Surface Water Waves Research Articles

Compressible ocean waves generated by sudden seabed rise near a step-type topography

A typical tsunami generation occurs through submarine earthquakes leading to large volume displacement. The corresponding mathematical problem involves modeling surface water waves generated by an arbitrary temporal motion of the ocean floor. The propagation of tsunami wave and the subsequent scattering from a sudden drop in bathymetry away from the ground motion is studied following linearized water wave theory and a weakly compressible ocean, including static oceanic background compression. The Fourier transformation and eigenfunction expansion techniques are employed to find the surface displacement and pressure profiles by leveraging appropriate matching conditions between regions of different depths. A novel energy balance relationship is derived by considering both the pure-gravity and acoustic-gravity modes. The model is validated in the limit that the depth difference approaches zero, showing a vanishing reflection contribution from the depth change. An efficient numerical code is developed that accurately captures the contribution of the cutoff frequencies of acoustic-gravity modes. Apart from the time-domain propagation of tsunami waves away from the origin, standing wave formations are observed within the shallow region, supported by significantly large pressure fluctuations in time. These standing waves or, equivalently, the pressure fluctuations sustain longer for larger ocean depth. The increase in tsunami speed in the deeper region is readily visible in the time-domain simulations. A three-dimensional axisymmetric solution is also developed, and results show a more gradual sloping tsunami wavefront compared to the equivalent two-dimensional solution for shallower depths. Animation movies corresponding to the two- and three-dimensional surface profiles are provided for better visualization.

Focusing Monochromatic Water Surface Waves by Manipulating the Phases Using Submerged Blocks

Focusing Monochromatic Water Surface Waves by Manipulating the Phases Using Submerged Blocks

Extraction of Underwater Acoustic Signals across Sea–Air Media Using Butterworth Filtering

Direct wireless communication through sea–air media is essential for constructing an integrated communication network that spans space, air, land, and sea. The amplitude of acoustically induced micromotion surface waves is much smaller than the noise interference in complex sea states, making the accurate extraction of these signals from the raw signals detected by an FMCW millimeter-wave radar a major challenge. In this paper, Butterworth filtering is used to extract underwater acoustic signals from the surface waves detected by radar. The physical processes of the channel were simulated theoretically and verified experimentally. The results demonstrate a fitting coefficient of 0.99 between the radar-detected water surface waves and the simulation outcomes, enabling the effective elimination of noise interference and the extraction of acoustically induced micromotion signals in environments with a signal-to-noise ratio (SNR) of −20 dB to −10 dB. Experiments modifying frequency and linear frequency modulation have verified that the usable frequency range for underwater acoustic signals is at least 400 Hz, meeting the frequency requirements of Binary Frequency Shift Keying (2FSK) modulation encoding methods. This research confirms the accuracy of the simulation results and the feasibility of filtering and extracting underwater acoustic signals, providing a theoretical basis and an experimental foundation for building cross-media communication links.

Interaction Between Long Internal Waves and Free Surface Waves in Deep Water

Interaction Between Long Internal Waves and Free Surface Waves in Deep Water

Heterostructure channel designs for the topological interface state of surface water waves using topology optimization

The increase of the concentrated density of wave energy is conducive to improving the generation efficiency of wave power generation. Interface states induced in the heterostructure channels can be applied to concentrate the surface water wave. The optimal designs of heterostructure channels can be found through the topology optimization based on the multiple population genetic algorithm to induce a topological interface state with high transmission at the desired frequency. The introduction of the topological interface state effectively and steadily increases the wave energy density in a certain space and improves the robustness and the localization of the water wave concentrator. This topology optimization method provides a design scheme for the wave energy concentrator in the field of ocean engineering.

Construction of some new traveling wave solutions to the space-time fractional modified equal width equation in modern physics

Nonlinear fractional evolution equations are important for determining various complex nonlinear problems that occur in various scientific fields, such as nonlinear optics, molecular biology, quantum mechanics, plasma physics, nonlinear dynamics, water surface waves, elastic media and others. The space-time fractional modified equal width (MEW) equation is investigated in this paper utilizing a variety of solitary wave solutions, with a particular emphasis on their implications for wave propagation characteristics in plasma and optical fibre systems. The fractional-order problem is transformed into an ordinary differential equation using a fractional wave transformation approach. In this article, the polynomial expansion approach and the sardar sub-equation method are successfully used to evaluate the exact solutions of space-time fractional MEW equation. Additionally, in order to graphically represent the physical significance of created solutions, the acquired solutions are shown on contour, 3D and 2D graphs. Based on the results, the employed methods show their efficacy in solving diverse fractional nonlinear evolution equations generated across applied and natural sciences. The findings obtained demonstrate that the two approaches are more effective and suited for resolving various nonlinear fractional differential equations.

Vortex lattice state transitions in water surface waves

Surface waves can generate an ordered vortex lattice of fluid particles on the air-water interface. Here, the transitions of the lattice structure are observed through experiments and modelled analytically. A fully-immersed square waveguide system is positioned at the center of a larger bath which directs particles into counter-rotating vortices. Flow interactions with the bath free-surface alter the ordered structure, and a state transition is initiated by the increase of the waveguide immersion depth. It manifests as a change in the orbital momentum and spin properties of the vortices, and develops through the combination of reflected-wave attenuation and mean flow effects from the classical Stokes drift and Eulerian currents. Transitions from a perfect antiferromagnetic state to weakly-ordered ones are achieved, including a monopole vortex reminiscent of spectral condensates in thin fluid layers. Order in the disordered flow is uncovered through velocity field corrections after invoking time-scale separation. The lattice structures are modelled analytically through a superposition of mean flow contributions from the waveguide and bath modes. The results open a new platform for investigating the dynamics of wave and vortex lattice interactions, and devising new techniques to characterize complex flow phenomena on the air-water interface.

Oceanic Shallow-Water Investigations on a Variable-Coefficient Davey–Stewartson System

In this paper, a variable-coefficient Davey–Stewartson (vcDS) system is investigated for modeling the evolution of a two-dimensional wave-packet on water of finite depth in inhomogeneous media or nonuniform boundaries, which is where its novelty lies. The Painlevé integrability is tested by the method of Weiss, Tabor, and Carnevale (WTC) with the simplified form of Krustal. The rational solutions are derived by the Hirota bilinear method, where the formulae of the solutions are represented in terms of determinants. Furthermore the fundamental rogue wave solutions are obtained under certain parameter restrains in rational solutions. Finally the physical characteristics of the influences of the coefficient parameters on the solutions are discussed graphically. These rogue wave solutions have comprehensive implications for two-dimensional surface water waves in the ocean.

Experimental and numerical investigations of the water surface profile and wave extrema of supercritical flows in a narrow channel bend

Supercritical flows in channel bends, e.g., in steep streams, chute spillways, and flood and sediment bypass tunnels (SBTs), experience cross-waves, which undulate the free surface. The designs of these hydraulic structures and flood protection retaining structures in streams necessitate computing the locations and water depths of the wave extrema. This study numerically and experimentally investigates the water surface profiles along the sidewalls, the wave extrema flow depths, and their angular locations in a narrow channel bend model of the Solis SBT in Switzerland. The 0.2 m wide and 16.75 m long channel has a bend of 6.59 m radius and 46.5° angle of deviation. The tested flow conditions produced Froude numbers ≈ 2 and aspect ratios ranging from 1.14 to 1.83. Two-phase flow simulations were performed in OpenFOAM using the RNG k–ε turbulence closure model and the volume-of-fluid method. The simulated angular locations of the first wave extrema and the corresponding flow depths deviate marginally, within ± 6.3% and ± 2.1%, respectively, from the experimental observations, which signifies good predictions using the numerical model. Larger deviations, especially for the angular locations of the wave extrema, are observed for the existing analytical and empirical approaches. Therefore, the presented numerical approach is a suitable tool in designing the height of the hydraulic structures with bends and conveying supercritical flows. In the future, the model’s application shall be extended to the design of the height and location of retaining walls, embankments, and levees in steep natural streams with bends.

The long wavelength limit of periodic solutions of water wave models

AbstractThe present essay is concerned with providing rigorous justification of a long‐standing practice in numerical simulation of partial differential equations. Theory often sets initial‐value problems on all of or . If the initial data are localized in space, it has been usual practice to approximate the problem by an associated periodic problem or a homogeneous Dirichlet problem set on a finite interval. While these strategies are commonplace, rigorous justification of the practice is sparse. It is our purpose here to indicate justification of this practice in the concrete context of a surface water wave model. While the theory worked out here is specific to the particular partial differential equation, it will be apparent to the reader that more general results may be derived using the same approach.

Hilbert transform view of water-wave theory

A general rethinking of the mathematical foundations of water surface waves from the perspective of the Hilbert transform uncovers shortcomings of the standard multiple-scale approach as well as elucidates the interplay of non-local and dispersive effects. Application of the Hilbert transforms to planar and cylindrical settings allows us to deduce new weakly nonlinear models, including an alternative to Zakharov's equation and an envelope equation for cylindrical waves on deep water, as well as to highlight the crucial differences between these geometries.

Free surface water waves generated by instability of an exponential shear flow in arbitrary depth

The stability of an exponential current in water to infinitesimal perturbations in the presence of gravity and capillarity is revisited and reformulated using the Weber and Froude numbers. Some new results on the generation of gravity-capillary waves are presented, which supplement the previous works of Morland et al. [“Waves generated by shear layer instabilities,” Proc. Math. Phys. Sci. 433, 441–450 (1991)] and Young and Wolfe [“Generation of surface waves by shear-flow instability,” J. Fluid Mech. 739, 276–307 (2014)] on finite depth. To consider perturbations at much larger scales, special attention is given to the stability of exponential currents only in the presence of gravity. More precisely, the present investigation reveals significant insights into the stability of exponential shear currents under different environmental conditions. Notably, we have identified that the dimensionless growth rate increases with the Froude number, providing a deeper understanding of the interplay between shear layer thickness and surface velocity. Furthermore, our analysis elucidates the dimensional wavelength of the most unstable mode, emphasizing its relevance to the characteristic shear layer thickness. Additionally, within the realm of gravity-capillary instabilities, we have established a sufficient condition for the stability of exponential currents based on the Weber number. Our findings are supported by stability diagrams at finite depth, showing how the size of stable domains correlates with the characteristic thickness of the shear layer. Moreover, we have explored the stability of a thin film of liquid in an exponential shearing flow, further enriching our understanding of the complex dynamics involved in such systems.

INVESTIGATION OF THE EFFECT OF SPACE VARYING WIND INPUT ON HYDRODYNAMIC MODELING IN MANILA BAY AND LAGUNA LAKE

Abstract. Surface water currents and waves are largely driven by wind forcing by inducing shear stress to the water surface. The circulations formed carry with it various materials and pollutants all over a large body of water like the Manila Bay and Laguna Lake. Considering the spatial and temporal variability of wind over the Bay and the Lake is essential to model the hydrodynamics of water more accurately. This study simulated bay hydrodynamics using high resolution space- and time-varying wind data from Weather Research Forecasting (WRF) as input and compared the results with using uniform-directed wind. The downscaled winds from WRF demonstrated patterns in agreement with the country’s seasonal monsoon wind dynamics. Its effect on the bay hydrodynamics is more pronounced during the dry season as it changes the flow direction of water at the bay mouth. On the other hand, the hydrodynamic difference in circulation patterns for the lake was accentuated with a more defined clockwise gyre circulation during the wet season where prevailing winds are stronger. Thus, it is imperative to incorporate spatially varying wind input to accurately characterize the bay water movement. Results also showed that global weather inputs can be used in areas with scarce monitoring stations as long as they are validated.

Interaction of surface water waves with partial porous structure and floating elastic plate in the presence of sea wall

ABSTRACT This study proposes a model composed of either bottom-standing porous structure (BSPS) or surface-piercing porous structure (SPPS) in combination with an elastic plate (EP) placed at a distance from one another to protect a sea wall. The study uses the governing equation and the boundary conditions to coin a system of equations, and the system of equations is solved to identify the hydrodynamics coefficients. Further, it is noticed that length, frictional coefficient, porosity of the porous structure, and flexural rigidity of EP play a crucial role in reducing the force on the sea wall, water elevation and plate deflection. The SPPS exhibits a nearly 60% reduction in wall force coefficient due to a 50% increase in wave-damping when compared to BSPS for k 0 H = 0.85. These results are crucial for developing floating structures that can resist harsh wave environments and minimize the effects of waves close to the shore.

Numerical study of the Amick–Schonbek system

AbstractThe aim of this paper is to present a survey and a detailed numerical study on a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. In the one‐dimensional case, this system can be viewed as a dispersive perturbation of the hyperbolic Saint‐Venant (shallow water) system. The asymptotic stability of the solitary waves is numerically established. Blow‐up of solutions for initial data not satisfying the noncavitation condition as well as the appearance of dispersive shock waves are studied.

Importance of sign conventions on analytical solutions to the wave-induced cyclic response of a poro-elastic seabed

This paper discusses the influence of different sign conventions for strains and stresses, i.e. the solid mechanics sign convention and the soil mechanics sign convention, on the form of governing partial differential equations (the static equilibrium equations and the continuity equation) used to describe the wave-induced cyclic response of a poro-elastic seabed due to propagation of a sinusoidal surface water-wave. Some selected analytical solutions, obtained by different authors and published in specialist literature in the form of complex functions describing the wave-induced pore-fluid pressure, effective normal stress and shear stress oscillations in the seabed, have been analysed and compared with each other mainly with respect to different sign conventions for stains and stresses and also with regard to different orientations of the positive vertical axis of the two-dimensional coordinate system and different directions of surface water-wave propagation. The performed analyses of the analytical solutions has indicated many inaccuracies, or even evident errors and exemplary mistakes of wrong-signed values of basic wave-induced response parameters (the shear stress in particular), thereby disqualifying these solutions and their final equations from practical engineering applications. Most of the mistakes found in the literature must be linked to authors’ lack of understanding and consistency in an uniform application of a certain sign convention for strains and stresses in the soil matrix at both stages of mathematical formulation of the governing problem and correct interpretation of equations of the final analytical solution. The present paper, based mostly on a thorough literature review, ought to draw attention and arouse interest among coastal scientists and engineers in proper identification and use of the existing analytical solutions to the wave-induced cyclic seabed response – solutions which differ very often in the applied sign convention for stresses in the soil matrix.

Exploring solitary wave solutions to the simplified modified camassa-holm equation through a couple sophisticated analytical approaches

The simplified modified Camassa-Holm equation, a developed Korteweg-de Vries equation, is an integrable nonlinear dispersive water wave equation with potential applications in diverse fields such as shallow water waves, liquid drop patterning, water surface waves in channels, tsunamis in coastal regions, ocean engineering, etc. In this study, we derived solitary wave solutions to the described equation, employing two reliable approaches: the enhanced modified simple equation and the extended Kudryashov methods. The enhanced modified simple equation technique yields solutions with variable coefficients through a generalized wave transformation. On the other hand, the extended Kudryashov method exploits the solutions of the Riccati and Bernoulli differential equations. The determined results include diverse soliton solutions expressed in the form of trigonometric, hyperbolic, and rational functions. Notably, for specific parameter values, these solutions exhibit wave of distinct shapes, including kink, smooth kink, flat kink, periodic, singular periodic, one-sided kink, etc. To apparently explain the physical behavior and the impact of the fractional parameter in the solutions, we plotted three- and two-dimensional graphs. The obtained solutions have potential applications in oceanography, spanning offshore rigs, ocean gravity waves, and wave energy.

Water-Wave Vortices and Skyrmions.

Topological wave structures-phase vortices, skyrmions, merons, etc.-are attracting enormous attention in a variety of quantum and classical wave fields. Surprisingly, these structures have never been properly explored in the most obvious example of classical waves: water-surface (gravity-capillary) waves. Here, we fill this gap and describe (i)water-wave vortices of different orders carrying quantized angular momentum with orbital and spin contributions, (ii)skyrmion lattices formed by the instantaneous displacements of the water-surface particles in wave interference, and (iii)meron (half-skyrmion) lattices formed by the spin-density vectors, as well as (iv)spatiotemporal water-wave vortices and skyrmions. We show that all these topological entities can be readily generated in linear water-wave interference experiments. Our findings can find applications in microfluidics and show that water waves can be employed as an attainable playground for emulating universal topological wave phenomena.

Necessary conditions for convex-periodic, elliptic-periodic, inclined-periodic, and rogue wave-solutions to exist for the multi-dispersions Schrodinger equation

In this study, we revisit the modified Schrödinger equation, which incorporates multiple dispersion terms, including linear, nonlinear, and random dispersion. We establish the essential constraints on the model’s parameters to ensure the presence of complex-valued solutions. Subsequently, we employ effective and explicit techniques such as the extended tanh-coth expansion, rational sine-cosine functions, and rational sinh-cosh functions to derive innovative types of periodic solutions for the proposed model. These solutions demonstrate unique physical properties applicable to various complex media, such as surface water waves, optical fiber pulses, and plasma waves.

Numerical Modeling of Composite Load-Induced Seabed Response around a Suction Anchor

Suction anchors play a crucial role as marine supporting infrastructure within mooring systems. In engineering practice, the composite load comprising nonlinear waves and cyclic pull-out loads can have adverse effects on the seabed soil, posing a threat to the pull-out bearing capacity of the suction anchor. While existing research predominantly focuses on cyclic pull-out loads, the influence of nonlinear wave actions at the seabed surface remains overlooked. This study employs a two-dimensional integrated numerical model to investigate the dynamic soil response around a suction anchor under the influence of both nonlinear waves and cyclic pull-out loads, focusing on the mechanisms that lead to liquefaction and the deterioration of the interfacial friction due to the excess pore pressure buildup. The numerical results reveal that the cyclic pull-out load is the primary factor in the deterioration of the frictional resistance at the suction–soil interface, especially when the pull-out load is inclined with the suction anchor. Parametric studies indicate that the relative difference in frictional resistance deterioration between cases considering and excluding surface water waves becomes more pronounced in soils characterized by a small consolidation coefficient (Cv) and relative density (Dr).