Propagation Of Water Waves Research Articles

Surface waves over currents and uneven bottom

The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution for the initial depth. Emergence of new solitons is observed as a result of the wave interaction with the uneven bottom.

Water wave interaction with dual asymmetric non-uniform permeable plates using integral equations

In this study, we analyse the effect of two submerged unequal permeable plates in the propagation of water waves under the assumptions of linear water wave theory. The permeability of the plates varies along the depth of submergence of the plates. The plates are submerged in water of uniform depth. The velocity potential is expanded by using Havelock’s expansion of water wave potential. The associated boundary value problem is transformed into two coupled Fredholm type integral equations with the help of the Havelock’s inversion theorem and the porous plate condition. A multi-term Galerkin approximation in terms of Chebyshev polynomials is used to solve the vector integral equations and to obtain the numerical estimates for the reflection and the transmission coefficients. The computed numerical results for the reflection coefficient are depicted graphically for various values of several parameters. The present results are validated against the known results for the case of two identical impermeable plates and a single permeable plate submerged in water of finite depth.

Particle trajectories and mass transport under mechanically generated nonlinear water waves

A theoretical model is developed to study the kinematics of water particles and mass transport of wave-induced flow generated in a closed flume. A semi-analytical pseudo-spectral solution to the problem of mechanically generated nonlinear water waves propagating at a constant depth is derived under the potential flow assumptions. Velocity potential and free-surface displacement functions are represented in a form based on Fourier series. The eigenfunction expansions are resolved by means of a Fast Fourier Transform technique and a higher order time-stepping procedure. The derived nonlinear solution of the wavemaker problem is based on Taylor series representation of the free-surface and wavemaker boundary conditions expanded up to an arbitrary truncation order. This technique is employed to study the evolution of a velocity field and particle trajectories under regular gravity waves generated in a wave flume. The instantaneous velocity fields are integrated in time to calculate the particle trajectories and time-averaged spatial distribution of Lagrangian and Eulerian mean velocities. The theoretical results are compared with the available experimental data. A good agreement is observed, which confirms the applicability of the presented theory to the problems of transport processes associated with the propagation of water waves and their generation in the flume.

Nonlocal symmetries, conservation laws and interaction solutions for the classical Boussinesq–Burgers equation

We consider the classical Boussinesq–Burgers (BB) equation, which describes the propagation of shallow water waves. Based on the truncated painleve expansion method and consistent Riccati expansion method, we successfully obtain its nonlocal symmetry and Backlund transformation. By introducing auxiliary-dependent variables for the nonlocal symmetry, we find the corresponding Lie point symmetries. By considering the consistent tanh expansion method, the interaction solution of soliton–cnoidal wave for the classical BB equation is studied by using the Jacobi elliptic function. The multi-solitary wave solutions are also obtained by introducing a linear combination of N exponential functions. Moreover, the conservation laws of the equation are successfully obtained with a detailed derivation.

Bäcklund Transformations, Nonlocal Symmetries and Soliton–Cnoidal Interaction Solutions of the (2 + 1)-Dimensional Boussinesq Equation

Under investigation in this paper are the nonlocal symmetries and consistent Riccati expansion integrability of the (2 + 1)-dimensional Boussinesq equation, which can be used to describe the propagation of long waves in shallow water. By constructing the Backlund transformation, we obtain the truncated Painleve expansion of the system. Its Schwarzian form is also derived, whose nonlocal symmetry is localized to provide the corresponding nonlocal group. Furthermore, we verify that the system is solvable via the consistent Riccati expansion (CRE). Based on the CRE, the interaction solutions between soliton and cnoidal periodic wave are explicitly studied.

Periodic and almost periodic solutions for the damped Korteweg‐de Vries equation

The Korteweg‐de Vries equation is an important model for propagation of some surface water waves along a channel. In this paper, we discuss the damped Korteweg‐de Vries equation in a bounded domain. First, we study the existence and uniqueness of the strong solution. Then, we prove that the strong solution is periodic (or almost periodic) if the coefficient and external force are periodic (or almost periodic).

Nearshore wave processes numerical study for a better prediction of hydrodynamic loads on coastal structures

Taking into account the sensible approach in the coastal zones, in these types of areas were found different ways of understanding and description of the phenomena occurring during the water wave propagation. The waves hit the zone with a force that can affect the shoreline. Coastal protection measures were implemented, which include the hydrodynamic structures. The hydrodynamic process plays an important role in coastal area which involves the need for knowledge on the prediction of hydrodynamic loading required up to a very detailed level, such as maximum or minimum pressures. In this paper, we will present a study of wave fields that propagates in a simplified, constant-slope coastal model and relations between waves and hydrodynamics structures. The processes of wave fields include dissipative mechanisms such as depth-induced wave breaking, bottom friction and the interaction between wave field and coastal dike. The numerical models were constructed using ANSYS-Fluent program for modelling fluid flow and to solve the unsteady, two dimensional Navier-Stokes equations of incompressible fluid. Water waves are generated in two-phase fluid domain, where Volume of Fluid Model is used for generation of the two-phase flow model - the water-air interaction.

Diamond shaped standing wave patterns of a two-dimensional Boussinesq system

We prove the existence of a large family of two-dimensional diamond shaped standing waves for a Boussinesq system which describes two-way propagation of water waves in a channel. Our proof uses the Lyapunov–Schmidt method to find the bifurcation standing waves.

Numerical study on the propagation of solitary waves in the near-shore

The propagation and transformation of water waves in the near-shore region lead complicated wave-current field, which plays a significant role in the study of the mechanism of sediment transport and coastal evolution. Solitary wave is supposed as an initially incoming wave because of its widespread use in the near-shore. The Reynolds-averaged Navier-Stokes (RANS) equations were incorporated into a k-ε turbulence model and applied to simulate the run-up and hydrodynamic characteristics of solitary waves under the influences of different incident wave height and beach slope. The simulation results were validated with theoretical and experimental results from the literature. The effects of the non-linear terms associated with the curl of the fluid, Reynolds stresses and viscous stresses in the governing equations of fluid as well as the turbulent production term, convection term and diffusion term in the k-ε model were analyzed. The analysis shows that wave breaking is of great importance to the hydrodynamic characteristics of the wave-current field in the near-shore. The run-up heights of breaking solitary waves increase with beach slope, and the velocity and vorticity reach the maximum after wave breaking. The non-linear (curl and convection) terms and turbulent production term contribute most to the nonlinearities of the near-shore hydrodynamics, and increase with beach slope under these conditions. Nevertheless, under the conditions of wave non-breaking, the wave run-up height, the maximum of velocity and vorticity decrease with increasing beach slope. Meanwhile, the effects of fluid diffusion and Reynolds stresses increase gradually with increasing beach slope.

Formation, breaching and flood consequences of a landslide dam near Bujumbura, Burundi

Abstract. This paper investigates the possible formation of a landslide dam on the Kanyosha River near Bujumbura, the capital of Burundi, as well as the interplay between the breaching of this landslide dam and the flooding along the river. We present an end-to-end analysis, ranging from the origin of the landslide up to the computation of flood waves induced by the dam breaching. The study includes three main steps. First, the mass movement site was investigated with various geophysical methods that allowed us to build a general 3-D model and detailed 2-D sections of the landslide. Second, this model was used for dynamic landslide process modelling with the Universal Distinct Element Code. The results showed that a 15 m high landslide dam may form on the river. Finally, a 2-D hydraulic model was set up to find out the consequences of the breaching of the landslide dam on flooding along the river, especially in an urban area located downstream. Based on 2-D maps of maximum water depth, flow velocity and wave propagation time, the results highlight that neglecting the influence of such landslide dams leads to substantial underestimation of flood intensity in the downstream area.

The effect of seawater layer on cable-stayed bridge under tri-direction spatial varying ground motions

In recently years, many sea-crossing bridges were built in some countries. For the complexity of seafloor condition and the stochastic characteristics of earthquakes, it is necessary to research the seismic responses of these sea-crossing bridges located on seawater layer and irregular bottom conditions. In this paper, a theory of the spatial varying ground motions was derived considering the wave propagation in soil and water. The effects of sea water layer, wave passage, coherence, local site and soil saturation on the seismic responses of a cable-stayed bridge were researched. The transfer function was used to calculate the local site effect and soil saturation effect. The seawater layer effect was studied via a simple medal from Crouse and Quilter. Multi-support and tri-direction excitations were utilized with large mass method. The seismic responses of a long span cable-stay bridge in the site conditions with and without seawater were compared. The results present that the seawater layer affects the earthquake response of bridge greatly, and the soil types have different effects on the different component of bridge. The research will help reasonably evaluate the security of sea-crossing bridge under earthquake excitation.

Rational solutions of the classical Boussinesq–Burgers system

We study rational solutions of the classical Boussinesq–Burgers (CBB) system which describes the propagation of shallow water waves. The main tools applied in this work to derive these solutions are the bilinear method and the Kadomtsev–Petviashvili hierarchy reduction technique. The solutions are given in terms of determinants whose matrix elements are related to Schur polynomials and have simple algebraic expressions. Moreover, the dynamics of these rational solutions are investigated analytically and graphically. For different values of the parameter coming from the CBB system, the solutions may describe the interaction of double-peak (M-shape) waves or single-peak waves. It is also shown that, depending on the choices of free parameters in the solutions, the maximum amplitude of the interaction wave could be higher or lower than the amplitudes before collision. In addition, some of the rational solutions may blow up to infinity at finite time under special choices of parameters.

Modeling and simulation of hydro-acoustic signal propagation in the Romanian Black Sea coast

Sound energy is the primary method of detecting and locating submarines and mines. The study of the propagation of sound waves in sea water is the most important issue in assessing sonar systems performances. The variation of the sound speed in the marine environment radically influences the propagation paths of the acoustic signals. This paper presents a modeling and simulation model of hydro-acoustic signal propagation for a specific sound speed profile from the Romanian Black Sea shore.

Fission and fusion interaction phenomena of mixed lump kink solutions for a generalized (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

In this paper, a generalized (3[Formula: see text]+[Formula: see text]1)-dimensional B-type Kadomtsev–Petviashvili (gBKP) equation is investigated by using the Hirota’s bilinear method. With the aid of symbolic computation, some new lump, mixed lump kink and periodic lump solutions are derived. Based on the derived solutions, some novel interaction phenomena like the fission and fusion interactions between one lump soliton and one kink soliton, the fission and fusion interactions between one lump soliton and a pair of kink solitons and the interactions between two periodic lump solitons are discussed graphically. Results might be helpful for understanding the propagation of the shallow water wave.

Wind generation of waves: Energy and momentum transfer - An overview with physical discussion

The study considers the generation of surface water waves by wind through pressure and shear stress acting on the surface. The situations of temporal growth of an infinitely long uniform wave train and of down-wind growth of a stationary non-uniform wave field are treated. The mechanisms of energy and momentum transfer between the wind and the waves are considered and it is explained how the ‘wave Reynolds stress’ and the wave set-down are contributing to a force balance over the water column. The role of the wind forcing for the wave drift and a mean current is shown. The analogy between energy dissipation by wave breaking and wave generation by a harmonic surface shear stress is discussed together with the transfer of momentum to the ocean currents by breaking waves.

Generation of Waves Due to a Disturbance on the Running Stream

In the present paper we have studied the problem of generation of water waves due to a disturbance on the surface of ocean with uniform current. The problem is formulated under the assumption of linearised theory of water waves, as an initial cum boundary value problem with Laplace equation as the governing differential equation with two types of initial conditions prescribed on the free surface. One condition arises when the disturbance is such that the initial depression of the free surface is prescribed. The other condition arises when the disturbance in the form of an impulsive pressure applied to the free surface is prescribed. Employing Laplace transform in time and Fourier transform in space, the free surface depression is obtained which is then evaluated asymptotically using the method of stationary phase at a large distance and after a long time after the occurrence of the disturbance. The free surface depression is presented graphically for various values of the stream velocity. In absence of running stream, the known results for the free surface depression are recovered. The graphical results show that in absence of running stream, the free surface depression exhibits uniform oscillatory behaviour at large distance and after a long time of the occurrence of the disturbance. However in the presence of the uniform current, it is observed that when the wave velocity approaches the stream velocity or vice versa, then there occurs an interaction between the wave and the stream, due to which the amplitude as well as frequency of oscillation of free surface depression gradually increase. On the other hand, if the stream velocity differs much from the wave velocity then it is observed that free surface depression gradually decreases to its mean position.This observation has an important bearing in determination of the place and the time of occurrence of the disturbance.

Backscattering reduction for resonating obstacle in water-wave channel

We consider the propagation of water waves in a waveguide with a surface-piercing circular cylinder. A plane wave interacting with the cylinder leads to a Fano resonance resulting in strong scattering with a large reflection coefficient. Using a smoothly varying bathymetry whose shape is optimized, we show both numerically and experimentally that broadband and robust backscattering reduction can be obtained below the first cutoff frequency.

Videos of ultrasonic wave propagation through transparent acrylic objects in water for introductory physics courses produced using refracto-vibrometry

This project used refracto-vibrometry to produce full-field videos of ultrasonic wave propagation in water; these videos could be incorporated into high school and college physics courses to illustrate wave behaviors. Refracto-vibrometry (RV) is an interferometric method for optically measuring sound waves. The measurement beam from a Polytec PSV-400 scanning laser Doppler vibrometer was directed through a water tank towards a stationary retroreflective surface. Acoustic wave fronts (density variations) which pass through the measurement laser cause variations in the integrated optical path length. By superimposing tens of thousands of scan points, videos enable visualization of the ultrasound propagation. In one experiment, ultrasonic waves in water (1484 m/s) are incident on a submerged acrylic block at a non-zero angle. The waves are refracted as they travel at about 2700 m/s through the block. Students can determine this speed of sound by measuring the angle of refraction and lateral deflection of the wave fronts in the video. In another experiment, ultrasonic waves passed through an acrylic cylinder, producing a Mach cone in water. Measurement of the Mach cone angle enables determination of the acrylic speed of sound. Links for videos and sample worksheets will be provided.

Study of Absorption Loss Effects on Acoustic Wave Propagation in Shallow Water Using Different Empirical Models

<p><span lang="EN-US">Efficient underwater acoustic communication and target locating systems require detailed study of acoustic wave propagation in the sea. Many investigators have studied the absorption of acoustic waves in ocean water and formulated empirical equations such as Thorp’s formula, Schulkin and Marsh model and Fisher and Simmons formula. The Fisher and Simmons formula found the effect associated with the relaxation of boric acid on absorption and provided a more detailed form of absorption coefficient which varies with frequency. However, no simulation model has made for the underwater acoustic propagation using these models. This paper reports the comparative study of acoustic wave absorption carried out by means of modeling in MATLAB. The results of simulation have been evaluated using measured data collected at Desaru beach on the eastern shore of Johor in Malaysia. The model has been used to determine sound absorption for given values of depth (D), salinity (S), temperature (T), pH, and acoustic wave transmitter frequency (f). From the results a suitable range, depth and frequency can be found to obtain best propagation link with low absorption loss.</span></p>

( $$\frac{G^{'}}{G^{2}}$$ G ′ G 2 )-Expansion method: new traveling wave solutions for some nonlinear fractional partial differential equations

In this study, some new traveling wave solutions for fractional partial differential equations (PDEs) have been developed. The time-fractional Burgers equation, fractional biological population model and space-time fractional Whitham Broer Kaup equations have been considered. These equations have significant importance in different areas such as fluid mechanics, determination of birth and death rates and propagation of shallow water waves. The analytical technique ( $$\frac{G^{'}}{G^{2}}$$ ) has been utilized for finding the new traveling wave solutions of the considered fractional PDEs. ( $$\frac{G^{'}}{G^{2}}$$ )-expansion method is a very useful approach and exceptionally helpful as contrast with other analytical methods. The proposed method provides three unique sort of solutions such as hyperbolic, trigonometric and rational solutions. This approach is likewise applicable to other nonlinear fractional models.