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The horizontal records of ocean‐bottom seismometers (OBS) are usually highly noisy, generally due to ocean‐bottom currents tilting the instrument, which greatly limits their practical usage in ocean‐bottom seismology. In shallow water, water waves with energy concentration around 0.07 Hz induce additional noise on OBSs. Such noise is not well understood. In this article, we propose a noise model to explain the horizontal noise around 0.07 Hz. The noise model consists of three types of noise, that is, water‐wave‐induced noise, current noise with a relatively constant orientation, and background random noise. The wave‐induced horizontal acceleration is theoretically shown to be proportional to the time derivative of ocean‐bottom pressure. We validate the noise model and related theories using realistic observations. Results are potentially applicable to determine the propagation direction of water waves nearshore, and also provide constraints on the underlying Earth structure. The results can also be applied to the removal of wave‐induced noise, achieving a typical maximum improvement in the signal‐to‐noise ratio of 10–20 dB for time periods with strong wave noise. Plain Language Summary: Ocean Bottom Seismometers (OBSs) are important instruments for seafloor seismology. However, OBS recordings are highly noisy, and the noise mechanism is not well understood. Currently, most research focuses on the noise in the vertical channel, and understanding of the horizontal noise has been limited. In this study we investigate one specific type of OBS noise, which is commonly observed in shallow water is associated with water waves. We propose a noise model to explain the noise, and also develop analytical theories for the noise generation. The noise model and related theories are verified by realistic recordings. Based on the theories, we propose potential applications, for example, derivation of the water‐wave propagation direction and subsurface structure inversion using the noise. A method of noise removal is also developed, which highly improves the signal‐to‐noise ratio. Key Points: We propose a noise model to explain the horizontal OBS noise around 0.07 Hz in shallow waterThe noise model and related theories are validated by realistic observationsPotential applications to determine water‐wave direction, Earth structure inversion and noise removal are discussed [ABSTRACT FROM AUTHOR]

This paper investigates the hydroelastic response of a multi-patch floating photovoltaic (FPV) structure in water waves over a stepped seabed. The resonance conditions and underlying mathematical mechanism of FPV patches are explored based on the linear potential-flow theory and the thin-plate model. An implicit function of the open-water wavelength and the FPV patch's structural wavelength is derived. Resonance conditions occur in the FPV patch when the patch length and structural wavelength (rather than the water wavelength, as commonly believed) satisfy certain proportions. Mathematical derivations are conducted to interpret the value of each proportion. Two resonance conditions are recognized based on the mathematical structure of the solution. The effects of a stepped seabed and adjacent patches on the resonance conditions and hydroelastic behavior of FPV structures are also investigated. For a given stiffness parameter, the resonance conditions of FPV patches are solely determined by the water depth. The distance between adjacent patches does not alter the resonance conditions of each patch. Resonance occurs in the water body between two patches when the ratio of patch distance to water wavelength takes certain proportional values. A resonant water body tends to amplify the oscillation amplitude of both patches. However, when two FPV patches and a constrained water body reach their theoretical resonance conditions at the same time, the oscillation amplitudes of both the seaward patch and the constrained free surface are evidently suppressed. The transmitted waves of an FPV structure are largely determined by the dynamics of the leeward patch. [ABSTRACT FROM AUTHOR]

In this paper, a new extended (3 + 1)‐dimensional generalized Kadomtsev–Petviashvili (KP)–Boussinesq equation, with two additional terms utt$$ {u}_{tt} $$ and uxz$$ {u}_{xz} $$, is proposed and investigated. This new equation models both left and right going waves like the Boussinesq equation and describes the transmission of tsunami waves at the bottom of the ocean and nonlinear ion‐acoustic waves in the magnetized dusty plasm. We have constructed one set of breathers and first order periodic waves from the two‐soliton solution. Moreover, the four‐soliton solution consists of two sets of breathers, second order periodic waves, and a hybrid of breathers and periodic line waves. Then, we introduce two kinds of "long wave" limits to obtain the rational and semi‐rational solutions for N=2,3,4$$ N=2,3,4 $$. Under specific parametric constraints, the obtained rational and semi‐rational solutions are nonsingular. The rational solution can be classified as first order line rogue wave, single breather, second order line rogue wave, double breather, a hybrid of breather and line rogue wave, a hybrid of breather, and single soliton. The semi‐rational solution can be classified as the first and second order kink‐shaped rogue wave, a hybrid of breather and one (two) soliton(s), a hybrid of a set of breathers, and a single soliton (breather). In addition, we give Theorem 2.1 for the higher order rational solutions. [ABSTRACT FROM AUTHOR]

In this study, a three-dimensional entirely nonlinear model was used for simulating the wave generation problem caused by seabed movement. This study focuses on the waveform of the initial stage of wave generation. The numerical model was verified by comparing the simulated results with existing experimental results. Satisfactory results of the waveforms and flow fields were obtained. The simulations of the free surface disturbances and flow field velocities caused by the sudden rising or falling of a circular cylinder with the dimensionless radius ( r 0 ) and height ( b m ) normalized by still-water depth are discussed. We considered the combinations of r 0 = 2 –10 and b m = 0. 1 –0.3. For the moving cylinder with a moderate height (e.g. b m = ± 0. 2 and ± 0. 2 5) and r 0 ≥ 4 , it is found that the water-surface shape is closer to the shape of the terrain. The central water level ( ζ c ) varying with time is also focused herein. For the rising cylinder, when b m ≤ 0. 1 5 , the maximum ζ c is always less than its corresponding b m for any r 0 . For the falling cylinder, if r 0 is larger than five times the still water depth, then the maximum ζ c will exceed its corresponding b m . This result provides a further understanding of the basic phenomenon of the initial waves caused by the movement of the seabed topography. [ABSTRACT FROM AUTHOR]

Although tsunamis are dispersive water waves, hazard maps for earthquake-generated tsunamis neglect dispersive effects because the spatial dimensions of tsunamis are much greater than the water depth, and dispersive effects are generally small. Furthermore, calculations that include non-dispersive effects tend to predict higher tsunamis than ones that include dispersive effects. Although non-dispersive models may overestimate the tsunami height, this conservative approach is acceptable in disaster management, where the goal is to save lives and protect property. However, we demonstrate that offshore frequency dispersion amplifies tsunamis caused by outer-rise earthquakes, which displace the ocean bottom downward in a narrow area, generating a dispersive short-wavelength and pulling-dominant (water withdrawn) tsunami. We compared observational evidence and calculations of tsunami for a 1933 Mw 8.3 outer-rise earthquake along the Japan Trench. Dispersive (Boussinesq) calculations predicted significant frequency dispersion in the 1933 tsunami. The dispersive tsunami deformation offshore produced tsunami inundation heights that were about 10% larger than those predicted by non-dispersive (long-wave) calculations. The dispersive tsunami calculations simulated the observed tsunami inundation heights better than did the non-dispersive tsunami calculations. Contrary to conventional practice, we conclude that dispersive calculations are essential when preparing deterministic hazard maps for outer-rise tsunamis. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is twofold: first, to derive a consistent model free-surface runup flow problems over deformable beds. The authors couple the nonlinear one-dimensional shallow water equations, including friction terms for the water free-surface and the two-dimensional second-order solid elastostatic equations for the bed deformation. Second, to develop a robust hybrid finite element/finite volume method for solving free-surface runup flow problems over deformable beds. The authors combine the finite volume for free-surface flows and the finite element method for bed elasticity. Design/methodology/approach: The authors propose a new model for wave runup by static deformation on seabeds. The model consists of the depth-averaged shallow water system for the water free-surface coupled to the second-order elastostatic formulation for the bed deformation. At the interface between the water flow and the seabed, transfer conditions are implemented. Here, hydrostatic pressure and friction forces are considered for the elastostatic equations, whereas bathymetric forces are accounted for in the shallow water equations. As numerical solvers, the authors propose a well-balanced finite volume method for the flow system and a stabilized finite element method for elastostatics. Findings: The developed coupled depth-averaged shallow water system and second-order solid elastostatic system is well suited for modeling wave runup by deformation on seabeds. The derived coupling conditions at the interface between the water flow and the bed topography resolve well the condition transfer between the two systems. The proposed hybrid finite volume element method is accurate and efficient for this class of models. The novel technique used for wet/dry treatment accurately captures the moving fronts in the computational domain without generating nonphysical oscillations. The presented numerical results demonstrate the high performance of the proposed methods. Originality/value: Enhancing modeling and computations for wave runup problems is at an early stage in the literature, and it is a new and exciting area of research. To the best of our knowledge, solving wave runup problems by static deformation on seabeds using a hybrid finite volume element method is presented for the first time. The results of this research study, and the research methodologies, will have an important influence on a range of other scientists carrying out research in related fields. [ABSTRACT FROM AUTHOR]

The presence of a sill alters the traditional flat seabed conditions, imposing significant effects on hydrodynamic characteristics of the wave-body interaction problem. Eigenfunction matching method (EMM), which is a typical analytical method, is employed to precisely evaluate these effects on two-dimensional radiation of linear water waves by a rectangular buoy. The agreement with the published data and numerical results by the boundary element method (BEM) indicates the correctness of the present EMM. Four aspects involving varying height of the sill, varying width of the sill, varying water depth of the right semi-infinite subdomain, and varying relative positions between the buoy and the sill are considered. Analytical results show that among all the hydrodynamic coefficients, the added mass coefficient of heave is affected most by the varying sill. [ABSTRACT FROM AUTHOR]

Net enclosure aquaculture is a newly developed eco-friendly marine aquaculture method and has been applied extensively in China because of the advantages of large water body, wide space for fish activities, closer to nature culture environment and closer to wild culture objects. Pile-type and floating-rope-type are two main construction types of enclosure engineering, and the pile-type is more preferable owing to its higher performance in withstanding harsh ocean environment. The pile-type aquaculture engineering consists of net panel system and pile system configured in mono or multi rows. In practice, the overturn and breakage of the piles have occurred and lead to the escape of cultured fishes, resulting in great economic loss. In order to solve these problems and improve the stability and safety of piles, the mechanical characteristics of piles in marine dynamic environment were analyzed in this study, and the pile-type aquaculture site located at Taohua island, Zhoushan was chosen as the study case. The subgrade reaction method, representing the soil surrounding of the pile by a series of discrete horizontal springs was adopted to investigate the effects of water depth, current velocity, wave height and combined action of wave and current, together with the embedded depth on the dynamic response of piles. The results showed that the maximum displacement was found at the top of the pile and increased with the increase of current velocity, wave height and water depth, and decreased with the increase of embedded depth. The positive and negative bending moment in the sides of the vertical line of zero bending moment increased first and then decreased along the pile, showing a shape of symmetrical S. The maximum bending moment was found about 2 m underneath the sea bed and exhibited a similar dynamic tendency to that of the maximum lateral deflection. As for the case of pure current, the piles kept stable and safety at the current velocity of 0.8, 1.0, 1.2 and 1.5 m/s. However, it could be damaged when the wave height exceeded 5 m or in the combined action of wave height of 3.0 m and current velocity of 1.0 m/s. For the engineering case in this study, the embedded depth should be larger than 17 m when the wave height of 5 m was considered as the lateral loading. In addition, a ratio of the length above the sea bed surface and embedded in the sea bed of the pile not more than 0.8 was advisable. Filed observation of the piles lateral deflection and stress force should be monitored in a long period so as to improve the analytical method specially used for net enclosure engineering. The results can provide guidance for the net enclosure design and construction. [ABSTRACT FROM AUTHOR]

To simulate the wave-induced response of coupled pore fluids and a solid skeleton in shallow water, a set of solutions with different formulations (fully dynamic, partly dynamic, and quasi-static) corresponding to each soil behavior assumption is presented. To deal with Jacobian elliptic functions involved in the cnoidal theory, a Fourier series approximation is adopted for expanding the boundary conditions on the seabed surface. The parametric study indicates the significant effect of nonlinearity for shallow water wave, which also enhances the effect of soil characteristics. The investigation of the applicability of reduced formulations reveals the necessity of a partly or even fully dynamic formulation for the wave-induced seabed response problem in shallow water, especially for thickened seabed. The analysis of liquefaction in the seabed indicates that the maximum depth of liquefaction is shallower, and the width of liquefaction is broader under cnoidal wave loading. The present analytical model can provide more reasonable result for the wave-induced seabed response in the range of shallow water wave. [ABSTRACT FROM AUTHOR]

A hybrid material point/finite volume method for the numerical simulation of shallow water waves caused by large dynamic deformations in the bathymetry is presented. The proposed model consists of coupling the nonlinear shallow water equations for the water flow and a dynamic elastoplastic system for the seabed deformation. As a constitutive law, we consider a linear elastic-non-associative plastic model with the Drucker-Prager yield criterion allowing for large deformations under undrained cases. The transfer conditions between these models are achieved by using forces sampled from the hydraulic pressure and the friction terms along the interface between the seabed soil and shallow water. A detailed description regarding the coupled algorithm for the hybrid material point/finite volume method is presented. Several numerical examples are investigated to demonstrate the performance of the finite volume method for simulations of shallow water flow and the material point method for capturing the large deformation process of the solid phase. We also present numerical simulations of an undrained clay column collapse that induced shallow water waves and a dam-break problem to demonstrate the excellent performance of the proposed hybrid material point/finite volume method. [ABSTRACT FROM AUTHOR]

• The peak uplift resistance of the offshore slender structures shallowly buried in the sloping seabed considering wave actions is numerically investigated. • The normalized peak uplift resistance decreases as the slope angle increases, especially for smaller burial ratios. • The traditional peak uplift resistance is weakened by the presence of wave troughs. • A preliminary formula for the reduction in the peak uplift resistance of shallowly-buried offshore slender structures was proposed to consider the slope effect and wave effect. The current practice for the pipe-soil interaction mainly focuses on the pipelines which are buried in the level ground, and ocean waves are rarely considered. However, sloping topographies and wave actions are often encountered by offshore slender structures. This study numerically investigated their peak uplift resistances, taking multiple factors, i.e., the slope effect and wave effect, into account simultaneously. The numerical model was first verified by the available analytical and experimental results. It was found that the normalized peak uplift resistance decreases as the slope angle increases, especially for smaller burial ratios. The presence of wave troughs weakens the traditional peak uplift resistance. For the given burial ratio and slope angle, the reduction in the peak uplift resistance increases almost linearly with the local wave steepness. For steeper slopes and smaller burial ratios, this reduction becomes larger because of more intense upward seepage. The effects of local relative water depth and wave period were also studied. Finally, a preliminary formula for the reduction in the peak uplift resistance of shallowly-buried offshore slender structures was proposed to consider the slope effect and wave effect. [ABSTRACT FROM AUTHOR]

• 2D modelling of solute transport into deformable sediments driven by ocean waves. • The effects of wave-induced soil deformation on solute transport into sediments. • Parametric analysis on solute transport into a deformable seabed under ocean waves. • The effect of different wave types on solute transport into deformable sediments. Most existing studies do not consider the effect that the deformability of submarine sediments may have on solute transport under the action of ocean waves. In this study a two-dimensional numerical model based on Biot's poro-elastic consolidation theory and an advection–dispersion equation is established to investigate the transport of non-reactive solute into a deformable porous seabed under the influence of ocean waves. The numerical model is then validated against experimental and analytical results in order to demonstrate its accuracy and robustness. The simulation results indicate that ignoring the deformability of seabed soil and associated seepage force due to ocean waves may lead to a significant underestimation of the rate of solute transport in shallow layers of marine sediment, particularly fine sand or silt. The effects of parameters such as the shear modulus, non-dimensional mechanical dispersion coefficient (related to particle size and permeability), dimensionless sediment thickness, wave steepness and the relative water depth have on solute transport into deformable sediments were investigated. The results indicate that the ratio of the longitudinal coefficient of mechanical dispersion between deformable and non-deformable sediments that can represent the enhancement of solute migration due to soil deformation may reach up to 85. This becomes more pronounced as the shear modulus and permeability of sediments decrease and the depth of water increases when the sediment thickness is less than 0.8 times the wavelength. The rate of solute transport in deformable sediments reaches its maximum when the sediment thickness is about 0.2 times the wavelength. In fact, as the relative water depth increases from 0.1 to 0.3, the enhancement of solute migration due to wave-induced soil deformation increases by about 60%-80%. In comparison to linear waves, shallow water waves, e.g., the first-order cnoidal waves, can increase the transport of solute more due to its strong non-linear behaviour, particularly in deformable seabed. [ABSTRACT FROM AUTHOR]

Waves on the submerged sloping seabed tend to transform and even break, inducing seabed response and exerting force on the shallowly-buried pipeline. In this study, a series of flume tests were carried out to characterize the wave propagation on a submerged sloping sandy seabed. Subsequently, seabed response considering the pipeline burial effect and ensuing force on the pipeline were investigated. Experimental results indicate that wave varies drastically on the sloping sandy seabed, accompanied with the nonlinearity strengthened. High-order nonlinear seabed response, at least the second order here, cannot be ignored. Pipeline presence, forming a smooth, impermeable and fixed circular boundary, makes the seabed response different from that without pipeline. The significance of the local hydrodynamics is highlighted after a heuristic investigation on the effect of pipeline relative water depth. For the pipeline buried in the shallow water, wave-induced horizontal force may be as important as the vertical force and should be taken into account in engineering. The relative burial depth and wave steepness at the toe are also found to affect the results obviously. • Wave-induced seabed response and force on the pipeline buried in a submerged sandy slope is physically modelled. • Wave propagation on the submerged slope is characterized. • The response of the sloping seabed with pipeline buried is compared with that without pipeline. • Effects of relative burial depth, pipeline relative water depth and wave steepness on the results are investigated. [ABSTRACT FROM AUTHOR]

The attenuation of shallow-water waves over stratified seabed mud is investigated. A two-layer viscoelastic mud model is introduced, in which the upper layer of fluid mud is described by the Maxwell model and the lower layer of deformable mud bed is described by the Kelvin-Voigt model. Based on the perturbation analysis and the Laplace transformation, a set of Boussinesq-type equations for wave attenuation is established. The Boussinesq-type equations are consistent with literature results when the mud model degenerates to single-layer models. Based on the Boussinesq-type equations, the damping rate of linear long waves and the evolution formula of solitary-wave amplitude are obtained. In the case of linear sinusoidal waves, the wave energy is mainly dissipated by shear motions within the upper mud layer. When resonance occurs, the wave damping is significantly enhanced. In the case of a solitary wave, the loss of wave energy is due to the viscous dissipation within the upper mud layer as well as the elastic absorbing within the lower mud layer. The viscosity of the lower mud layer has little influence on the damping of solitary waves. Modal analysis shows that the mud motion is always dominated by the first mode. [ABSTRACT FROM AUTHOR]

A series of wave flume tests have been performed in this paper to investigate the responses of clayey sloping seabed under wave actions, including the characteristics of wave shoaling, seabed topography and excess pore pressure. Different wave heights H , water depths D and two slope angles β (4° and 10°) were adopted and their effects were analyzed. It is found that obvious wave shoaling appears during the process of wave propagation along the sloping seabed. There are primarily two failure modes of the clayey sloping seabed under wave actions: for the bank sloping seabed, waves propagate and break on the slope and the seabed soil is scoured as pieces; for the submerged sloping seabed, a large area of shallow landslide occurs along the slope from top to bottom. It is also found that under plunging wave actions, the pore pressure response in clayey sloping seabed can be divided into three modes. The changes of three-dimensional seabed topography in the tests were captured and the quantity of clay scoured by waves was evaluated. Based on the experimental data, an advanced formula has been proposed to assess the critical failure condition and the quantity of the sloping clayey seabed scoured under wave actions. • The failure mode, seabed topography and wave-induced pore pressure in the clayey sloping seabed were investigated. • The three-dimensional topographic characteristics of clayey sloping seabed under wave actions were clarified. • An advanced formula is proposed for the critical failure condition and the scoured quantity of clay seabed under waves. [ABSTRACT FROM AUTHOR]

Abstract: The propagation of solitary wave in shallow water is investigated by using the Smoothed Particle Hydrodynamics (SPH) method. The present SPH model, which solves the weakly compressible Navier–Stokes equations and implements the wave absorbing scheme of Xu (2010) at downstream boundary, is first verified by the case of incident solitary wave propagating on a constant depth. A series of numerical experiments of solitary wave propagating over different bottom geometries are then conducted, which include the waves over a mild shelf or underwater steps with varied amplitude-depth ratios. The fission processes of both non-breaking and breaking solitary waves are discussed, numerical results of the free surface profiles and amplitude of the solitons show reasonable agreements with that of RANS model, as well as available experimental data. This paper demonstrates that the present method could reproduce the fission process with fairly good accuracy. [Copyright &y& Elsevier]

In this study, a wave-damping rate was derived for waves propagating over a multilayered, permeable seabed of finite depth. For a single-layer bed, a monogram is presented for the relationship between the wave-damping rate and the relative water depth for various depths of the permeable bed. The derived damping rate was used in the extended mildslope equation to calculate wave dissipation over the permeable bed. For a single-layer bed, the result from the extended mild-slope equation model was compared with the result from the integral equation method and showed good agreement. The extended mild-slope equation model was also used to examine the wave transmission over a permeable shoal with a various number of layers, each with a different permeability. In general, short waves are more influenced by the permeability of the shoal than long waves unless the water depth is so great that the influence of the permeable bed on the surface water waves disappears. For a multilayered bed, the influences of the permeability of the upper layer on wave dissipation and transmission are more significant than those of the lower layers. [ABSTRACT FROM AUTHOR]

To realize seabed behaviours under extreme waves in coastal regions, a wave-induced seabed response subjected to high-order cnoidal wave theory is studied via Biot's consolidation theory. An analytical model is proposed for a dynamic response comprising pore pressure and effective stresses in a permeable layer of the seafloor. The seabed pressure solutions yielded by cnoidal waves up to the third order are derived as an input loading under boundary conditions, and high-power Jacobian elliptic cosine functions involved in cnoidal wave theory are approximated in terms of a Fourier series to construct the seabed response via the superposition of harmonic solutions. For the present Fourier series approximation of Jacobian elliptic cosine functions, a convergence analysis is performed, and a verification of seabed pressure compared with experimental data shows good agreement. The characteristics of the present solution are investigated, and the discrepancies among the solutions for each order and a harmonic solution for linear waves are demonstrated on the profiles of effective stresses and excess pore pressure. Compared with the third-order solution, the harmonic solution provides a better prediction at the wave peak than the other solutions, but the prediction of excess pore pressure around the wave trough shows a remarkable overestimation for every solution except the second-order solution. The impact of seabed momentary liquefaction induced by shallow water waves is evaluated, and the influence of wave parameters, including wave height and wavelength, is determined. This study reveals the significance of the nonlinear effect on seabed response under high-order cnoidal waves and provides the underlying implication to liquefaction assessment. • A novel analytical solution of seabed responses under third-order cnoidal wave theory is proposed for the first time. • The third-order cnoidal wave solution shrinks the amplitude of the seabed surface pressure at both the wave peak and trough than the first-order solution. • Compared with the third-order cnoidal wave solution, the prediction of excess pore pressure around the wave trough shows a remarkable overestimation for every solution except the second-order solution. • Our analysis highlights the importance of adopting a high-order cnoidal wave solution to provide a more accurate prediction, particularly for the assessment of seabed liquefaction in shallow water. [ABSTRACT FROM AUTHOR]

Wave breaking occurs when waves reach a critical level of amplitude, which results in releasing a significant amount of energy. Predicting the wave heights, locations and other characteristics of breaking waves in shallow water is an important area of research. The breaking wave height, which is the most important characteristic, depends on various parameters such as deepwater wavelength, breaking water depth and seabed slope. In this study, new formulae are proposed for predicting the breaking wave height focusing on two types of breaking waves, namely spilling and plunging. The breaking wave types can be classified by using the Iribarren number. A comprehensive set of laboratory and field observations is utilized to develop new formulae based on the Gene Expression Programming (GEP) numerical method. The datapoints representing individual waves whose breaking types have been determined to be different according to different wave breaking classification criteria have been ignored. In comparison with previous formulae, the new formulae proposed based on different breaking types have almost higher accuracy, especially in the plunging case. Therefore, it might be concluded that developing different formulae based on different breaking types, rather than a general one for all types, would lead to more accurate results. • New wave breaker prediction formulae are proposed using the gene expression programming. • Different formulae are proposed depending on the wave breaking type. • A wide range of laboratory, field and numerical data has been applied. • Comparisons are made between the proposed formulae and the previous ones. [ABSTRACT FROM AUTHOR]