with extra direct skip connections between different levels of encoders and the corresponding decoders. Instead of using field data directly in network training, the training set is carefully synthesized based on the prior water-layer information of the field data; thus, a fully sampled field data set, which is difficult to obtain, is not needed for training in our workflow. An inversion-based approach — closed-loop SRME — is used for the surface multiple removal, in which the primaries are directly estimated via full-waveform inversion in a data-driven manner. Finally, the effectiveness of our workflow is determined based on 2D North Sea field data in a shallow-water scenario (92.5 m water depth) with a relatively large minimum offset (150 m).

A Fast Algorithm for the Prediction of Ship-Bank Interaction in Shallow Water

The hydrodynamic interaction induced by the complex flow around a ship maneuvering in restricted waters has a significant influence on navigation safety. In particular, when a ship moves in the vicinity of a bank, the hydrodynamic interaction forces caused by the bank effect can significantly affect the ship’s maneuverability. An efficient algorithm integrated in onboard systems or simulators for capturing the bank effect with fair accuracy would benefit navigation safety. In this study, an algorithm based on the potential-flow theory is presented for efficient calculation of ship-bank hydrodynamic interaction forces. Under the low Froude number assumption, the free surface boundary condition is approximated using the double-body model. A layer of sources is dynamically distributed on part of the seabed and bank in the vicinity of the ship to model the boundary conditions. The sinkage and trim are iteratively solved via hydrostatic balance, and the importance of including sinkage and trim is investigated. To validate the numerical method, a series of simulations with various configurations are carried out, and the results are compared with experiment and numerical results obtained with RANSE-based and Rankine source methods. The comparison and analysis show the accuracy of the method proposed in this paper satisfactory except for extreme shallow water cases.

Catalogue of rogue waves occurred in the World Ocean from 2011 to 2018 reported by mass media sources

A catalogue of anomalously large waves (rogue or freak waves) occurred in the World Ocean during 2011–2018 reported in mass media sources and scientific literature has been compiled and analyzed. It includes 210 hazardous events caused damages or human losses. The majority of events is based on eyewitness accounts, and as a rule is not confirmed by direct measurements. All collected events divided into deep water cases, shallow water cases and occurrences on the coast (gentle beach or rocks). The following parameters have been determined: date, location, damage, description, reference, and weather conditions. The most dangerous areas in the World Ocean in terms of freak waves are highlighted.

Renewable energy from the high seas: Geo-spatial modelling of resource potential and legal implications for developing offshore wind projects beyond the national jurisdiction of coastal States

Offshore wind energy projects are currently restricted to the exclusive economic zones of coastal States. Recent advances in technology are raising the prospect of utilising excellent wind resources on the high seas.Using a global geo-spatial model we identify potential resource areas for this. In the shallow water case for bottom fixed foundations the largest locations are found on the Mascarene Plateau in the Indian Ocean and the Grand Banks in the North Atlantic. The deep water case for floating platforms identifies the largest regions on the Grand Banks/Flemish Cap and Rockall Bank/Hatton Ridge, both in the North Atlantic. The overall legal framework for wind energy projects on the high seas is the United Nations Convention in the Law of the Sea. Flag states will play a central regulatory role for high seas wind energy developments. There is the danger that flags of convenience might evolve and unduly undercut environmental and safety standards that are in place for projects on the territorial sea and EEZ. Such abuse of high seas freedom could compromise the UNCLOS principle of ‘due regard’. Marine spatial planning approaches and the establishment of cooperative mechanisms, led by the IMO, could safeguard against such potential misappropriation.

Dimension-Reduced Model for Deep-Water Waves

Starting from the 2D Euler equations for an incompressible potential flow, a dimension-reduced model describing deep-water surface waves is derived. Similar to the Shallow-Water case, the z-dependence of the dependent variables is found explicitly from the Laplace equation and a set of two one- dimensional equations in x for the surface velocity and the surface elevation remains. The model is nonlocal and can be formulated in conservative form, describing waves over an infinitely deep layer. Finally, numerical solutions are presented for several initial conditions. The side-band instability of Stokes waves and stable envelope solitons are obtained in agreement with other work. The conservation of the total energy is checked.

Offshore power generation with carbon capture and storage to decarbonise mainland electricity and offshore oil and gas installations: A techno-economic analysis

This study investigates the techno-economic potential of offshore power generation from natural gas with carbon capture and storage to reduce the climate impact of mainland electricity and the offshore oil and gas industry. This potential is assessed through techno-economic assessments over two relevant cases (“floating” and “shallow water” cases) including comparison with relevant reference concepts.In the base case evaluation, the offshore power plant concept toward decarbonising mainland electricity results in high costs (178 and 258 $/MWh respectively for the floating and shallow water cases) compared to a reference onshore power plant with carbon capture and storage (around 95 $/MWh). However, a stronger potential is identified for the concept toward decarbonising offshore oil and gas platforms as the concept results in costs more comparable with the reference electrification concept (137 compared to 133 $/MWh in the floating case and 207 compared to 166 $/MWh in the shallow water case).Although the base cases show a limited potential for the offshore concept, the results show that with technological improvements (advanced capture technology, reuse of infrastructure…) and more suited case characteristics (development based on associated gas…), the offshore concept offers a significant potential for cost-efficiently decarbonising the offshore oil and gas industry, while a more moderate potential is foreseen for the decarbonisation of mainland electricity.

Numerical study on characteristics of dam-break wave

The influence of the downstream water depth on dam-break wave is systematically and comparatively studied by simulating the physical experiments in this study. Commercial CFD software package FLOW-3D is chosen as the simulation tool and is validated firstly. Three experimental cases of different initial downstream water depth, including dry-bed case (r = 0), shallow downstream water case (r = 0.1) and deep downstream water case (r = 0.4) carried out by Ozmen-Cagatay and Kocaman (2010) are then simulated. The generation and propagation process of dam-break wave is divided into two and three stages, respectively, for dry-bed and wet-bed cases. And the characteristics of the dam-break wave including free surface profile, wave front velocity, mark point movement and trajectory, interface between upstream and downstream water, bottom resistance and turbulent kinetic energy are compared and analyzed elaborately in each stage for each case. The differences of the characteristics between different downstream water depth cases are achieved and the reasons of the differences are explored, which present a comprehensive understanding of dam-break wave generation and propagation.

Effects of the interface position of water-air flow on turbulent wall structures

Direct numerical simulations (DNS) are performed to investigate the effect of the interface position of water-air flow on turbulence statistics and flow structures in wall-bounded water-air turbulent flow through a straight channel. Water depths of 90 and 180 viscous wall units, referred to as shallow-water and deep-water cases, respectively, are examined. Water-to-air density and viscosity ratios of 831.7 and 55.56 are considered to model a realistic flow condition at temperature of 25 oC and pressure of 1 atm. The Reynolds number and Froude number are set to 180 and 1.22 x 10-4, respectively, for both shallow-water and deep-water case, based on the friction velocity at the bottom wall, the half depth of the channel, and water density and viscosity. The Navier-Stokes equations are solved using a timesplitting projection method on an octree grid structure, while the deformation of the interface between water and air is computed using a volume-of-fluid method. With the presence of the water-air interface, velocity profiles in deep-water and shallow-water cases are found to slightly deviate from the log-law profile for a single phase turbulent flow in a channel. The deviation is magnified when the interface is placed closer to the log-law region. Turbulent velocity fluctuations in the water stream are found to be associated with quasi-streamwise vortices and hairpin vortices. The quasi-streamwise vortices which are attached close to the wall are found in both deep-water and shallow-water cases. However, the hairpin vortices of which leading portions are lifted away from the wall are found to be diminished in the shallow-water case while they are clearly observed in the deep-water case.

Stability of an air–water flow in a semispherical container

This numerical study analyzes the stability of a steady axisymmetric air–water flow driven by a rotating top disk in a sealed semispherical container. A motivation is possible applications in aerial bioreactors. The centrifugal force pushes the air to periphery near the disk, downward near sidewall, toward the axis near the interface, and upward near the axis. This meridional circulation of air drives the water counter-circulation while the centrifugal force tends to induce the water co-circulation. Their competition results in the development of a three-eddy pattern as the rotation intensifies. The air circulation and the water co-circulation are separated by a thin layer of water counter-circulation. It is shown that the time-oscillatory helical instability emerges when the three-eddy pattern is well formed. The azimuthal wave number is m=1 in the shallow-water case and m=2 otherwise. The analysis of flow patterns and critical-disturbance energy distributions indicates that the instability emerges in the air domain and likely is of the shear-layer type.

Standardization of Offshore Surface Wind Speeds

AbstractWind measurement offers an essential data source for a wide range of practices in the fields of meteorology and wind engineering. However, records of surface winds are usually influenced by terrain/topographic effects, and direct usage of raw data may bring in nonignorable errors for follow-up applications. A data-driven standardization scheme was recently proposed by the authors to convert the surface wind measurements over rugged terrain into their potential values corresponding to reference conditions, that is, for neutral winds at a height of 10 m above open flat terrain (z0 = 0.03 m). As a complementary part of the preceding work, this study focuses on the standardization of surface wind speeds with marine exposures. The effect of wind strength on the roughness of the sea surface is further taken into account, with emphasis on the difference between deep-ocean and shallow-water cases. As an application example, wind measurements at a buoy site near the coastal line (water depth is 14 m) are adjusted to their potential values, which are then compared with those at a nearby station. The good agreement between the two sets of results demonstrates the accuracy and effectiveness of the standardization method. It is also found that the behavior of roughness length scale over shallow water may differ noticeably from that over deep ocean, especially under strong wind conditions, and an inappropriate usage of marine roughness predictors may result in significant estimation errors.

Removing multiple scattering in underwater target detection

Recent advances have been made in the field of optics to image through multiple-scattering media in a regime where classical imaging techniques, which rely on the single-scattering approximation, fail. Using results generated by random matrix theory, it is possible to filter the response matrix generated by a source/receiver array to remove the multiple scattering components of the received signals. After removing the multiple scattering components, classical imaging techniques can be used to image with the single-scattering components. We show how this single-scattering filter can be adapted for underwater acoustical imaging in cases where multiple scattering effects are large compared to the reflection from the target. A full-wave 3-dimensional time-domain scaled model is used to characterize filter performance as a function of target strength and environmental coherence length for a shallow-water case. Preliminary results indicate that the filter can be used to detect a target located at least 2 mean f...