Water Waves Research Articles

Peaked Stokes waves as solutions of Babenko’s equation

Babenko’s equation describes traveling water waves in holomorphic coordinates. It has been used in the past to obtain properties of Stokes waves with smooth profiles analytically and numerically. We show in the deep-water limit that properties of Stokes waves with peaked profiles can also be recovered from the same Babenko’s equation. In order to develop the local analysis of singularities, we rewrite Babenko’s equation as a fixed-point problem near the maximal elevation level. As a by-product, our results rule out a corner point singularity in the holomorphic coordinates, which has been obtained in a local version of Babenko’s equation.

Analysis of the wave solutions of the nonlinear evolution equations help of advanced exp⁡(-φ(ξ))-expansion scheme

With the assistance of emblematic calculation programming, the current paper explores the specific voyaging wave arrangements from the general (2+1)- layered nonlinear development conditions by utilizing the advanced exp⁡(-φ(ξ))-expansion with time-partial boundaries. As a result, the used technique is effectively utilized and recently created some precise voyaging wave arrangements. The recently created arrangements have been communicated regarding mathematical and exaggerated capabilities. The created arrangements have been inquired into their comparing condition with the guide of the emblematic calculation programming Maple. The elements of nonlinear wave arrangements are analyzed and shown by maple18 in 3D, and 2D plots, and form plots with explicit upsides of the mind boggling boundaries are plotted. The advanced exp⁡(-φ(ξ))-expansion strategy is a solid treatment for looking through fundamental nonlinear waves that enhance an assortment of water waves in the long-frequency system that emerges in designing fields.

Detection of Subarachnoid Hemorrhage Using CNN with Dynamic Factor and Wandering Strategy-Based Feature Selection.

Objectives: Subarachnoid Hemorrhage (SAH) is a serious neurological emergency case with a higher mortality rate. An automatic SAH detection is needed to expedite and improve identification, aiding timely and efficient treatment pathways. The existence of noisy and dissimilar anatomical structures in NCCT images, limited availability of labeled SAH data, and ineffective training causes the issues of irrelevant features, overfitting, and vanishing gradient issues that make SAH detection a challenging task. Methods: In this work, the water waves dynamic factor and wandering strategy-based Sand Cat Swarm Optimization, namely DWSCSO, are proposed to ensure optimum feature selection while a Parametric Rectified Linear Unit with a Stacked Convolutional Neural Network, referred to as PRSCNN, is developed for classifying grades of SAH. The DWSCSO and PRSCNN surpass current practices in SAH detection by improving feature selection and classification accuracy. DWSCSO is proposed to ensure optimum feature selection, avoiding local optima issues with higher exploration capacity and avoiding the issue of overfitting in classification. Firstly, in this work, a modified region-growing method was employed on the patient Non-Contrast Computed Tomography (NCCT) images to segment the regions affected by SAH. From the segmented regions, the wide range of patterns and irregularities, fine-grained textures and details, and complex and abstract features were extracted from pre-trained models like GoogleNet, Visual Geometry Group (VGG)-16, and ResNet50. Next, the PRSCNN was developed for classifying grades of SAH which helped to avoid the vanishing gradient issue. Results: The DWSCSO-PRSCNN obtained a maximum accuracy of 99.48%, which is significant compared with other models. The DWSCSO-PRSCNN provides an improved accuracy of 99.62% in CT dataset compared with the DL-ICH and GoogLeNet + (GLCM and LBP), ResNet-50 + (GLCM and LBP), and AlexNet + (GLCM and LBP), which confirms that DWSCSO-PRSCNN effectively reduces false positives and false negatives. Conclusions: the complexity of DWSCSO-PRSCNN was acceptable in this research, for while simpler approaches appeared preferable, they failed to address problems like overfitting and vanishing gradients. Accordingly, the DWSCSO for optimized feature selection and PRSCNN for robust classification were essential for handling these challenges and enhancing the detection in different clinical settings.

Floating periodic pontoons for broad bandgaps of water waves

Floating periodic pontoons for broad bandgaps of water waves

Non-existence of cusps for a free-boundary problem for water waves

In Varvaruca and Weiss (2011), Varvaruca and Weiss eliminate the existence of cusps for a free-boundary problem for two-dimensional water waves under assumptions that hold for solutions for which \{u>0\} is a “strip-like” domain in the sense of Varvaruca (2008). In this paper, it is proven that cusps do not exist in the natural setting for these free-boundary problems. In particular, non-strip-like domains are also allowed. This qualitative result follows from quantitative results which, roughly speaking, give lower bounds on the “slope” at which the free boundary approaches a stagnation point. This builds upon recent work on non-existence of cusps in McCurdy and Naples (2022) for local minimizers.

Multi-kink solitons, resonant soliton molecules and multi-lumps solutions to the (3+1)-dimensional shallow water wave equation

The objective of this research is to seek some new exact solutions to the [Formula: see text]-dimensional shallow water wave equation (SWWE). By means of the Cole–Hopf transformation, the Hirota bilinear expression of the considered equation is developed. Then, taking advantage of the Hirota bilinear approach, the multi-kink solitons solutions are developed. Based on this, the resonant soliton molecules are derived via imposing certain resonant conditions (RCs). Furthermore, the new homoclinic technique is applied to explore the multi-lump solutions. To reveal the performances of the extracted solutions, the corresponding profiles are unveiled graphically through the Maple. For all we know, the derived solutions in this paper have not been probed in other literature and can expand the exact solutions of the considered equation.

Intelligent energy management system of hydrogen based microgrid empowered by AI optimization technique

Microgrids powered by hydrogen often face challenges in effectively managing energy over an extended duration due to the intermittent nature of renewable energy sources (RES) and fluctuating loads. This research emphasizes the use of AI technologies, including machine learning to improve the efficiency of intelligent energy management system (IEMS), hydrogen storage, fuel cell consumption, and power system quality improvement. A novel approach integrating Isolation Forest Ensemble (IFE) and Modified Water Wave Optimization (MWWO) has been proposed to enhance energy management and to improve the power quality. This method combines the population size with precision and accuracy. The effectiveness of this study has been assessed against established methods (AVO, PSO & IPSO, MFO, SAG & XGBoost, MILP, and QTLBO) concerning numerous factors including component sizing, economics, reliability, and efficiency of microgrid. The precision level of the proposed technique is approximately 83 %. The primary benefit of this research is the improvement of power quality and cost-efficiency in hydrogen based microgrids, attained through optimized and intelligent energy management system. This article furnishes evidence indicating the superiority of the anticipated approach. This study utilizes MATLAB/Simulink and PyCharm framework for its investigation and projection.

Efficient numerical approximations for a nonconservative nonlinear Schrödinger equation appearing in wind‐forced ocean waves

AbstractWe consider a nonconservative nonlinear Schrödinger equation (NCNLS) with time‐dependent coefficients, inspired by a water waves problem. This problem does not have mass or energy conservation, but instead mass and energy change in time under explicit balance laws. In this paper, we extend to the particular NCNLS two numerical schemes which are known to conserve energy and mass in the discrete level for the cubic nonlinear Schrödinger equation. Both schemes are second‐order accurate in time, and we prove that their extensions satisfy discrete versions of the mass and energy balance laws for the NCNLS. The first scheme is a relaxation scheme that is linearly implicit. The other scheme is a modified Delfour–Fortin–Payre scheme, and it is fully implicit. Numerical results show that both schemes capture robustly the correct values of mass and energy, even in strongly nonconservative problems. We finally compare the two numerical schemes and discuss their performance.

Exploring the Diversity of Kink Solitons in (3+1)-Dimensional Wazwaz–Benjamin–Bona–Mahony Equation

The Wazwaz–Benjamin–Bona–Mahony (WBBM) equation is a well-known regularized long-wave model that examines the propagation kinematics of water waves. The current work employs an effective approach, called the Riccati Modified Extended Simple Equation Method (RMESEM), to effectively and precisely derive the propagating soliton solutions to the (3+1)-dimensional WBBM equation. By using this upgraded approach, we are able to find a greater diversity of families of propagating soliton solutions for the WBBM model in the form of exponential, rational, hyperbolic, periodic, and rational hyperbolic functions. To further graphically represent the propagating behavior of acquired solitons, we additionally provide 3D, 2D, and contour graphics which clearly demonstrate the presence of kink solitons, including solitary kink, anti-kink, twinning kink, bright kink, bifurcated kink, lump-like kink, and other multiple kinks in the realm of WBBM. Furthermore, by producing new and precise propagating soliton solutions, our RMESEM demonstrates its significance in revealing important details about the model behavior and provides indications regarding possible applications in the field of water waves.

Interaction of lump, periodic, bright and kink soliton solutions of the (1+1)-dimensional Boussinesq equation using Hirota-bilinear approach

In this paper, we explore the characteristics of lump and interaction solutions for a (1+1) dimensional Boussinesq equation. By employing the Hirota bilinear method, we derive and analyze the exact solutions of this equation. Specifically, we achieve the lump with bright-bright soliton solution, 1-lump,2-lumps and 3-lumps with single bright soliton solution, lump with periodic, kink, and anti-kink soliton solutions. Alongside deriving these solutions, we also illustrate their dynamic properties through graphical simulations. The Boussinesq equation holds significant importance due to its applications in various domains, such as water wave modeling, coastal engineering, and the numerical simulation of water wave dynamics in harbors and shallow seas. Our research shows that the employed method is straightforward, easy to understand, and highly efficient, providing valuable insights into the equation’s nature and its practical applications.

Instantaneous Tiltmeter Triggered by Dynamic Wetting Behavior.

A novel instantaneous tiltmeter with dynamic and static monitoring functions is reported that is based on liquid metal dynamic wetting behavior in a bio-fabricated anisotropic microchannel. The proposed system achieves instantaneous tiltmeter functionality, offering a broad detection range (-90°-90°) with high precision (0.05°), a rapid reaction time (0.11 s), and enhanced durability. Moreover, a seamless integration has enabled water wave detection, language programming, and human limb monitoring. Especially, the integration of tiltmeter and a t3D motion platform results in a surface structure scanning system capable of effectively performing large area (>200 cm2) and height difference scanning functions. This innovative approach holds great potential for transformative changes in the fields of advanced manufacturing, flexible robotics, and the flexible sensing, further facilitating widespread adoption.

Higher‐order integrable models for oceanic internal wave–current interactions

AbstractIn this paper, we derive a higher‐order Korteweg–de Vries (HKdV) equation as a model to describe the unidirectional propagation of waves on an internal interface separating two fluid layers of varying densities. Our model incorporates underlying currents by permitting a sheared current in both fluid layers, and also accommodates the effect of the Earth's rotation by including Coriolis forces (restricted to the Equatorial region). The resulting governing equations describing the water wave problem in two fluid layers under a “flat‐surface” assumption are expressed in a general form as a system of two coupled equations through Dirichlet–Neumann (DN) operators. The DN operators also facilitate a convenient Hamiltonian formulation of the problem. We then derive the HKdV equation from this Hamiltonian formulation, in the long‐wave, and small‐amplitude, asymptotic regimes. Finally, it is demonstrated that there is an explicit transformation connecting the HKdV we derive with the following integrable equations of a similar type: KdV5, Kaup–Kuperschmidt equation, Sawada–Kotera equation, and Camassa–Holm and Degasperis–Procesi equations.

ON WELL-POSED BOUNDARY CONDITIONS AND ENERGY STABLE FINITE-VOLUME METHOD FOR THE LINEAR SHALLOW WATER WAVE EQUATION

Abstract We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial boundary value problem is well-posed. A finite-volume method is developed based on the summation-by-parts framework with the boundary conditions implemented weakly using penalties. Stability is proven by deriving a discrete energy estimate analogous to the continuous estimate. The continuous and discrete analysis covers all flow regimes. Numerical experiments are presented verifying the analysis.

Lie symmetries, exact solutions and conservation laws of time fractional Boussinesq–Burgers system in ocean waves

In this paper, the Lie symmetry analysis method is applied to the time-fractional Boussinesq–Burgers system which is used to describe shallow water waves near an ocean coast or in a lake. We obtain all the Lie symmetries admitted by the system and use them to reduce the fractional partial differential equations with a Riemann–Liouville fractional derivative to some fractional ordinary differential equations with an Erdélyi–Kober fractional derivative, thereby getting some exact solutions of the reduced equations. For power series solutions, we prove their convergence and show the dynamic analysis of their truncated graphs. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equations studied.

Closed-Boundary Reflections of Shallow Water Waves as an Open Challenge for Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to traditional numerical methods for solving partial differential equations (PDEs) in fluid dynamics. By using PDE-derived loss functions and auto-differentiation, PINNs can recover solutions without requiring costly simulation data, spatial gridding, or time discretization. However, PINNs often exhibit slow or incomplete convergence, depending on the architecture, optimization algorithms, and complexity of the PDEs. To address these difficulties, a variety of novel and repurposed techniques have been introduced to improve convergence. Despite these efforts, their effectiveness is difficult to assess due to the wide range of problems and network architectures. As a novel test case for PINNs, we propose one-dimensional shallow water equations with closed boundaries, where the solutions exhibit repeated boundary wave reflections. After carefully constructing a reference solution, we evaluate the performance of PINNs across different architectures, optimizers, and special training techniques. Despite the simplicity of the problem for classical methods, PINNs only achieve accurate results after prohibitively long training times. While some techniques provide modest improvements in stability and accuracy, this problem remains an open challenge for PINNs, suggesting that it could serve as a valuable testbed for future research on PINN training techniques and optimization strategies.

Problem of Surface Waves on Water in Higher School Laboratory Workshop

Traditionally, in lecture courses on General Physics, the example of waves propagating on the water surface is used for the qualitative description of wave phenomena. At the same time, in corresponding laboratory courses, there are almost no quantitative tasks on the same topic, the purpose of which would be to measure the surface wave characteristics. The reason for this difference must be associated with the complexity of the physical mechanism of generation and propagation of waves on the water surface. In this work, a laboratory problem has been developed to measure the group velocity of circular waves traveling on the water surface. It uses a standard laboratory water tank equipped with a surface wave generator. The proposed experiment offers an opportunity for quantitative measurement of surface wave characteristics, a dispute of only qualitative observations of wave phenomena commonly found in current curricula, due to the introduction of two improvements. First, to produce the water waves’ rich in-contrast representations on a screen, the optimal generator amplitude is specially set for each experiment; and second, to measure the group wavelength, the device magnification is preliminary calculated based on the laws of geometric optics. The tests carried out have shown that the relative accuracy of these measurements is quite acceptable: within a few percent. The introduction of the problem of surface waves on water into the General Physics laboratory workshop for engineering specialties of technical universities will contribute to improving the quality of mastering the subject by students.

Effect of shoaling length on rogue wave occurrence

The impact of shoaling on linear water waves is well known, but it has only been recently found to significantly amplify both the intensity and frequency of rogue waves in nonlinear irregular wave trains atop coastal shoals. At least qualitatively, this effect has been partially attributed to the ‘rapid’ nature of the shoaling process, i.e. shoaling occurs over a distance far shorter than that required for waves to modulate themselves and adapt to the reduced water depth. Through a theoretical model and highly accurate nonlinear simulations, we disentangle the respective effects of the length and angle of a shoal's slope. We investigate the effects of the shoaling process rapidness on the evolution of key statistical and spectral sea-state parameters. We let the wave field evolve over a slope with constant angle in all cases while we vary the slope length. Our results indicate that the non-equilibrium dynamics is not affected by the slope length, because further extending the slope length does not influence the magnitude of the statistical and spectral measures as long as the non-equilibrium dynamics dominates the wave evolution. Thus, the shoaling effect on rogue waves is deduced to be mainly driven by the slope magnitude rather than the slope length.

High‐performance triboelectric nanogenerator based on a double‐spiral zigzag‐origami structure for continuous sensing and signal transmission in marine environment

AbstractWith the rapid evolution of emerging technologies like artificial intelligence, Internet of Things, big data, robotics, and novel materials, the landscape of global ocean science and technology is undergoing significant transformation. Ocean wave energy stands out as one of the most promising clean and renewable energy sources. Triboelectric nanogenerators (TENGs) represent a cutting‐edge technology for harnessing such random and ultra‐low frequency energy toward blue energy. A high‐performance TENG incorporating a double‐spiral zigzag‐origami structure is engineered to achieve continuous sensing and signal transmission in marine environment. Integrating the double‐spiral origami into the TENG system enables efficient energy harvesting from the ocean waves by converting low‐frequency wave vibrations into high‐frequency motions. Under the water wave triggering of 0.8 Hz, the TENG generates a maximum peak power density of 55.4 W m−3, and a TENG array with six units can generate an output current of 375.2 μA (density of 468.8 mA m−3). This power‐managed TENG array effectively powers a wireless water quality detector and transmits signals without an external power supply. The findings contribute to the development of sustainable and renewable energy technologies for oceanic applications and open new pathways for designing advanced materials and structures in the field of energy harvesting.

Linear waves in shallow water over an uneven bottom, slowing down near the shore

The exact solutions of the system of equations of the linear theory of shallow water are discussed, representing traveling waves with specific properties for the time propagation, which is infinite when approaching the shore and finite when leaving for deep water. These solutions are obtained by reducing one-dimensional shallow water equations to the Euler–Poisson–Darboux equation with a negative integer coefficient before the lower derivative. The analysis of the wave field dynamics is carried out. It is shown that the shape of a wave approaching the shore will be differentiated a certain number of times, which is illustrated by a number of examples. When a wave moves away from the shore, its profile is integrated. The solutions obtained in the framework of linear theory are valid only for a finite interval of depth variation.

Numerical Analyses of Ultrasonic Atomization Utilizing Acoustic Effects of a Beam Diaphragm

To study mechanisms of jet atomization, a novel method of experimentation utilizing the resonation of diaphragms made from thin steel plates has been previously developed. In the experiments, a diaphragm covered by a film of water emitted acoustic sounds, and jet atomization from the water film was observed. Experiments using diaphragms composed of different materials and fast Fourier transformation analysis of the acoustic sound revealed that jet atomization occurred under limited surface conditions of the diaphragm and a specific range of frequency. In this article, the dynamics of a resonating body composed of the diaphragm and water film were analyzed using the finite element method with a combination of theoretical analyses of surface waves of water, such as the well-known Lang’s equation. The present FEA results, from harmonic response analyses with consideration of viscous damping effect due to interaction between the diaphragm and water film, precisely confirmed the results of FFT analysis previously obtained by the experiment. Specifically, the peak frequency of the frequency response agreed well with the FFT results, and the shift of the peak frequency and attenuation due to the interaction in the analyses corresponded with the difference in surface conditions between the hydrophilic and hydrophobic materials of the diaphragm in the experiments. Our interpretation of the mechanism of jet atomization is expanded by the present numerical results.