Wave Period Research Articles

Experimental Study of Submarine Pipeline with Geotextile and Stone Cover Protection Under the Superposition of Waves and Currents

Submarine pipelines are the main transport carriers of marine resources. In order to protect these pipelines, geotextile and stone covering measures are adopted in this paper and the protective effect is studied. A sequence of physical model tests was conducted to carry out the research. The hydrodynamic characteristics and seabed oscillation response of the seabed surrounding the pipeline were analyzed with or without geotextile and stone cover protection, and it was found that they were affected by waves (and currents). The experimental results show the following: (1) comparing the regular wave and current with the regular wave alone, it is found that forward current promotes wave propagation and reverse current inhibits wave propagation; (2) the protective effect of geotextile and stone covering measures on different positions of the pipeline (the front, the bottom, and the back of the pipe) is basically same; (3) in the case of waves with large wave heights and long wave periods superimposed with ocean currents, the protective effect of geotextile and stone coverings on the hydrodynamic and seabed pore pressure around the pipeline is more significant.

$N$-periodic wave solutions to the ${\cal N} =1$ supersymmetric Sawada-Kotera-Ramani equation

Abstract The $N$-periodic wave solvability problem for the ${\cal N} =1$ supersymmetric Sawada-Kotera-Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function. The constraint equations and unknown parameters are redefined, and the numerical calculation process of the $N$-periodic wave solutions are derived. It has been verified that under some certain conditions, the asymptotic relations between $N$-periodic wave solutions and $N$-soliton solutions can be established. Some numerical solutions of three-periodic wave are presented. Under the influence of the Grassmann variable, the three-periodic wave solutions will generate an influence band in the middle region, and the amplitude becomes bigger as the distance from the influence band increases.

The profile of soliton molecules for integrable complex coupled Kuralay equations

Abstract This study focuses on mathematically exploring the Kuralay equation, which is applicable in diverse fields such as nonlinear optics, optical fibers, and ferromagnetic materials. This study aims to investigate various soliton solutions and analyze the integrable motion of the induced space curves. This study employs traveling wave transformation, converting the partial differential equation (PDE) into an ordinary differential equation (ODE). Soliton solutions are derived utilizing both the generalized Jacobi elliptic function expansion (JEFE) method and novel extended direct algebraic (EDA) methods. The outcomes encompass a diverse range of soliton solutions, including double periodic waves, shock wave solutions, kink-shaped soliton solutions, solitary waves, bell-shaped solitons, and periodic wave solutions, obtained using Mathematica. In contrast, the EDA method produces dark, bright, singular, combined dark-bright solitons, dark-singular combined solitons, solitary wave solutions, etc. Visual representation of these soliton solutions is accomplished through 3D, 2D, and contour graphics, with a meticulous selection of parametric values. The graphical presentation underscores the influence of the parameters on the soliton propagation.

Assessment of joint distributions of wave heights and periods

Short-term joint distributions of wave heights and periods provide information about the sea surface that is needed for engineering applications. In recent years much effort has been invested in predicting and validating the (univariate) distributions of wave heights; however, the same cannot be said about the joint probability of wave heights and periods. Comparisons of the joint distribution models with field observations are quite limited in terms of both the duration of the data and the number of locations considered. In addition, the often-contradicting demands for longer sea-state records and stationarity in the datasets have presented researchers with a bit of a conundrum. It is likely that some previous studies that aggregated data from several non-stationary sea states might have yielded improper inferences. The current study attempts a robust assessment of the available theoretical distribution models utilizing an extensive dataset of wave measurements around the UK coast. The results indicate that the Zhang and Guedes Soares (2106) model generally performs the best, and is perhaps a notable improvement over the somewhat bleak outlook laid out for these types of models in earlier years. The results also suggest that the discrepancy between the models and the data arises primarily from the poor ability of the marginal period distributions to capture reality.

Experimental study on the hydrodynamic behavior for a novel compound anti-vibration submerged floating tunnel system

Anchor cable-type submerged floating tunnel (SFT) is susceptible to large amplitude vibration responses under wave-current excitations. This becomes a critical issue to the safety, stationarity, and driving comfort of SFT. In this study, a novel compound anti-vibration SFT system is proposed, featuring a three-tube SFT reinforced with a rigid truss and an external floating energy dissipation device with polyvinyl chloride (PVC) porous media. The hydrodynamic behavior of the proposed compound SFT system is experimentally explored and compared with that of conventional SFTs utilizing a large wave-current flume. Sensitivity analysis for the key parameters of SFT is conducted using hydrodynamic parameters (such as wave height and wave period), structural type, and structural parameters (draft depths). The results show that the proposed SFT system has excellent anti-vibration performance when compared to conventional SFTs, reducing over 10 and 60 times in translational and rotational motion, respectively. The proposed SFT system with the floating tank at half draft depth shows the best anti-vibration performance under different wave-current excitations. The proposed SFT system achieves excellent anti-vibration performance without increasing the burden on cable tension, solving a common issue in conventional anti-vibration methods. The findings offer valuable insights into the anti-vibration design and application of SFT.

Data-Driven Models for Significant Wave Height Forecasting: Comparative Analysis of Machine Learning Techniques

Accurate prediction of significant wave height (SWH) is critical for coastal safety, marine operations, and disaster management. Traditional numerical models for wave prediction are computationally intensive and often lack accuracy, prompting a shift towards data-driven methods. This study explores the efficacy of machine learning (ML) models in forecasting SWH in the coastline of North Stradbroke Island, Queensland, Australia. Using a dataset spanning 2010 to 2022, the study employs wave characteristics such as maximum wave height (Hmax), wave periods (Tz, Tp), peak direction, and sea surface temperature (SST) as predictors. Three ML models—Linear Regression, Decision Tree, and Random Forest—were trained and evaluated using performance metrics like Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and R-squared (R²). The Random Forest model demonstrated the best predictive accuracy with the lowest MSE (0.0074) and highest R² (0.958), outperforming both Linear Regression and Decision Tree models. This improvement in prediction accuracy supports the model's application for coastal management, ensuring better forecasting of wave conditions. The proposed approach shows significant advantages, including better handling of non-linearities and reduced computational costs compared to conventional numerical methods, such as SWAN and WAM, making it highly applicable for real-time wave forecasting, particularly for regions with complex coastal dynamics such as North Stradbroke Island.

Experimental study of a backward bent duct buoy wave energy converter: Effects of the air chamber and center of gravity height

The backward-bent duct buoy (BBDB) wave energy converter (WEC) is a floating oscillating water column (OWC) device with high conversion efficiency and low mooring requirements. This study experimentally investigates the effects of air chamber volume, chamber top shape, and center of gravity height on the wave energy capture performance of BBDB WEC. The results indicate that increasing the air chamber's volume enhances conversion performance. When the air chamber volume is increased from 0.0162 m³ to 0.0233 m³, the maximum capture width ratio (CWR) increases by 0.14 and 0.13 at wave amplitudes of 0.015 m and 0.025 m, respectively. An oblique cut prism chamber improves performance under low wave periods. When using a chamber with an inclined top, conversion performance exceeds that of a rectangular chamber, with the maximum CWR increasing from 1.09 to 1.40 at a wave height of 0.015 m and from 0.82 to 1.01 at a wave height of 0.025 m. Additionally, changes in center of gravity height primarily affect conversion efficiency during the pitch resonance period. These findings contribute to the structural optimization and performance enhancement of BBDB WECs.

Predicting coastal wave conditions: A simple machine learning approach

Accurate and reliable nearshore wave predictions are highly valuable for a range of marine activities, including coastal engineering and maritime transport. However, in nearshore locations, predicting wave properties is challenging due to complex shallow water processes, requiring local wave models. This article develops an alternative data-driven framework to predict wave parameters (e.g. significant wave height) through the extension of wave buoy datasets using a trained Gaussian process regression (GPR — a supervised machine learning method). We present an easy-to-implement workflow, where the extensive range of input parameters (from ECMWF’s (1) ERA5 reanalysis and (2) IFS forecast global wave model, ≈50km resolution) drives the development of GPR models. At five contrasting locations around the United Kingdom’s coastline, the GPR models produce wave predictions (forecast and hindcast) with low bias scores and strong correlations with observations. When compared to the global (ERA5 reanalysis) and a benchmark shelf-scale (Atlantic-European North West Shelf reanalysis; AENWS, 1.5−3.0km resolution) model, the GPR hindcasts reduced significant wave height (Hs) root-mean-squared error (RMSE) from 0.46 m (ERA5) and 0.21 m (AENWS) to 0.16 m (GPR). For the average zero-crossing wave period (Tz) RMSE reduced from 1.46 s (ERA5) and 1.15 s (AENWS) to 0.58 s (GPR). Because our approach uses publicly available global data, it can be implemented at any historic or active buoy location. We provide proof of concept for an online forecast and hindcast tool which has the potential to improve accessibility to coastal wave predictions for many marine stakeholders.

Transformasi Gelombang Reguler Akibat Pemecah Gelombang Tiang Pancang Dua Baris Selang-Seling

Hydraulic experiments in a two-dimensional physical laboratory were conducted to evaluate the performance of pile breakwaters in reducing wave energy. The piles on the breakwater were arranged in a staggered pattern in two rows. A total of seventy-two simulation scenarios were run based on variations in the incoming wave height and period, and the spacing between the piles, using a 1:10 model scale. The data from the hydraulic tests were then processed using a spectral method that could separate the energy spectra of reflected and transmitted waves. These changes result in reflected and transmitted waves. The laboratory test data were used to estimate the values of the transmission coefficient and reflection coefficient. Both coefficients were then used to validate semi-empirical formulas for the two coefficients. The semi-empirical formulas for the two coefficients were developed based on a model for estimating the spatial porosity of pile breakwaters. The porosity estimation model takes into account the dimensions of the piles and the dimensional components of the breakwater, including the arrangement, number of rows, and spacing between the piles. The validation results of the semi-empirical formulas with the laboratory test data showed a coefficient of determination of 0.917 and a root mean square of 0.077. The staggered arrangement improves the effectiveness of the breakwater in reducing the transmission wave height. The developed semi-empirical model can be used to design the pile dimensions to achieve optimal reflected and transmitted wave heights for coastal protection. Keywords: pile breakwater, coastal protection, hydraulic experiment, physical wave simulation, wave transmission new formula

Numerical method for the characterization of sea states using realistic irregular waves on computational fluid dynamics simulations for application on wave energy converters

Energy demand grows along with technological advances, industrial expansion, and global urbanization. To supply this demand sustainably, there are several attempts to harness energy from renewable sources, among them, wave energy. The study of wave energy availability in energy conversion devices primarily focuses on two major areas: analysis of the fluid-dynamic behavior of the devices and the simulation of sea states to estimate theoretical energy potential. Despite advancements in both fields, there is a lack of methodologies that effectively integrate realistic irregular wave simulations and fluid-dynamic analysis of energy conversion devices. This research aims to integrate these areas by employing the WaveMIMO methodology, in which a sea state spectrum is converted into a statistically equivalent time series of water free surface elevation, then applied as an estimation of the velocity field in the water column to generate irregular waves. This study focuses on the development of a methodology to characterize the wave climate in the city of Rio Grande, in southern Brazil, for the year 2014, using a histogram to classify sea states according to their significant wave height and mean wave period, thus producing a bivariate histogram of wave conditions. A sea state spectrum was obtained for each pair of wave height and period and simulated using the computational fluid dynamics software Fluent to reproduce the realistic irregular waves of this sea state. The results indicated that the methodology for categorizing the sea state based on a histogram proved to be a computationally efficient alternative for the numerical simulation of wave climates in a given location for a long period of time, reducing the simulation time needed to approximately 0.5% of the total amount. In addition, an application of this methodology to investigate the wave energy conversion employing an oscillating water column device is presented as supplementary material.

Study on the match-filtering ability of the electromagnetic flowmeter signals based on the generalized dual-frequency walsh transform

This paper first considered the development of a generalized dual-frequency Walsh transform algorithm specifically for processing dual-frequency EMF signals, taking into account the measurement accuracy requirements in high-precision situations and the limited filtering performance of traditional methods. First, we build a mathematical model of the dual-frequency slurry EMF signal, which is essentially a superposition of interferences and an ideal EMF signal. Second, the match-filtering applicability of the generalized dual-frequency Walsh transform algorithm is verified by exploring the sequency-spectrum distributed features of the mathematical model. Finally, a series of theoretical measurement experiments was carried out, employing the signal-to-noise ratio (SNR) as the qualitative metric to assess the measurement performance of the proposed method. This research not only breaks the limitations of traditional excitation techniques on excitation frequency but also provides new research ideas for signal processing similar to periodic rectangular waves.

Wave climate projections off coastal French Guiana based on high-resolution modelling over the Atlantic Ocean

Global warming is altering the atmosphere and ocean dynamics worldwide, including patterns in the generation and propagation of ocean waves, which are important drivers of coastal evolution, flood risk, and renewable energy. In French Guiana (northern South America), where most of the population is concentrated in coastal areas, understanding future wave climate change is critical for regional development, planning and adaptation purposes. The most energetic waves typically occur in boreal winter, in the form of long-distance swell originating from the mid-latitude North Atlantic Ocean. However, existing high-resolution wave climate projections that cover the French Guiana region focus on the hurricane season only (summer-fall). In this study, we used a state-of-the-art basin-scale spectral wave model and wind fields from a high-resolution atmospheric global climate model to simulate present and future winter (November to April) wave climate offshore of French Guiana. The model performance was evaluated against wave data from ERA5 reanalysis, satellite altimetry and coastal buoys between 1984 and 2013. For the future greenhouse gas emission scenario (Representative Concentration Pathway) RCP-8.5, we found a statistically significant overall projected decrease (∼5 %) in wintertime average significant wave height and mean wave period, with a ∼1° clockwise rotation of mean wave direction. The results suggest that these decreasing trends are primarily driven by changes in large-scale patterns across the Atlantic that counteract an expected increase in local wind speed. We discuss the implications of such projections for mud-bank dynamics along coastal French Guiana, although further local studies are required to address future coastal evolution and hazards. Finally, we identify a need for more in situ wave data near French Guiana to improve quantitative assessments of model performance and allow a correction of possible model biases.

EXACT SOLUTIONS OF NONLINEAR FRACTIONAL CAHN–ALLEN EQUATION ARIES IN DIFFERENT NONLINEAR PHYSICAL PHENOMENON USING UNIFIED TECHNIQUE

The nonlinear fractional Cahn–Allen (NFCA) equation provides insight into phase modifications and pattern elaboration in natural structures, clarifying how various states of matter have changed throughout time. By using a unified technique, this study aims to present novel, precise solutions to the NFCA problem. This method has led to the discovery of a broad spectrum of soliton solutions, ranging from dark compactons and dark solitons to periodic kink behaviors, rough wave behaviors, and periodic patterns featuring peaked crests and troughs. It has also unveiled anti-kink periodic behaviors, periodic wave behaviors, bright-dark single solitons, periodic patterns displaying anti-peaked crests and anti-troughs, bright solitons, and compound soliton phenomena. Notably, these accomplishments have been made possible through the utilization of Maple software. These findings are important for fractional nonlinear dynamical models (FNLDMs). In order to clarify many dynamic behaviors that solutions of the NFCA equation display in other scientific fields, such as quantum mechanics, mathematical biology, and plasma physics, contour plots and 3D surface representations of these exact solutions are also featured. Through our investigation using the unified technique, we have unveiled a plethora of novel discoveries. Employing this method has revealed a total of 54 fresh findings. In contrast, Javeed et al. [S. Javeed, S. Saif and D. Baleanu, New exact solutions of fractional Cahn–Allen equation and fractional DSW system, Adv. Differential Equations 2018 (2018) 459] applied the first integral technique, resulting in only eight outcomes. Upon comparing their results with ours, our approach has yielded an additional four out of six innovative results. As far as we are aware, the application of our technique to the NFCA equation has not been previously documented. We anticipate that future research will expand this methodology to include other FNLDMs.

Stability of Standing Periodic Waves in the Massive Thirring Model

ABSTRACTWe analyze the spectral stability of the standing periodic waves in the massive Thirring model in laboratory coordinates. Since solutions of the linearized MTM equation are related to the squared eigenfunctions of the linear Lax system, the spectral stability of the standing periodic waves can be studied by using their Lax spectrum. We show analytically that each family of standing periodic waves is distinguished by the location of eight eigenvalues which coincide with the end points of the spectral bands of the Lax spectrum. The standing periodic waves are proven to be spectrally stable if the eight eigenvalues are located either on the imaginary axis or along the diagonals of the complex plane. By computing the Lax spectrum numerically, we show that this stability criterion is satisfied for some standing periodic waves.

Faster than real-time, phase-resolving, data-driven model of wave propagation and wave–structure interaction

A machine learning time-series prediction approach is proposed for wave propagation and wave load prediction. Under unidirectional wave conditions and variable bathymetry, given a wave gauge upstream, a model is shown to reproduce wave elevation or wave forces downstream under irregular steep and either non-breaking or breaking conditions. Attempts to perform the opposite calculation, predicting upstream conditions from downstream measurements, results in higher error, likely due to information loss under breaking conditions. For choice of machine learning approach, comparisons show that the Time-series Dense Encoder (TiDE) approach results in a good balance between model complexity, stability, computational time, and error. Over a flat bottom, time-series of wave elevation can be predicted up to 10 wavelengths away, though with a degraded accuracy compared to shorter distances. Similar results are shown for time-series of forces on a vertical cylinder, showing better results than a simple Morison approach, as used in engineering tools such as OpenFAST, but with a similarly fast computational time. Generalizations show that training on irregular wave data permit extrapolations to periodic wave cases. Finally, the same method also is also demonstrated at field-scale, comparing results between two offshore buoys.

Modulation instability, and dynamical behavior of solitary wave solution of time M- fractional clannish random Walker's Parabolic equation via two analytic techniques

The theory of solitary waves or solitons is crucial in nonlinear models due to their ability to propagate without distortion, making them essential in fields like physics, biology, engineering, and mathematics. This study explores solitary waves in the time fractional Clannish Random Walker's Parabolic equation using two effective approaches: polynomial expansion technique (PET) and unified technique (UT). This model is particularly significant in areas such as ecology, sociology, and urban planning, where understanding individual interactions within spatial contexts is vital. By solving this equation, we gain insights into group formation and navigation, enhancing our comprehension of emergent patterns and system design. The application of PET and UT allows us to derive various solutions, including exponential, hyperbolic, and trigonometric forms. Utilizing the Maple programming language, we visualize novel phenomena, such as kink waves, anti-kink waves, and periodic lump waves. This research demonstrates that the proposed methodologies can yield precise soliton solutions, contributing valuable insights to nonlinear science and engineering applications.

A case report of an individual with Creutzfeldt–Jakob disease characterized by prolonged isolated thalamic lesions and rare MM2-cortical-type pathology

BackgroundDiffusion-weighted magnetic resonance imaging (DWI) is essential for diagnosing Creutzfeldt–Jakob disease (CJD). Thalamic lesions are rarely detected by DWI in sporadic CJD (sCJD) cases with methionine homozygosity at polymorphic codon 129 (129MM) of the prion protein (PrP) gene. Here, we describe an unusual sCJD case, characterized by prolonged isolated thalamic diffusion hyperintensities and atypical brain pathology, in combination with the 129MM genotype.Case presentationA 72-year-old Japanese man developed a mild unsteady gait that had persisted for 1 year. DWI revealed isolated thalamic diffusion hyperintensities. Over the following 4 years, his condition progressed to include ataxia and cognitive decline. Repeated cerebrospinal fluid tests were negative for 14-3-3 protein, total tau protein, and real-time quaking-induced conversion assay. Electroencephalography did not show periodic sharp wave complexes or generalized periodic discharges. Despite these findings, thalamic DWI abnormalities persisted and evolved to include cortical lesions in the later stage of the disease. Genetic testing confirmed a 129MM genotype with no pathogenic PrP gene variants. Brain autopsy identified type 2 pathogenic PrP and the absence of the M2-thalamic prion strain, suggesting an MM2-cortical (MM2C)-subtype of sCJD. Histopathology revealed small vacuoles (sv) and patchy-perivacuolar PrP deposits without large vacuoles (lv). Patchy-perivacuolar deposits are a characteristic feature of the MM2C (lv) subtype and indicate MM2C (lv) pathology. Thus, this case was classified as a rare MM2C (sv + lv) subtype. No PrP protein staining was observed in the thalamus, despite spongiform changes with small vacuoles.ConclusionsThis case underscores the diagnostic challenges of atypical CJD with isolated thalamic abnormalities on DWI. Despite negative cerebrospinal fluid findings and clinical diagnostic criteria, persistent DWI abnormalities and evolving clinical symptoms continued to raise suspicion of CJD. A definitive diagnosis, being the MM2C (sv + lv) subtype of sCJD, was confirmed upon pathological examination. Even when atypical findings, such as isolated thalamic abnormalities, are observed and various tests are negative, if suspicion of CJD cannot be ruled out, it is important to confirm the diagnosis and pathological subtypes via postmortem analysis.

Evolution of coastal transgressive aeolian sand sheets over 75 years (1948-2023) at Concheiros Barrier - Southern Brazilian coast

Transgressive sand sheets (TSS) and transgressive dunefields (TDf) over time often present multiple phases of development and various morphologies controlled by biogeomorphological interactions related to abiotic processes, vegetation, and human interference. While dunefields have experienced increased vegetation cover over the last decades worldwide, a few places have shown increased dune mobility. In this study, a GIS analysis was conducted using aerial photographs and satellite imagery to investigate the evolution of a TDf, foredune collapse, new TSS formation, and vegetation cover on a Holocene coastal barrier in southern Brazil over the last 75 years (from 1948 to 2023). Wind speed (1994–2009), significant wave height (Hs) and peak wave period (Tp) (1940–2022) were analyzed to examine these potential drivers that could have caused geomorphological changes on the foredunes and dune system. Vegetation cover exhibited an increasing trend, and both an increase and decrease in TDf movement and TSS expansion were concurrent. Correlation analyses revealed a strong negative correlation between vegetation cover and TDf movement. Three transgressive sand sheet formation phases were identified between 1948 and 2023 (1964 to 1975,1996 to 2000, and from 2010 until 2023). Post-2003, a poorly vegetated nebkha-dominated foredune subsequently collapsed and was replaced by a TSS in less than a decade, being fully formed in 2010 and continuing to move inland at rapid rates. In the third phase, the highest total TSS expansion exceeded 700 m in 12 years (from 2010 to 2022). A small increase in wind velocity and subsequent decrease may possibly have contributed to the formation of the TSS second phase and the foredunes respectively. Other possible drivers for TSS formation include climatic modes, negative precipitation anomalies and groundwater level lowering, in addition to anthropogenic actions (especially water extraction) that might have caused a negative feedback in foredune sand-biding vegetation.

Existence of traveling wave solutions in continuous optimal velocity models

In traffic flow theory, hydrodynamic models, a subset of macroscopic models, can be derived from microscopic-level car-following models. Self-organized wave propagation, which characterizes congestion, has been replicated in these macroscopic models. However, the existence of wave propagation has only been validated using numerical technique or formal analyses and has not yet been rigorously proven. Therefore, analytical approaches are necessary to ensure their validity rigorously. This study investigates the properties of solutions corresponding to congestion with sparse and dense waves. Specifically, we demonstrate the existence of traveling back/front, traveling pulse, and periodic traveling wave solutions in macroscopic models. All theorems are proven using phase-plane analysis without local bifurcation theory. The key to the proofs is the monotonicity of solution trajectories concerning implicit parameters that naturally appear in the models. We also examine the global bifurcation structure for heteroclinic, homoclinic, and periodic orbits, which correspond to traveling back/front, traveling pulse, and periodic traveling wave solutions, via the numerical continuation package HomCont/AUTO.

Intermittency of gravity wave turbulence on the surface of an infinitely deep fluid: directional effects

This study investigates the influence of surface wave characteristics, specifically wave steepness and directional spreading, on intermittency in deep-water gravity wave turbulence through long-term numerical simulations of three-dimensional potential fully nonlinear periodic gravity waves. We conducted this investigation by estimating the scaling exponent of the surface elevation under different sea state conditions. With our numerical methods, we were able to evaluate the scaling exponents of the structure-function up to 12th order. The observed increased intermittency in directionally narrower sea states and in higher steepness conditions aligns with known effects of quasi-resonant wave–wave interactions and wave breaking. Comparative analyses reveal that both the conventional She–Leveque model and the multifractal models, also used to represent intermittency in wave turbulence of a different nature, exhibit a strong correlation in this study. This observation underscores the universality of intermittency phenomena within wave turbulence.