Search Results (340)

This work aims to highlight the effects of nonlinearity on the crest shape of large directional water wave events. To simulate such events, we chose to focus frequencies on a pre-determined time step over a wavefield with randomised phases, running the simulations with HOS-ocean, a fully nonlinear potential flow solver. By also applying a phase separation scheme, we were able to identify the contributions of the various orders of nonlinearity to the formation of these large wave events. The findings show a significant change in the shape of these large water waves compared to linear theory, particularly in shallower water depth. In addition, the phase separation reveals the increased significance of high-order harmonics in finite water depths compared to deep water. Full article

The strong nonlinearity of shallow-water waves significantly affects the dynamic response of floating offshore wind turbines (FOWTs), introducing additional complexity in motion behavior. This study presents a series of 1:80-scale experiments conducted on a 5 MW FOWT at a 50 m water depth, under regular, irregular, and focused wave conditions. The tests were conducted under regular, irregular, and focused wave conditions. The results show that, under both regular and irregular wave conditions, the platform’s motion and mooring tension increased as the wave period became longer, indicating a greater energy transfer and stronger coupling effects at lower wave frequencies. Specifically, in irregular seas, mooring tension increased by 16% between moderate and high sea states, with pronounced surge–pitch coupling near the natural frequency. Under focused wave conditions, the platform experienced significant surge displacement due to the impact of large wave crests, followed by free-decay behavior. Meanwhile, the pitch amplitude increased by up to 27%, and mooring line tension rose by 16% as the wave steepness intensified. These findings provide valuable insights for the design and optimization of FOWTs in complex marine environments, particularly under extreme wave conditions. Additionally, they contribute to the refinement of relevant numerical simulation methods. Full article

The shallow water equations (SWEs) model fluid flow in rivers, coasts, and tsunamis. Their nonlinearity challenges analytical solutions. We present a numerical algorithm combining the finite integration method with Chebyshev polynomial expansion (FIM-CPE) to solve one- and two-dimensional SWEs. The method transforms partial differential equations into integral equations, approximates spatial terms via Chebyshev polynomials, and uses forward differences for time discretization. Validated on stationary lakes, dam breaks, and Gaussian pulses, the scheme achieved errors below ${10}^{-12}$ for water height and velocity, while conserving mass with volume deviations under ${10}^{-5}$. Comparisons showed superior shock-capturing versus finite difference methods. For two-dimensional cases, it accurately resolved wave interactions over complex topographies. Though limited to wet beds and small-scale two-dimensional problems, the method provides a robust simulation tool. Full article

In 2071, the Hydraulic community will commemorate the second centenary of the Baré de Saint-Venant equations, also known as the Shallow Water Equations (SWE). These equations are fundamental to the study of open-channel flow. As non-linear partial differential equations, their solutions were largely unattainable until the development of computers and numerical methods. Following 1960, various numerical schemes emerged, with Preissmann’s scheme becoming the most widely employed in many software applications. In the 1990s, some researchers identified a significant limitation in existing software and codes: the inability to simulate transcritical flow. At that time, Preissmann’s scheme was the dominant method employed in hydraulics tools, leading the research community to conclude that this scheme could not handle transcritical flow due to suspected instability. In response to this concern, several researchers suggested modifications to Preissmann’s scheme to enable the simulation of transcritical flow. This paper will demonstrate that these accusations against the Preissmann scheme are unfounded and that the proposed improvements are unnecessary. The observed instability is not due to the numerical method itself, but rather a mathematical instability inherent to the SWE, which can lead to ill-posed conditions if a specific derived condition is not met. In the context of a friction slope formula based on Manning or Chézy types, the condition for ill-posedness of the 1D shallow water equations simplifies to the Vedernikov number condition, which is necessary for roll waves to develop in uniform flow. This derived condition is also relevant for the formation of roll waves in unsteady flow when the 1D shallow water equations become ill-posed. Full article

The Korteweg–de Vries (KdV) equation is a nonlinear evolution equation that reflects a wide variety of dispersive wave occurrences with limited amplitude. It has also been used to describe a range of major physical phenomena, such as shallow water waves that interact weakly and nonlinearly, acoustic waves on a crystal lattice, lengthy internal waves in density-graded oceans, and ion acoustic waves in plasma. The KdV equation is one of the most well-known soliton models, and it provides a good platform for further research into other equations. The KdV equation has several forms. The aim of this study is to introduce and investigate a (2+1)-dimensional generalized fifth-order KdV equation with power law nonlinearity (gFKdVp). The research methodology employed is the Lie group analysis. Using the point symmetries of the gFKdVp equation, we transform this equation into several nonlinear ordinary differential equations (ODEs), which we solve by employing different strategies that include Kudryashov’s method, the $(G^{\prime }/G)$ expansion method, and the power series expansion method. To demonstrate the physical behavior of the equation, 3D, density, and 2D graphs of the obtained solutions are presented. Finally, utilizing the multiplier technique and Ibragimov’s method, we derive conserved vectors of the gFKdVp equation. These include the conservation of energy and momentum. Thus, the major conclusion of the study is that analytic solutions and conservation laws of the gFKdVp equation are determined. Full article

In this study, we focus on solving the nonlinear time-fractional Hirota–Satsuma coupled Korteweg–de Vries (KdV) and modified Korteweg–de Vries (MKdV) equations, using the Yang transform iterative method (YTIM). This method combines the Yang transform with a new iterative scheme to construct reliable and efficient solutions. Readers can understand the procedures clearly, since the implementation of Yang transform directly transforms fractional derivative sections into algebraic terms in the given problems. The new iterative scheme is applied to generate series solutions for the provided problems. The fractional derivatives are considered in the Caputo sense. To validate the proposed approach, two numerical examples are analysed and compared with exact solutions, as well as with the results obtained from the fractional reduced differential transform method (FRDTM) and the q-homotopy analysis transform method (q-HATM). The comparisons, presented through both tables and graphical illustrations, confirm the enhanced accuracy and reliability of the proposed method. Moreover, the effect of varying the fractional order is explored, demonstrating convergence of the solution as the order approaches an integer value. Importantly, the time-fractional Hirota–Satsuma coupled KdV and modified Korteweg–de Vries (MKdV) equations investigated in this work are not only of theoretical and computational interest but also possess significant implications for achieving global sustainability goals. Specifically, these equations contribute to the Sustainable Development Goal (SDG) “Life Below Water” by offering advanced modelling capabilities for understanding wave propagation and ocean dynamics, thus supporting marine ecosystem research and management. It is also relevant to SDG “Climate Action” as it aids in the simulation of environmental phenomena crucial to climate change analysis and mitigation. Additionally, the development and application of innovative mathematical modelling techniques align with “Industry, Innovation, and Infrastructure” promoting advanced computational tools for use in ocean engineering, environmental monitoring, and other infrastructure-related domains. Therefore, the proposed method not only advances mathematical and numerical analysis but also fosters interdisciplinary contributions toward sustainable development. Full article

Extreme surface winds and wave heights of tropical cyclones (TCs)—pose serious threats to coastal community, infrastructure and environments. In recent decades, progress in numerical wave modeling has significantly enhanced the ability to reconstruct and predict wave behavior. This review offers an in-depth overview of TC-related wave modeling utilizing different computational schemes, with a special attention to WAVEWATCH III (WW3) and Simulating Waves Nearshore (SWAN). Due to the complex air–sea interactions during TCs, it is challenging to obtain accurate wind input data and optimize the parameterizations. Substantial spatial and temporal variations in water levels and current patterns occurs when coastal circulation is modulated by varying underwater topography. To explore their influence on waves, this study employs a coupled SWAN and Finite-Volume Community Ocean Model (FVCOM) modeling approach. Additionally, the interplay between wave and sea surface temperature (SST) is investigated by incorporating four key wave-induced forcing through breaking and non-breaking waves, radiation stress, and Stokes drift from WW3 into the Stony Brook Parallel Ocean Model (sbPOM). 20 TC events were analyzed to evaluate the performance of the selected parameterizations of external forcings in WW3 and SWAN. Among different nonlinear wave interaction schemes, Generalized Multiple Discrete Interaction Approximation (GMD) Discrete Interaction Approximation (DIA) and the computationally expensive Wave-Ray Tracing (WRT) A refined drag coefficient (C_d) equation, applied within an upgraded ST6 configuration, reduce significant wave height (SWH) prediction errors and the root mean square error (RMSE) for both SWAN and WW3 wave models. Surface currents and sea level variations notably altered the wave energy and wave height distributions, especially in the area with strong TC-induced oceanic current. Finally, coupling four wave-induced forcings into sbPOM enhanced SST simulation by refining heat flux estimates and promoting vertical mixing. Validation against Argo data showed that the updated sbPOM model achieved an RMSE as low as 1.39 m, with correlation coefficients nearing 0.9881. Full article

The icebreaking process of water-exiting vehicles involves complex nonlinear interactions as well as multi-physical field coupling effects among ice, solids, and fluids, which poses enormous challenges for numerical calculations. Addressing the low solution accuracy of traditional grid methods in simulating large deformation and destruction of ice layers, a numerical model was established based on the FEM-SPH-SALE coupling algorithm to study the dynamic characteristics of the water-exiting vehicle on the icebreaking process. The FEM-SPH adaptive algorithm was used to simulate the damage performance of ice, and its feasibility was verified through the four-point bending test and vehicle breaking ice experiment. The S-ALE algorithm was used to simulate the process of fluid/structure interaction, and its accuracy was verified through the wedge-body water-entry test and simulation. On this basis, numerical simulations were performed for different ice thicknesses and initial velocities of vehicles. The results show that the motion characteristics of the vehicle undergoes a sudden change during the ice-breaking. The head and middle section of the vehicle are subject to greater stress, which is related to the transmission of stress waves and inertial effect. The velocity loss rate of the vehicle and the maximum stress increase with the thickness of ice. The higher the initial velocity of the vehicle, the larger the acceleration and maximum stress in the process of the vehicle breaking ice. The acceleration peak is sensitive to the variation in the vehicle’s initial velocity but insensitive to the thickness of the ice. Full article

In this study, we study the trapping of linear water waves by infinite arrays of three-dimensional fixed periodic structures in a three-layer fluid. Each layer has an independent uniform velocity field with respect to the fixed ground in addition to the internal modes along the interfaces between layers. Dynamical stability between velocity shear and gravitational pull constrains the layer velocities to a neighbourhood of the diagonal $U_1=U_2=U_3$ in velocity space. A non-linear spectral problem results from the variational formulation. This problem can be linearized, resulting in a geometric condition (from energy minimization) that ensures the existence of trapped modes within the limits set by stability. These modes are solutions living the discrete spectrum that do not radiate energy to infinity. Symmetries reduce the global problem to solutions in the first octant of the three-dimensional velocity space. Examples are shown of configurations of obstacles which satisfy the stability and geometric conditions, depending on the values of the layer velocities. The robustness of the result of the vertical column from previous studies is confirmed in the new configurations. This allows for comparison principles (Cavalieri’s principle, etc.) to be used in determining whether trapped modes are generated. Full article

This study addresses the limitations of conventional evaluation methods caused by low porosity, strong heterogeneity, and complex pore structures in tight sandstone reservoirs. Through integrated rock physics experiments and multi-physical field modeling, the research systematically investigates the coupled response mechanisms between electrical and elastic parameters. The experimental approach includes pore structure characterization, quantitative mineral composition analysis, resistivity and polarizability measurements under various saturation conditions, P- and S-wave velocity testing, and scanning electron microscopy (SEM) imaging. The key findings show that increasing porosity leads to significant reductions in resistivity and elastic wave velocities, while also increasing surface conductivity. Specifically, clay minerals enhance surface conductivity through interfacial polarization effects and decrease rock stiffness, which exacerbates wave velocity attenuation. Furthermore, resistivity exhibits a nonlinear negative correlation with water saturation, with sharp increases at low saturation levels due to the disruption of conductive pathways. By integrating the Modified Generalized Effective Medium Theory of Induced Polarization (MGEMTIP) and Kuster–Toksöz models, this study establishes quantitative relationships between porosity, saturation, and electrical/elastic parameters, and constructs cross-plot templates that correlate elastic wave velocities with resistivity and surface conductivity. These analyses reveal that high-porosity, high-saturation zones are characterized by lower resistivity and wave velocities, coupled with significantly higher surface conductivity. The proposed methodology significantly improves the accuracy of reservoir evaluation and enhances fluid identification capabilities, providing a solid theoretical foundation for the efficient exploration and development of tight sandstone reservoirs. Full article

For a significant fluid model and the truncated M-fractional (1 + 1)-dimensional nonlinear generalized water wave equation, distinct types of truncated M-fractional wave solitons are obtained. Ocean waves, tidal waves, weather simulations, river and irrigation flows, tsunami predictions, and more are all explained by this model. We use the improved $(G^{\prime }/G)$ expansion technique and a modified extended direct algebraic technique to obtain these solutions. Results for trigonometry, hyperbolic, and rational functions are obtained. The impact of the fractional-order derivative is also covered. We use Mathematica software to verify our findings. Furthermore, we use contour graphs in two and three dimensions to illustrate some wave solitons that are obtained. The results obtained have applications in ocean engineering, fluid dynamics, and other fields. The stability analysis of the considered equation is also performed. Moreover, the stationary solutions of the concerning equation are studied through modulation instability. Furthermore, the used methods are useful for other nonlinear fractional partial differential equations in different areas of applied science and engineering. Full article

Steel lazy wave risers (SLWRs) are critical in offshore hydrocarbon transport for linking subsea wells to floating production facilities in deep-water environments. The incorporation of buoyancy modules reduces curvature-induced stress concentrations in the touchdown zone (TDZ); however, extended operational exposure under cyclic environmental and operational loads results in repeated seabed contact. This repeated interaction modifies the seabed soil over time, gradually forming a trench and altering the riser configuration, which significantly impacts stress patterns and contributes to fatigue degradation. Accurately reconstructing the riser’s evolving profile in the TDZ is essential for reliable fatigue life estimation and structural integrity evaluation. This study proposes a simulation-based framework for the autonomous tracking of SLWRs using a fin-actuated autonomous underwater vehicle (AUV) equipped with a monocular camera and multibeam echosounder. By fusing visual and acoustic data, the system continuously estimates the AUV’s relative position concerning the riser. A dedicated image processing pipeline, comprising bilateral filtering, edge detection, Hough transform, and K-means clustering, facilitates the extraction of the riser’s centerline and measures its displacement from nearby objects and seabed variations. The framework was developed and validated in the underwater unmanned vehicle (UUV) Simulator, a high-fidelity underwater robotics and pipeline inspection environment. Simulated scenarios included the riser’s dynamic lateral and vertical oscillations, in which the system demonstrated robust performance in capturing complex three-dimensional trajectories. The resulting riser profiles can be integrated into numerical models incorporating riser–soil interaction and non-linear hysteretic behavior, ultimately enhancing fatigue prediction accuracy and informing long-term infrastructure maintenance strategies. Full article

This study presents a one-dimensional solver of the shallow water equations designed for the wet-bed step Riemann problem. Nonlinear mass and momentum equations incorporating shock and rarefaction waves in a straight one-dimensional channel are expressed as a pair of equations that depend solely on local depth values either side of the step. These unified equations are uniquely designed for the four conditions involving shock and rarefaction waves that can occur in the Step Riemann Problem. The Levenberg–Marquardt method is used to solve these simplified nonlinear equations. Four verification tests are considered for shallow free surface flow in a wet-bed channel with a step. These cases involve two rarefactions, opposing shock-like hydraulic bores, and a rarefaction and shock-like bore. The numerical predictions are in close agreement with existing theory, demonstrating that the method is very effective at solving the wet-bed step Riemann problem. Full article

The primary aim of this research article is to investigate the soliton dynamics of the M-truncated derivative nonlinear Kodama equation, which is useful for optical solitons on nonlinear media, shallow water waves over complex media, nonlocal internal waves, and fractional viscoelastic wave propagation. We utilized two recently developed analytical techniques, the generalized Arnous method and the generalized Kudryashov method. First, the nonlinear Kodama equation is transformed into a nonlinear ordinary differential equation using the homogeneous balance principle and a traveling wave transformation. Next, various types of soliton solutions are constructed through the application of these effective methods. Finally, to visualize the behavior of the obtained solutions, three-dimensional, two-dimensional, and contour plots are generated using Maple (2023) mathematical software. Full article

In this article, we present the extended simple equations method (SEsM) for finding exact solutions to systems of fractional nonlinear partial differential equations (FNPDEs). The expansions made to the original SEsM algorithm are implemented in several directions: (1) In constructing analytical solutions: exact solutions to FNPDE systems are presented by simple or complex composite functions, including combinations of solutions to two or more different simple equations with distinct independent variables (corresponding to different wave velocities); (2) in selecting appropriate fractional derivatives and appropriate wave transformations: the choice of the type of fractional derivatives for each system of FNPDEs depends on the physical nature of the modeled real process. Based on this choice, the range of applicable wave transformations that are used to reduce FNPDEs to nonlinear ODEs has been expanded. It includes not only various forms of fractional traveling wave transformations but also standard traveling wave transformations. Based on these methodological enhancements, a generalized SEsM algorithm has been developed to derive exact solutions of systems of FNPDEs. This algorithm provides multiple options at each step, enabling the user to select the most appropriate variant depending on the expected wave dynamics in the modeled physical context. Two specific variants of the generalized SEsM algorithm have been applied to obtain exact solutions to two time-fractional shallow-water-like systems. For generating these exact solutions, it is assumed that each system variable in the studied models exhibits multi-wave behavior, which is expressed as a superposition of two waves propagating at different velocities. As a result, numerous novel multi-wave solutions are derived, involving combinations of hyperbolic-like, elliptic-like, and trigonometric-like functions. The obtained analytical solutions can provide valuable qualitative insights into complex wave dynamics in generalized spatio-temporal dynamical systems, with relevance to areas such as ocean current modeling, multiphase fluid dynamics and geophysical fluid modeling. Full article