Surface Water Waves Research Articles

Rogue wave generation in wind-driven water wave turbulence through multiscale phase-amplitude coupling, phase synchronization, and self-focusing by curved crests

Rogue wave events (RWEs), localized high amplitude extreme events, uncertainly emerge in various nonlinear waves. For RWE generation, modulation instability leading to amplitude soliton formation for one-dimensional (1D) systems; and the additional wave directional property and the ratio of nonlinearity to spectrum bandwidth on the modulation instability for two-dimensional (2D) systems, are the accepted mechanisms. However, those studies have mainly focused on RWEs in weakly disordered wave states dominated by a single scale, but to a much lesser extent on wave turbulence with multiscale excitations. Wind-driven water surface wave turbulence widely occurs in nature. Unraveling RWE generation in wind-driven water surface wave turbulence is an important issue. Here, using multidimensional empirical mode decomposition, we experimentally investigate the dynamics of decomposed multiscale spatiotemporal waveforms of wind-driven water wave turbulence in the 2 + 1D space. We demonstrate how the cascaded amplitude modulation of the faster (higher frequency) modes by the phases of the slower modes, the phase synchronization of the largest peaks in the bursts of fast modes emerging in the crest regions of the medium modes, and self-focusing by the curved crests of the three fastest modes lead to RWE generation.

3D Ocean Water Wave Surface Analysis on Airborne LiDAR Bathymetric Point Clouds

Water wave monitoring is a vital issue for coastal research and plays a key role in geomorphological changes, erosion and sediment transportation, coastal hazards, risk assessment, and decision making. However, despite missing data and the difficulty of capturing the data of nearshore fieldwork, the analysis of water wave surface parameters is still able to be discussed. In this paper, we propose a novel approach for accurate detection and analysis of water wave surface from Airborne LiDAR Bathymetry (ALB) large-scale point clouds data. In our proposed method we combined the modified Density-Based Spatial Clustering of Applications with Noise (DBSCAN) clustering method with a connectivity constraint and a multi-level analysis of ocean water surface. We adapted for most types of wave shape anatomies in shallow waters, nearshore, and onshore of the coastal zone. We used a wavelet analysis filter to detect the water wave surface. Then, through the Fourier Transformation Approach, we estimated the parameters of wave height, wavelength, and wave orientation. The comparison between the LiDAR measure estimation technique and available buoy data was then presented. We quantified the performance of the algorithm by measuring the precision and recall for the waves identification without evaluating the degree of over-segmentation. The proposed method achieves 87% accuracy of wave identification in the shallow water of coastal zones.

Wind wave growth in the viscous regime

How water surface waves grow under wind forcing has long been an interesting and challenging question. For short gravity-capillary waves, the viscous effects are important but have not been well studied. In this paper, we simulate the wind-wave growth by directly solving the two-phase Navier-Stokes equations. The numerical method features a momentum conserving scheme, interface reconstruction using Volume of Fluid, and adaptive mesh refinement (AMR). As a result, we observe concurrent growth of the irrotational traveling wave and the rotational drift layer (current). The growth rate of the wave and the evolution of the drift layer under different forcing parameters are discussed respectively.

Characteristics of Low-Frequency Horizontal Noise of Ocean-Bottom Seismic Data

AbstractHorizontal records of ocean-bottom seismographs are usually noisy at low frequencies (< 0.1 Hz). The noise source is believed to be associated with ocean-bottom currents that may tilt the instrument. Currently horizontal records are mainly used to remove the coherent noise in vertical records, and there has been little literature that quantitatively discusses the mechanism and characteristics of low-frequency horizontal noise. In this article, we analyze in situ ocean-bottom measurements by rotating the data horizontally and evaluating the coherency between different channels. Results suggest that the horizontal noise consists of two components, random noise and principle noise whose direction barely changes in time. The amplitude and the direction of the latter are possibly related to the intensity and direction of ocean-bottom currents. Rotating the horizontal records to the direction of the principle noise can largely suppress the principle noise in the orthogonal horizontal channel. In addition, the horizontal noise is incoherent with pressure, indicating that the noise source is not ocean surface water waves (infragravity waves). At some stations in shallow waters (<300 m), horizontal noise around 0.07 Hz is found to be linearly proportional to the temporal derivative of pressure, which is explained by forces of added mass due to infragravity waves.

Miles’ mechanism for generating surface water waves by wind, in finite water depth and subject to constant vorticity flow

The Miles’ theory of wave amplification by wind is extended to the case of finite depth h and a shear flow with (constant) vorticity Ω. Vorticity is characterised through the non-dimensional parameter ν=ΩU1/g, where g the gravitational acceleration, U1 a characteristic wind velocity. The notion of ’wave age’ is generalised to account for the effect of vorticity. Several widely used growth rates are derived analytically from the dispersion relation of the wind/water interface, and their dependence on both water depth and vorticity is derived and discussed. Vorticity is seen to shift the maximum wave age, similar to what was previously known to be the effect of water depth. At the same time, a novel effect arises and the growth coefficients, at identical wave age and depth, are shown to experience a net increase or decrease according to the shear gradient in the water flow.

Investigation on the effects of Bragg reflection on harbor oscillations

Periodic undulating topographies (such as sandwaves and sandbars) are very common in coastal and estuarine areas. Normally incident water surface waves propagating from open sea to coastal areas may interact strongly with such topographies. The wave reflection by the periodic undulating topography can be significantly amplified when the surface wavelength is approximately twice the wavelength of the bottom undulations, which is often called as Bragg resonant reflection. Although the investigations on the hydrodynamic characteristics related to Bragg reflection of a region of undulating topography have been widely implemented, the effects of Bragg reflection on harbors have not yet been studied. Bragg resonant reflection can effectively reduce the incident waves. Meanwhile, however, it can also significantly hinder the wave radiation from the harbor entrance to the open sea. Whether Bragg reflection can be utilized as a potential measure to alleviate harbor oscillations is unknown.In the present study, Bragg reflection and their interactions with the harbor are simulated using a fully nonlinear Boussinesq model, FUNWAVE 2.0. For the purpose, an elongated harbor with constant depth is considered, and a series of sinusoidal bars with various amplitudes and numbers are deployed outside the harbor. The incident waves considered in this paper include regular long waves and bichromatic short wave groups. It is revealed for the first time that for both kinds of incident waves, Bragg resonant reflection can significantly alleviate harbor resonance. The influences of the number and the amplitude of sinusoidal bars on the mitigation effect of harbor resonance and on the optimal wavelength of sinusoidal bars that can achieve the best mitigation effect are comprehensively investigated, and it is found that the former two factors have remarkable influences on the latter two parameters. The present research provides a new option for the mitigation of harbor oscillations via changing the bottom profile, which is feasible as long as the navigating depth is guaranteed.

Numerical Simulation of Three-Dimensional Flow of Sudden Dam-Break over the Porous Bed

Dam break is a very important problem due to its effects on the economy, security, human casualties and environmental consequences. In this study, 3D flow due to dam break over the porous substrate is numerically simulated and the effect of porosity, permeability and thickness of the porous bed and the water depth in the porous substrate are investigated. Classic models of dam break over a rigid bed and water infiltration through porous media were studied and results of the numerical simulations are compared with existing laboratory data. Validation of the results is performed by comparing the water surface profiles and wave front position with dam break on the rigid and porous bed. Results showed that, due to the effect of dynamic wave in the initial stage of dam break, a local peak occurs in the flood hydrograph. The presence of porous bed reduces the acceleration of the flood wave relative to the flow over the solid bed and it decreases with the increase of the permeability of the bed. By increasing the permeability of the bed, the slope of the ascending limb of the flood hydrograph and the peak discharge drops. Furthermore, if the depth and permeability of the bed are such that the intrusive flow reaches the rigid substrate under the porous bed, saturation of the porous bed, results in a sharp increase in the slope of the flood hydrograph. The maximum values of the peak discharge at the end of the channel with porous bed occurred in saturated porous bed conditions.

Study on Earthquake-Induced Sloshing Waves in Moraine-Dammed Lakes

Large surface water waves can be triggered in moraine-dammed lakes during earthquakes and may lead to the overtopping failure of moraine dams. In the earthquake-prone Himalayas, there are thousands of moraine-dammed lakes; their outburst may lead to catastrophic disasters (e.g. floods and debris flow), posing severe threats to humans and infrastructures downstream. This paper experimentally studied earthquake-induced water waves (EWWs) in moraine-dammed lakes and examined the effects of several factors (e.g. water depth, earthquake parameters, and uneven lake basin). The experimental results suggest that the EWWs positively correlate to the earthquake wave, and the maximum height of the EWWs increases by 10%–15% when the effect of the uneven lake basin is considered. Based on the experiment data, we derived a calculation equation to estimate the maximum amplitude of EWWs considering the basin effect, and proposed a fast risk assessment method for moraine lakes due to overtopping EWWs. Finally, based on the method, we assessed the failure risk of the moraine lakes located in the Gyirong river basin where the China–Nepal corridor crosses. The study broadens understandings of the risk source of moraine-dammed lakes.

Local Discontinuous Galerkin Methods for the abcd Nonlinear Boussinesq System

Boussinesq type equations have been widely studied to model the surface water wave. In this paper, we consider the abcd Boussinesq system which is a family of Boussinesq type equations including many well-known models such as the classical Boussinesq system, the BBM-BBM system, the Bona-Smith system, etc. We propose local discontinuous Galerkin (LDG) methods, with carefully chosen numerical fluxes, to numerically solve this abcd Boussinesq system. The main focus of this paper is to rigorously establish a priori error estimate of the proposed LDG methods for a wide range of the parameters a, b, c, d. Numerical experiments are shown to test the convergence rates, and to demonstrate that the proposed methods can simulate the head-on collision of traveling wave and finite time blow-up behavior well.

Waves interacting with a partially immersed obstacle in the Boussinesq regime

This paper is devoted to the derivation and mathematical analysis of a wave-structure interaction problem which can be reduced to a transmission problem for a Boussinesq system. Initial boundary value problems and transmission problems in dimension d= 1 for $2\times2$ hyperbolic systems are well understood. However, for many applications, and especially for the description of surface water waves, dispersive perturbations of hyperbolic systems must be considered. We consider here a configuration where the motion of the waves is governed by a Boussinesq system (a dispersive perturbation of the hyperbolic nonlinear shallow water equations), and in the presence of a fixed partially immersed obstacle. We shall insist on the differences and similarities with respect to the standard hyperbolic case, and focus our attention on a new phenomenon, namely, the apparition of a dispersive boundary layer. In order to obtain existence and uniform bounds on the solutions over the relevant time scale, a control of this dispersive boundary layer and of the oscillations in time it generates is necessary. This analysis leads to a new notion of compatibility condition that is shown to coincide with the standard hyperbolic compatibility conditions when the dispersive parameter is set to zero. To the authors' knowledge, this is the first time that these phenomena (likely to play a central role in the analysis of initial boundary value problems for dispersive perturbations of hyperbolic systems) are exhibited.

Polarization singularities and Möbius strips in sound and water-surface waves

We show that polarization singularities, generic for any complex vector field but so far mostly studied for electromagnetic fields, appear naturally in inhomogeneous yet monochromatic sound and water-surface (e.g., gravity or capillary) wave fields in fluids or gases. The vector properties of these waves are described by the velocity or displacement fields characterizing the local oscillatory motion of the medium particles. We consider a number of examples revealing C-points of purely circular polarization and polarization Möbius strips (formed by major axes of polarization ellipses) around the C-points in sound and gravity wave fields. Our results (i) offer a new readily accessible platform for studies of polarization singularities and topological features of complex vector wave fields and (ii) can play an important role in characterizing vector (e.g., dipole) wave–matter interactions in acoustics and fluid mechanics.

Predicting the occurrence of rogue waves in the presence of opposing currents with a high-order spectral method

This work concerns the study of surface water waves in the presence of a horizontally varying opposing current. We demonstrate experimentally and numerically that spatial inhomogeneity increases the occurrence probability of extreme and rogue waves in the course of unidirectional wave propagation. We clearly report the transition between Gaussian and strongly non-Gaussian properties. An existing experimental model of wave-current interaction is revisited by comparing it against numerical simulations from current-modified Euler equations. The latter substantiate that the underlying physics is associated with quasi-resonant nonlinear interactions that are triggered by the background current.

Numerical and analytical study of undular bores governed by the full water wave equations and bidirectional Whitham–Boussinesq equations

Undular bores, also termed dispersive shock waves, generated by an initial discontinuity in height as governed by two forms of the Boussinesq system of weakly nonlinear shallow water wave theory, the standard formulation and a Hamiltonian formulation, two related Whitham–Boussinesq equations, and the full water wave equations for gravity surface waves are studied and compared. It is found that the Whitham–Boussinesq systems give solutions in excellent agreement with numerical solutions of the full water wave equations for the positions of the leading and trailing edges of the bore up until the onset on modulational instability. The Whitham–Boussinesq systems, which are far simpler than the full water wave equations, can then be used to accurately model surface water wave undular bores. Finally, comparisons with numerical solutions of the full water wave equations show that the Whitham–Boussinesq systems give a slightly lower threshold for the onset of modulational instability in terms of the height of the initial step generating the undular bore.

USE OF GALERKIN TECHNIQUE TO THE ROLLING OF A PLATE IN DEEP WATER

The classical problems of surface water waves produced by small oscillations of a thin vertical plate partially immersed as well as submerged in deep water are reinvestigated here. Each problem is reduced to an integral equation involving horizontal component of velocity across the vertical line outside the plate. The integral equations are solved numerically using Galerkin approximation in terms of simple polynomials multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge(s) of the plate. Fairly accurate numerical estimates for the amplitude of the radiated wave at infinity due to rolling and also for swaying of the pate in each case are obtained and these are depicted graphically against the wave number for various cases.

WATER WAVE SCATTERING BY A THIN VERTICAL SUBMERGED PERMEABLE PLATE

An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock’s expansion of water wave potential, the associated boundary value problem is reduced to a second kind hypersingular integral equation of order 2. The unknown function of the hypersingular integral equation is expressed as a product of a suitable weight function and an unknown polynomial. The associated hypersingular integral of order 2 is evaluated by representing it as the derivative of a singular integral of the Cauchy type which is computed by employing an idea explained in Gakhov’s book [7]. The values of the reflection coefficient computed with the help of present method match exactly with the previous results available in the literature. The energy identity is derived using the Havelock’s theorems.

Defect modes in non-Bragg resonant structures for guided surface water waves

We report our experimental observation of a single and stable defect mode arising in the non-Bragg bandgap of surface water waves by introducing a defect element into a water channel with periodically corrugated sidewalls. By investigating the existence of the non-Bragg defect mode and its frequency shifting, we find that unlike the Bragg defect mode which arises within an extended region around the Bragg gap in the spectrum, the non-Bragg type defect mode exists within a much smaller region. It is further proved by the experiments that the frequency shifting property of the defect mode in the non-Bragg gap is comparable to that of the Bragg type. The results show that the location of the defect mode in the bandgap is dependent on the length of the defect element. The ability to tune the defect modes for surface water waves would guide existing and next-generation wave energy control and coastal protection technologies.

Whitham modulation theory for generalized Whitham equations and a general criterion for modulational instability

AbstractThe Whitham equation was proposed as a model for surface water waves that combines the quadratic flux nonlinearity of the Korteweg–de Vries equation and the full linear dispersion relation of unidirectional gravity water waves in suitably scaled variables. This paper proposes and analyzes a generalization of Whitham's model to unidirectional nonlinear wave equations consisting of a general nonlinear flux function and a general linear dispersion relation . Assuming the existence of periodic traveling wave solutions to this generalized Whitham equation, their slow modulations are studied in the context of Whitham modulation theory. A multiple scales calculation yields the modulation equations, a system of three conservation laws that describe the slow evolution of the periodic traveling wave's wavenumber, amplitude, and mean. In the weakly nonlinear limit, explicit, simple criteria in terms of general and establishing the strict hyperbolicity and genuine nonlinearity of the modulation equations are determined. This result is interpreted as a generalized Lighthill–Whitham criterion for modulational instability.

A Non‐Encapsulated Polymorphous U‐Shaped Triboelectric Nanogenerator for Multiform Hydropower Harvesting

AbstractVarious structures for triboelectric nanogenerators (TENGs) have been designed to generate clean, low‐frequency hydropower, and provide solutions for next‐generation sustainable power supplies, including the solid–liquid contact electrification mode and full‐packaged solid–solid contact electrification mode. However, most of them can only adapt to a single form of hydropower. Moreover, electrostatic shielding in water and corrosion of the triboelectric material in the solid–liquid mode are inevitable. In addition, the devices in the fully enclosed mode have the disadvantages of complexity, low cost‐effectiveness, and complex disassembly, which hinder its development and practicality. Herein, a non‐encapsulated polymorphous U‐shaped TENG for multiform hydropower harvesting with effective robustness is designed, which contains two joinable parts: one U‐shaped multilayered TENG unit, and three trigger ends chosen according to actual requirements. The joinable design can directly reduce the waterproof treatment of U‐shaped multilayer section, performance degradation caused by humidity, and effectively avoids electrostatic shielding caused by water and corrosion of triboelectric materials. Furthermore, different forms of hydropower collection, such as the energy of surface water wave, underwater wave/flow, and water droplet can be achieved using the corresponding trigger end. This study provides a feasible scheme for efficient and economical multiform hydropower collection based on triboelectric technology.

Experimental Insights on the Propagation of Fine‐Grained Geophysical Flows Entering Water

AbstractGranular flows that propagate down a mountainside, then reach the sea, a lake or a river and finally, travel underwater, is a common event on the Earth's surface. To help the description of such events, laboratory experiments on gas‐fluidized granular flows entering water are performed, analyzed, and compared to those propagating in air. The originality of this study lies in the fluidization process, which improves the laboratory modeling of geophysical flows by taking their high mobility into account. Qualitatively, the presence of the water body promotes the generation of a granular jet over the water surface, a leading and largest wave, and a particle‐driven gravity current underwater. Hydrodynamic forces mainly play a dissipative role by slowing and reducing the spreading of the granular mass underwater, but a low amount of grains are still transported by the turbulent fluid as a gravity current far away. The temporal evolution of the granular jet and the particle‐driven gravity current are well described by ballistic motion theory and scaling laws of homogeneous gravity currents, respectively. Most currents propagate with a constant flow‐front velocity along the horizontal bottom, which is controlled by the flow height depending on the water depth. In contrast, the bulk volume concentration of particles in the current is estimated to be nearly constant, interpreted as a critical concentration above which the excess of particles cannot be maintained by the turbulent fluid. This experimental study highlights the complexity of the dynamics and deposits of granular masses when they encounter a water body.

Diagrams of static stability of a ship in rough conditions

Static stability diagram, solid-state model of a ship when constructing a static diagram of a ship in accordance with the requirements Of the rules of classification societies, it is necessary to take into account special navigation conditions: icing, the presence of liquid cargo in tanks, etc. In this case, the presence of the ship's side pitching caused by the action of waves is taken into account only at the time of determining the restoring moments. This article analyzes the influence on the stability diagram of the shape of the water surface (wave profile) on which the inclination occurs. Building a complex form of volume displacement, caused not only by the form of a surface ship, but a change in waterline, made with the use of solid modeling theoretical hull and volume of the water pool in the environment of Autodesk AutoCAD and Visual Lisp. For test calculations, it is found that the possible deviation of the static stability arm and the area under the positive part of the diagram can reach twelve percent.