Propagation Of Water Waves Research Articles

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.

Experimental and numerical modelling of water waves in sewer networks during sewer/surface flow interaction using a coupled ODE‐SWE solver

AbstractFlooding in urban areas is expected to increase its magnitude and frequency in the future. Therefore, there is a strong need to better model sewer–surface flow interactions. Existing numerical methods are commonly based on simplified representations of sewer/surface mass exchange, and mainly validated in steady flow conditions. Current methodologies describing the propagation of transient conditions/waves through interaction nodes are simplified, rely on empirical coefficients and/or lack detailed validation. In this paper, an integrated numerical approach for modelling the propagation of water waves through interaction nodes (e.g., manholes) is presented. In this solution, the shallow water equations are used to simulate the free‐surface propagation inside the sewer network, and an ordinary differential equation is employed for modelling flow regimes through pipes and manholes. The model proposed is validated against the well‐known STAR‐CD modelling software for a number of test cases. Finally, further validation is performed against experimental data describing the evolution of water depth around a manhole in unsteady surcharging conditions.

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.

Acoustic and gravity waves in the ocean: a new derivation of a linear model from the compressible Euler equation

In this paper, we construct an accurate linear model describing the propagation of both acoustic and gravity waves in water. This original model is obtained by the linearization of the compressible Euler equations, written in Lagrangian coordinates. The system is studied in the isentropic case, with a free surface, an arbitrary bathymetry, and vertical variations of the background temperature and density. We show that our model is an extension of some models from the literature to the case of a non-barotropic fluid with a variable sound speed. Other models from the literature are recovered from our model through two asymptotic analyses, one for the incompressible regime and one for the acoustic regime. We also propose a method to write the model in Eulerian coordinates. Our model includes many physical properties, such as the existence of internal gravity waves or the variation of the sound speed with depth.

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.

Modulation effect of linear shear flow, wind, and dissipation on freak wave generation in finite water depth

This paper studies the modulation effect of linear shear flow (LSF), comprising a uniform flow and a shear flow with constant vorticity, combined with wind and dissipation on freak wave generation in water of finite depth. A nonlinear Schrödinger equation (NLSE) modified by LSF, strong wind, and dissipation is derived. This can be reduced to consider the effects of LSF, light wind, and dissipation, and further reduced to include only LSF. The relation between modulational instability (MI) of the NLSE and freak waves represented as a modified Peregrine Breather solution is analyzed. When considering only LSF, the convergence (divergence) effect of uniform up-flow (down-flow) and positive (negative) vorticity increases (decreases) the MI growth rate and promotes (inhibits) freak wave generation. The combined effect of LSF and light wind shows that a light adverse (tail) wind can restrain (amplify) MI and bury (trigger) freak waves. Under the effect of a light tailwind, LSF has the same effect on the MI growth rate and freak wave generation as the case without any wind. The combination of LSF and strong wind enables both adverse and tail winds to amplify MI and trigger freak waves. In the presence of strong wind, LSF has the opposite effect to the case of a light tailwind.

Hydraulic characteristics of the river flow and sediment transport conditions in the downstream pool of the hydroelectric complex

In this paper, the navigable section of the Svir River, located in the lower reaches of the Nizhne-Svirsky hydroelectric complex, is considered. Special in-situ observations were made in this section to study the hydraulic regime of the river flow under the conditions of unsteady water movement. The study has showed that the kinematic characteristics of the flow in the downstream pool vary with the distance from the site of the waterworks and depend on the regime of the discharge flows. The nature of the transformation of releases in the downstream under open channel and ice conditions has been studied. The values and intensity of changes in the main characteristics of the river flow during the propagation of the tail water wave in the lower reaches such as the nature of changes in the level regime and the slopes of the free surface on the hydraulic structures, the regime of water flow velocities, have been evaluated. The main hydraulic parameters of the river flow such as the values of the Froude number, the Chézy’s coefficient and the water flow modulus are determined. The character of changes in local and convective accelerations is studied and their contribution to the general value of energy losses along the stream length is evaluated. Numerical experiments make it possible to identify the peculiarities of sediment movement in conditions of unsteady water flow and to develop recommendations for modelling channel transformations in such conditions. It is found that during daily and weekly regulation of the river discharge, sediment transport is activated at the moment when a wave of daily water discharge is passing from the upstream reservoir of the hydroelectric power plant. At the same time, the basic parameters of sediment transport such as the speed of dune movement and sediment discharge increase in comparison with the stationary movement of the water.

2D Modeling of Wave Propagation in Shallow Water by the Method of Characteristics

2D Modeling of Wave Propagation in Shallow Water by the Method of Characteristics

Variational RANS modeling of hydraulic jumps

The hydraulic jump is a phenomenon which frequently appears in nearshore, estuarine and riverine regions; it plays a major role for example in the development and migration of sand waves in mobile beds, and in controlling the propagation of infra-gravity water waves from the nearshore into the river through bar-built, shallow estuaries. Although the prediction of these natural flows becomes crucial in many circumstances, it is difficult because hydraulic jumps are complex flows, and their modeling is far from simple. The steady-state hydraulic jump may be undular or broken, and their physical properties differ significantly. Undular jump profiles are dominated by the deviation of the fluid pressure from hydrostatic conditions, with turbulence playing a secondary role. In contrast, broken hydraulic jumps are determined by the differential advection of momentum due to breaking, and turbulence stresses. Between both types, there is a complex transition involving the interaction of non-hydrostaticity and turbulence, which is difficult to mimic with depth-averaged models. Simulations of these flows are typically conducted by resorting to vertically-averaged models either using the Saint-Venant or the Serre-Green-Naghdi equations, but none of them are fully satisfactory. In this work, an alternative approach for hydraulic jumps is proposed by developing a variational Reynolds-Averaged Navier-Stokes (RANS) model which uses Kantorovich-Krylov expansions of the flow variables, and a novel depth-averaged, eddy viscosity approach suitable for non-hydrostatic flows. The model is validated through results of simulations of both undular and broken jumps compared against detailed experiments. New experiments were conducted in a simplified bar-built shallow river inlet; the variational RANS model was found to reproduce well the flow profile over the bar, the hydraulic jump position and dynamic pressures over the bar surface.

Machine learning simulation of one-dimensional deterministic water wave propagation

Deterministic phase-resolved prediction of the evolution of surface gravity waves in water is challenging due to their complex spatio-temporal dynamics. Physics-based methods of varying complexity are available, but the conflicting objectives of numerical efficiency and accuracy impede real-time wave prediction. Data-driven methods may be able to overcome this challenge by using training data generated by complex numerical methods. This work explores the potential of a machine learning (ML) approach based on a fully convolutional encoder–decoder architecture for the efficient and accurate prediction of water waves. The high-order spectral (HOS) method forms the foundation for the generation of the training data. The HOS method is applied for different, consecutive orders of nonlinearity starting from first order up to fourth order. The JONSWAP wave energy spectrum serves as the basis for modeling the one-dimensional irregular sea states. The overall objective of this work is to evaluate whether the complex non-linear physical processes can be identified and learned by the ML approach. The trained ML flow mapper is used to perform time integration of an initial sea state. The results indicate that the proposed ML approach is able to reproduce the distinctive physical processes of the different orders of nonlinearities. It is shown that the ML approach enables fast and accurate predictions of one-dimensional waves over a time horizon that spans multiple peak periods.

Strongly non-linear Boussinesq-type model of the dynamics of internal solitary waves propagating in a multilayer stratified fluid

We propose a system of first-order balance laws that describe the propagation of internal solitary waves in a multilayer stratified shallow water with non-hydrostatic pressure in the upper and lower layers. The construction of this model is based on the use of additional variables, which make it possible to approximate the Green–Naghdi-type dispersive equations by a first-order system. In the Boussinesq approximation, the governing equations allow one to simulate the propagation of non-linear internal waves, taking into account fine density stratification, a weak velocity shear in the layers, and uneven topography. We obtain smooth steady-state soliton-like solutions of the proposed model in the form of symmetric and non-symmetric waves of mode-2 adjoining to a given multilayer constant flow. Numerical calculations of the generation and propagation of large-amplitude internal waves are carried out using both the proposed first-order system and Green–Naghdi-type equations. It is established that the solutions of these models practically coincide. The advantage of the first-order equations is the simplicity of numerical implementation and a significant reduction in the calculation time. We show that the results of numerical simulation are in good agreement with the experimental data on the evolution of mode-2 solitary waves in tanks of constant and variable height.

A new paradigm of reservoir computing exploiting hydrodynamics

Nonlinear waves have played a significant role in the development of the science of complexity throughout history. More recently, they have also contributed to the emergence of a novel paradigm in reservoir computing called neuromorphic computing by waves. In this paradigm, information is transmitted through wave dynamics, which process the data to perform complex tasks with minimal energy consumption. Leveraging nonlinear hydrodynamic waves for computational purposes, we have created the Aqua-Photonic-Advantaged Computing Machine by Artificial Neural Networks (Aqua-PACMANNs). This system utilizes wave propagation in shallow water as the primary physical phenomenon, with minimal electronic components required, limited to a camera for detection purposes. As a proof of concept, we have successfully implemented an exclusive-not-or logic gate using the Aqua-PACMANN architecture. This accomplishment demonstrates the potential of fluid dynamic neuromorphic computing and opens up possibilities for a new class of computing systems.

Sensitivity analysis of SPH parameters for long-distance water wave propagation

The hydrodynamics field continues to be interested in one of the classic free surface flow problems, the propagation of water waves. In this paper, long-distance water wave propagation is investigated using smoothed particle hydrodynamics (SPH). One of the mesh-free, Lagrangian particle approaches is SPH. The study’s goal is to derive a set of parameters appropriate for water wave propagation in a large wave tank. A 24.6 m wave gauge was placed in front of the piston wavemaker, which was used to replicate regular waves. Several SPH parameters are subjected to the sensitive analysis. In this investigation, DualSPHysics version 5.0, an open-source SPH solver, was employed. The findings demonstrated that a parameter with a substantial impact on the accuracy of wave profile is double-precision, particle distance, and coefficient of artificial viscosity.

Derivation of an improved smoothed particle hydrodynamics model for establishing a three-dimensional numerical wave tank overcoming excessive numerical dissipation

This paper presents an improved smoothed particle hydrodynamics (SPH) model through a rigorous mathematical derivation based on the principle of virtual work, aiming at establishing a three-dimensional numerical wave tank overcoming excessive numerical dissipation that has been usually encountered in traditional SPH models in practical applications. In order to demonstrate the accuracy and convergence of the new scheme, the viscous damping of a standing wave is first investigated as a quantitative validation, with particular attention on emphasizing (1) its physical rationality with respect to energy conservation and (2) its ability to alleviate wave over-attenuation even using fewer neighbors compared with the traditional δ-SPH model. Subsequently, several fully three-dimensional engineering problems, with respect to water wave propagation and the interaction with structures, are investigated to demonstrate the effectiveness of the new scheme in alleviating wave over-attenuation. It is demonstrated that the present model can be performed with relatively few neighbors (i.e., higher computational efficiency) to obtain accurate and convergent numerical results for those SPH simulations involving long-term and long-distance water wave propagation.

Investigation on the cavitation and atomization characteristics of multiphase fluids in underwater explosion near a free surface

The characteristics of cavitation and atomization induced by underwater explosion near a free surface have been investigated by the multiphase fluid model based on two-fluid phase transition. This numerical method can provide the phase transition between liquid and its vapor phases during shock wave and rarefaction wave propagation at any time in underwater explosion. The detailed density, pressure, vapor, and liquid phases of volume fraction contours in cavitation and atomization zones can be obtained. The phase transition model was first used to quantitatively research the phenomenon of vapor liquefaction after shock wave propagation in initial water containing different trace amounts of vapor. Then the contribution of phase transition to the formation of cavitation and atomization in underwater explosion was investigated through a shock tube test and two typical underwater explosion cases. It is found that the phase transition effect between the vapor and liquid phases contributes more than 60% to the formation of the cavitation zone. Two charges under two different water surface conditions have been investigated by comparison with the case of a single charge. We can conclude that it is very necessary to introduce the phase transition model into the simulation of underwater explosion, which can provide details of the flow field in the cavitation and atomization zones that cannot be obtained by the one-fluid cavitation model.

Numerical study of water wave generation by granular-liquid mixture collapse using two-phase material point method

Debris flow sliding with high-speed and its possible interactions with a confined water body may lead to dangerous hazard. Therefore, it is important in practical applications to accurately predict the granular-liquid flows and their possible interactions with the water body. A two-phase material point method (MPM) with double-point formulation was applied in this paper to simulate the generation of the water wave by granular-liquid mixtures collapse into water. In our study, the debris flow was idealized as a granular-liquid mixture, the liquid phase was considered as a compressible viscous fluid, the granular response was modeled using the Mohr–Coulomb yield criterion and the granular-liquid interaction forces including viscous drag force and buoyancy force. Two experimental tests of dam-breaking flow and the wave generation by a dry granular column collapse were simulated, the accuracy and effectiveness of the proposed approach has been proven by comparing the numerical results with experimental data. We performed an experiment of saturated granular column collapsed into water and the test results were used to validate the proposed method, then applied the validated method to simulate the water wave generation by granular-liquid mixture collapse into water and investigate the effects of the initial degree of saturation defined as the initial depth ratio of water to granular material on the time evolution of the granular front and the amplitude of leading wave.

Numerical Simulation of Nonlinear Wave Propagation from Deep to Shallow Water

Herein, a numerical model is proposed to simulate the nonlinear wave propagation from deep to shallow water and wave breaking phenomena. In the numerical model, the governing equations selected, in which the momentum equations were added to the eddy-viscous breaking and bottom friction terms to simulate the wave breaking phenomenon, are suitable for the wave propagation from deep to shallow water. The spatial derivations of the governing equations are discretized with the hybrid scheme, combining the finite-difference and finite-volume methods. To numerically simulate the nonlinear wave propagation in waters with various depths accurately, the non-conservative governing equations are reorganized as conservative to facilitate a total variation diminishing (TVD) type scheme using a Riemann solver. Extensive numerical tests of nonlinear wave propagation have been realized in waters with large relative water depths and varying water depths. The comparisons between numerical and analytical or experimental results indicated that the numerical results are reasonable and reliable, and the present numerical model can effectively simulate the wave-breaking phenomenon.

On H 2-solutions for a Camassa-Holm type equation

Abstract Camassa-Holm type equations arise as models for the unidirectional propagation of shallow water waves over a flat bottom. They also describe finite length, small amplitude radial deformation waves in cylindrical compressible hyperelastic rods. Under appropriate assumption on the initial data, on the time T T , and on the coefficients of such equation, we prove the well-posedness of the classical solutions for the Cauchy problem.

Validation of multiphase water wave propagation using smoothed particle hydrodynamics

Water wave propagation is one of the classical problems in free surface flow that involved water and air. There are a lot of studies have been conducted on both experimental and numerical methods. One numerical method is computational fluid dynamics (CFD), which is divided into two major i.e. CFD mesh-based and meshfree. In this paper, smoothed particle hydrodynamics (SPH) is used to carry out a study of water wave propagation. SPH is a mesh-free CFD and Lagrangian approach that is suitable for free surface flow such as water waves. Two-phase SPH was used to reproduce long-distance propagation using a piston-type wavemaker. The wave probe was set 24.6 m in front of the wavemaker with a water depth is 0.75 m. The wave period is 1.15 s with an amplitude of the wavemaker is 33.0 mm. The simulation is carried out with a water and air phase (multiphase). The results indicate SPH is in reasonable agreement with experimental for the wave height, celerity, and amplitude.

Achieving Complete Band Gaps of Water Waves with Shallow-Draft Cylinder Arrays

Conventionally, band gaps of water waves can be obtained with periodic arrays of bottom-mounted obstacles or vertical cylinders. However, such structures need to possess a large ratio of volume in water, and may not be easy to build and move in practical ocean engineering. Here, we theoretically propose and experimentally demonstrate that when the water surface is pierced by a fixed, rigid cylinder array, a complete band gap of water waves can be achieved, in which the propagation of water waves is forbidden in all the directions. Such a band gap can exist even when the cylinders have a draft much smaller than the water depth ($d\ensuremath{\ll}h$). Based on the complete band gap, a semicircular shape of the fixed-surface disk array is further constructed, which can block omnidirectional water waves generated by a point source.