Shallow Water Waves Research Articles

Impact of Climate Change on Maximum Sustained Wind Radius and its Associated Storm Surge Estimation along the Coast of Bangladesh

This research is a basic study on cyclones. The changing behaviour of storm surge in the Bay of Bengal due to the impact of climatic changes has been analyzed in this study. Certain characteristics of cyclones, such as the maximum sustained wind radius, have been analyzed, and their effect due to climatic change has been determined. The correlation between the maximum sustained wind radius and surge height was observed for this purpose. To accurately determine surge height, the vertically integrated shallow water wave model equation was employed, and it was solved using the semi-implicit finite difference method through the Arakawa-C grid. The surge model was performed by increasing and decreasing its wind radius by 10% to 20%, based on changes in the maximum sustained wind radius due to the effects of climate change. A strong conclusion was reached from the obtained results, indicating a significant effect of the maximum sustained wind radius on storm surge. But if it increases, there is a visible change in storm in some area of the coast of Bangladesh. For example, 1% increase in wind radius, the surge height increases by 0.032m, where the storm strikes. In some areas far away from where the storm hits the rising rate of the surge height is much lower. Finally, it may be stated that the surge height is affected by the maximum sustained wind radius and that it is altered by climatic impacts.

Structure of Analytical and Numerical Wave Solutions for the Nonlinear (1 + 1)-Coupled Drinfel’d–Sokolov–Wilson System Arising in Shallow Water Waves

In this article, we successfully obtain novel solutions for the coupled Drinfel’d–Sokolov–Wilson DSW system utilizing various methods. These include soliton solutions characterized by hyperbolic, rational, and trigonometric functions. Specifically, the generalized exponential rational function method (GERFM) and a modified version of the new Kudryashov method (MVNK) are employed to derive diverse soliton solutions for the system. Additionally, we demonstrate numerical solutions for the coupled Drinfel’d–Sokolov–Wilson system using adaptive moving mesh and uniform mesh methods. Also, we study the stability and error analysis of the numerical schemes. To validate the accuracy and reliability of the exact solutions obtained through analytical methods, we compare them with the numerical solutions both analytically and graphically. The techniques presented in this article are deemed suitable and acceptable and can be effectively applied to solve other nonlinear evolution systems.

Bosonization, symmetry reductions, mapping and deformation method for B-extension of Sawada–Kotera equation

An extended (2+1)-dimensional shallow water wave (SWW) model governs the evolution of nonlinear shallow water wave propagation in two spatial and a temporal coordinate. The multi-linear variable separation approach is applied to the SWW equation. The variable separation solution consisting of two arbitrary functions is given. By choosing the arbitrary functions as the exponential and trigonometric forms, some novel fission and fusion phenomena including the semifoldons, peakons, lump, dromions and periodic waves are graphically and analytically studied. The results enhance the variety of the dynamics of the nonlinear wave fields related by engineering and mathematical physics.

Computational approach and dynamical analysis of multiple solitary wave solutions for nonlinear coupled Drinfeld–Sokolov–Wilson equation

In this article, the coupled Drinfeld–Sokolov–Wilson equation under investigation base on computational approach named extension of modified rational expansion approach. By this computational approach secured various kinds of solitons named kink solitons, dark solitons, anti kink solitons, periodic solitons, bright solitons, kink dark solitons, kink bright solitons, anti kink dark solitons, anti kink bright solitons for coupled DSW system. The calculated results are interesting, precise, novel, and different which have not been secured in the previous research. We represent the graphical behaviour of determined solutions by 2-D, 3-D and contour through computational software. The determined results may helpful and play significant role in the study of nonlinear behaviour in various branches of physical sciences such as laser optics, communication system, fluid dynamics, transfer of heat, shallow water waves, acoustics, optics and many others. The constructed results prove that proposed computational approach is concise, powerful, and straightforward for securing the solitons results of other nonlinear partial differential equations.

The dynamical study and analysis of diverse bright-dark and breathers wave solutions of nonlinear evolution equations and their applications

In this work, we establish novel solitary wave solutions of three nonlinear evolution dynamical models, namely, Boussinesq model, [Formula: see text]-dimensional generalized shallow water wave (SWW) and [Formula: see text]-dimensional Fokas dynamical models by applying two-variable [Formula: see text]- expansion technique. The SWW equations are usually appropriate when the fluid is in a state where the vertical length scale is significantly smaller than the length of horizontal scale. In computer simulations for ocean engineering, Boussinesq-type models are frequently used to represent water waves in harbors and shallow seas. In order to understand the physical processes of waves inside and on the surface of water, the Fokas dynamical model plays a crucial part in wave theory. Analytical solutions in different forms such as solitons, solitary waves, trigonometric, hyperbolic, rational function solutions, breathers-type waves and more wave solutions are devised through using the proposed method. The exact solutions are also presented in graphical form having applications in engineering and other areas of applied sciences. The obtained results show that the given technique is universal and efficient. In addition, this technique can also be applied on lots of other nonlinear dynamical wave models occurring in many scientific real-world application domains, including engineering sciences, mathematics physics, and many more.

Exploring the new soliton solutions to the nonlinear M-fractional evolution equations in shallow water by three analytical techniques

This paper explores the new soliton solutions of the evolution equations named as truncated M-fractional (1+1)-dimensional non-linear Kaup-Boussinesq system by utilizing the expa function, modified simplest equation and Sardar sub-equation techniques. This system is used in the analysis of long waves in shallow water. The attained results involving trigonometric, hyperbolic and exponential functions. The effect of fractional order derivative is also discussed. Obtained results are very close to the approximate results due to the use of M-fractional derivative. Achieved results are verified by Mathematica tool. Few of the gained results are also explained through 2-D, 3-D and contour graphs. At the end, these techniques are straight forward, useful and effective to deal with non-linear FPDEs.

Analytical soliton solutions of the beta time-fractional simplified modified Camassa-Holm equation in shallow water wave propagation

In this study, the analytical soliton solutions of the beta time-fractional simplified modified Camassa-Holm equation, a mathematical model used to describe the propagation of shallow water waves characterized by weak dispersion and nonlinearities, is determined. The (G′/G,1/G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({G}^{\\prime}/G,1/G)$$\\end{document}-expansion method, a powerful and reliable technique, is exploited to formulate the soliton solutions for the equation. The process yields a wide range of solutions, including trigonometric, rational, and hyperbolic functions with free parameters. Various original soliton solutions are generated for different parameter values, including bell-shaped, anti-bell-shaped, periodic, compacton, singular bell-shaped, singular periodic and flat kink solitons. To visually comprehend the physical characteristics of the obtained solutions, two- and three-dimensional graphs, as well as contour plots, are plotted. Thorough comparisons with previous results are conducted to ensure the originality of the derived solutions. The insights gained from understanding soliton behavior in shallow water can be helpful in improving tsunami warnings, coastal protection systems, underwater data transmission, submarine cables, and marine sensing networks.

Standing waves on holidays

Standing waves are a common phenomenon in nature, but sometimes difficult to understand by the students. Many of them do not realise, for example, that the sound coming from the musical instruments is due to standing waves that are formed in strings, membranes, or cavities on those instruments. In this paper, we describe a simple activity that occurred in a circular pool during holidays which excited people for generating standing waves with their own body. This was also an opportunity for talking about this phenomenon with young people and make simple calculations of the speed of waves in shallow water. This is an example that summertime is not just for relaxing and teachers may find good examples of applied physics to bring to their classes and help students to better understand physics contents.

Investigations on the shallow water wave attenuation over continuous porous oyster reef-like structure

Observations over the decades have found that oyster reefs in shallow estuarine environments have the potential to protect shorelines or offshore structures by dissipating wave energy. Laboratory experiments were conducted to observe the shallow water wave attenuation in different terrains of the continuous porous oyster reef-like structures. To better reproduce this process, a numerical wave flume that is within the OpenFOAM scheme was developed in this study. The volume-averaged Reynolds-Averaged Navier–Stokes (VARANS) equations were solved for two-phase incompressible flow around the porous structures and the VOF method was used for tracking the free surface. The model was first validated by the present laboratory experiments. Subsequently, dimensional analysis was conducted to address the factors influencing wave attenuation over continuous porous reef-like structures. The model was then applied to evaluate the impacts of wave factors and morphological factors of porous oyster reef-like structures on the wave attenuation. By the end, an empirical formula was proposed to predict the wave transmission coefficient based on the numerical results and the experimental data.

Interaction solution to the (3+1)-D negative-order KdV first structure

We derive N-solitons and interaction solution for the (3+1)-D negative-order KdV first structure that arises in shallow-water waves. We use the bilinear scheme and the simplified Hirota technique for this solution. From the multiple solitons solution, we obtain a lump-shaped breather wave, a lump-shaped breather with a kink wave, and two lump-shaped breather waves from 2-solitons, 3-solitons, and 4-solitons, sequentially, by choosing complex conjugates of related parametric constants. Additionally, we show some novel interactions of the Jacobian elliptic transformation with periodic function, single soliton, and two solitons. Owing to these collisions, periodic waves with a kink wave, periodic breathers with a kink wave, and numerous bright and dark breather waves are created. We illustrate the properties of these solutions with 3D, density, and contour plots by selecting the appropriate values for the parameters. The obtained solutions will serve as milestones for studying the properties of nonlinear structures in the physical sciences and engineering fields.

The interaction of three long shallow-water waves with different dispersion relations modeled by generalized Hirota–Satsuma KdV systems with some variable coefficients

The interaction of three long shallow-water waves with different dispersion relations modeled by generalized Hirota–Satsuma KdV systems with some variable coefficients

Multi-Peak and Propagation Behavior of M-Shape Solitons in (2 + 1)-Dimensional Integrable Schwarz-Korteweg-de Vries Problem

This paper examines the propagation of M-shape solitons and their interactions with kink waves to the (2 + 1)-dimensional integrable Schwarz-Korteweg-de Vries (ISKdV) problem by applying the symbolic computation with ansatz functions technique and logarithmic transformation. The governing model usually appears in the nonlinear shallow water waves and fluid mechanics. We discuss various nonlinear waves like multiwave solutions (MSs), homoclinic breather (HB), M-shape solitons, single exponential form (one-kink), and double exponential form (two-kink). These waves have lot of applications in fluid dynamics, nonlinear optics, chemical reaction networks, biological systems, climate science, and material science. We also study interaction among M-shape solitons with kink wave. At the end, we discuss the stability characteristics of all solutions.

Exact Solutions of the Stochastic Conformable Broer–Kaup Equations

In this article, the exact solutions of the stochastic conformable Broer–Kaup equations with conformable derivatives which describe the bidirectional propagation of long waves in shallow water are obtained using the modified exponential function method and the generalized Kudryashov method. These exact solutions consist of hyperbolic, trigonometric, rational trigonometric, rational hyperbolic, and rational function solutions, respectively. This shows that the proposed methods are competent and sufficient. In addition, it is aimed to better understand the physical properties by drawing two- and three-dimensional graphics of the exact solutions according to different parameter values. When these exact solutions obtained by two different methods are compared with the solutions attained by other methods, it can be said that these two methods are competent.

Hybrid and physical interaction phenomena solutions to the Hirota bilinear equation in shallow water waves theory

The purpose of this research paper is to investigate the (3+1)-dimensional Hirota bilinear equation that arises in nonlinear waves in fluid dynamics, plasma physics and shallow water waves. We use Hirota’s bilinear approach and a long-wave method to explore the dynamical features of the suggested equation. Multiple M-lump waves mixed with soliton solutions are constructed. Also, the breather wave and its interaction with one-soliton and M-lump waves are derived. These solutions are believed to play a role in understanding the dynamical aspects of the (3+1)-dimensional Hirota bilinear equation.

Numerical study on maneuvering a container ship in shallow water waves

Numerous practical and mathematical techniques have been piloted to study ships’ behavior in deep water conditions with and without waves, and shallow water conditions without waves, while only limited investigations have been carried out to assess ships’ behavior in shallow waters with wave conditions as the flow around the stern region and appendages and the interaction effects are intricate. Therefore, this study attempts to understand the infrequently explored subset of a vessel’s behavior in regular waves in shallow water conditions (channel depth to ship draft ratio taken as 1.5). A container ship (S175) model scaled at 1:36 was the subject of a numerical study in which it was subjected to static and dynamic maneuver simulations in head sea conditions. The waves were induced using the dispersion relationship of waves in a given depth. The trends of forces and moments acting on the hull while undergoing maneuvering motions were obtained using a smooth particle hydrodynamics-based computational fluid dynamics solver. The resulting periodic trends of forces and moments were analyzed using the Fourier series method to extract the Fourier coefficients and, in turn, calculate the hydrodynamic derivatives. The trajectories in turning circle and zigzag maneuvers were also simulated using a MATLAB code. The results demonstrate an increase in trajectory parameters and improvement in counter maneuverability owing to the complex flow physics around the hull when encountering regular waves in shallow water conditions compared to waves in deep waters and a lack of waves in shallow waters.

The (3+1)-dimensional Boussinesq equation: Novel multi-wave solutions

The Boussinesq equation is a partial differential equation that describes the behavior of waves in shallow water. In this paper, we address some new dynamical behaviors to the (3+1)-dimensional Boussinesq equation, which are not constructed beforehand. Various solutions namely: multi-soliton, multi-M-lump, and the hybrid soliton solutions are reported. New explored features of equation are presented graphically to better analyze the gained solutions. For different period of time multi-soliton, multi-lump solutions are plotted. The results have important applications in oceanography, geophysics, fluid dynamics, and also used to study the behavior of waves in complex three-dimensional domains, particularly in situations where the nonlinear effects are strong.

Constructing Families of Solutions to an Integrable Time-Dependent Shallow Water Wave Equation in (1+1)-Dimensions

In this paper, an integrable shallow water wave equation with timedependent coefficients in (1+1)-dimensions is taken into account. Through employing the generalized three-wave methods, a series of (double) solitary wave solutions and periodic (solitary) wave solutions to the considered equation are presented with the aid of symbolic calculation. Furthermore, by specifying relevant functions and parameters, the localized structures of some resulting solutions are displayed via some figures. These results enrich the diversity of nonlinear waves in physics.

Reconstructions of time-evolving sound-speed fields perturbed by deformed and dispersive internal solitary waves in shallow water

The high-fidelity reconstruction of sound speeds is crucial for predicting acoustic propagation in shallow water where internal solitary waves (ISWs) are prevalent. Mapping temperatures from time series to spatial fields is an approach widely used to reproduce the sound speed perturbed by deformed internal waves. However, wave-shape distortions are inherent in the modeling results. This paper analyzes the formation mechanism and dynamic behavior of the distorted waveform that is shown to arise from the mismatch between the modeled and real propagation speeds of individual solitons within an ISW packet. To mitigate distortions, a reconstruction method incorporating the dispersion property of an ISW train is proposed here. The principle is to assign each soliton a real speed observed in the experiment. Then, the modeled solitons propagate at their intrinsic speeds, and the packet disperses naturally with time. The method is applied to reconstruct the sound speed perturbed by ISWs in the South China Sea. The mean and median of the root-mean-square error between the reconstructed and measured sound speeds are below 2 m/s. The modeled shape deformations and packet dispersion agree well with observations, and the waveform distortion is reduced compared with the original method. This work ensures the high fidelity of waveguide-environment reconstructions and facilitates the investigation of sound propagation in the future.

Fractional-stochastic shallow water equations and its analytical solutions

In this paper, the stochastic shallow water wave equation with M-Truncated derivative is taken into account. New rational, trigonometric and hyperbolic solutions are produced using the He’s semi-inverse method and modified extended tanh-function method. The solutions found can be used to simulate a wide range of fascinating physical phenomena since the shallow water equation has numerous applications including weather simulations, tsunami prediction, tidal waves, and river irrigation flows. Also, we generalize some previous results. To show how M-Truncated Derivative and white noise affect the analytical solutions of the stochastic shallow water wave equation with M-Truncated derivative, we create different two dimension and three dimension graphs.

Line-soliton, lump and interaction solutions to the (2+1)-dimensional Hirota-Satsuma-Ito equation with time-dependent via Hirota bilinear forms

In this paper, we consider the (2+1)-dimensional generalized Hirota-Satsuma-Ito equation with time-dependent, which has applications in describing the propagation of shallow water waves. Based on the bilinear formalism and with the aid of symbolic computation, we obtain line-soliton, lump, one-lump-one-stripe and one-lump-one-soliton using various ansatze’s function. To realize dynamics, we use diverse plots to analyze these solutions. Obtained solutions are reliable in the mathematical physics and engineering.