The present study aims to determine the appropriate size of mesh or the number of the element (NoE) for flat- and curved plates, which is suggested to assess its safety subjected to axial compression based on the ultimate limit state (ULS) design and analysis concept. The unstiffened panel (= plate) and stiffened panel, considered primary members of ships and ship-shaped offshore structures, are subjected to repeated axial compression and tension caused by continued vertical bending moments applied to the hull girder. Plates are attached with stiffeners by welding, and 6, 8 or 10 elements are generally recommended to allocate in flat-plate's breadth direction in between stiffeners for finite-element (FE) modelling, which enables the presentation of the shape of initial deflection applied to the plate. In the case of the load-shorting curve for curved plate, it is reported that the nonlinear behaviour characteristics, i.e., snap-through, snap-back, secondary buckling and others, appear in typical flank angle. To take this into account, we investigated the preferred number of elements (6, 8 or 10) generally applied to the flat plate whether it is an appropriate or more fine-sized element (or mesh) that should be considered. A useful guide is documented based on obtained outcomes which may help structural engineers select optimised mesh-size to predict ultimate strength and understand its characteristic of the flat and curved plates.

Highlights

● The general shape of the empirical formulation in predicting the ultimate strength of the plate is proposed.

● An empirical formulation in predicting ULS of initially deflected and simply supported edged plate under longitudinal compression is developed based on general shape by determining four coefficients.

● The results of ULS by NLFEM, semi-analytical method, and direct calculation method by empirical formulations are compared, and its accuracy has been verified.

Turbulence is strongly associated with the vast majority of fluid flows in nature and industry. Traditionally, results given by the direct numerical simulation (DNS) of Navier-Stokes (NS) equations that relate to a famous millennium problem are widely regarded as ‘reliable' benchmark solutions of turbulence, as long as grid spacing is fine enough (i.e. less than the minimum Kolmogorov scale) and time-step is small enough, say, satisfying the Courant-Friedrichs-Lewy condition (Courant number < 1). Is this really true? In this paper a two-dimensional sustained turbulent Kolmogorov flow driven by an external body force governed by the NS equations under an initial condition with a spatial symmetry is investigated numerically by the two numerical methods with detailed comparisons: one is the traditional DNS, the other is the ‘clean numerical simulation' (CNS). In theory, the exact solution must have a kind of spatial symmetry since its initial condition is spatially symmetric. However, it is found that numerical noises of the DNS are quickly enlarged to the same level as the ‘true' physical solution, which finally destroy the spatial symmetry of the flow field. In other words, the DNS results of the turbulent Kolmogorov flow governed by the NS equations are badly polluted mostly. On the contrary, the numerical noise of the CNS is much smaller than the ‘true' physical solution of turbulence in a long enough interval of time so that the CNS result is very close to the ‘true' physical solution and thus can remain symmetric, which can be used as a benchmark solution for comparison. Besides, it is found that numerical noise as a kind of artificial tiny disturbances can lead to huge deviations at large scale on the two-dimensional Kolmogorov turbulence governed by the NS equations, not only quantitatively (even in statistics) but also qualitatively (such as spatial symmetry of flow). This highly suggests that fine enough spatial grid spacing with small enough time-step alone could not guarantee the validity of the DNS of the NS equations: it is only a necessary condition but not sufficient. All of these findings might challenge some of our general beliefs in turbulence: for example, it might be wrong in physics to neglect the influences of small disturbances to NS equations. Our results suggest that, from physical point of view, it should be better to use the Landau-Lifshitz-Navier-Stokes (LLNS) equations, which consider the influence of unavoidable thermal fluctuations, instead of the NS equations, to model turbulent flows.

Highlights

● A two-dimensional Kolmogorov flow is numerically solved by means of the direct numerical simulation (DNS) and clean numerical simulation (CNS), respectively.

● It is found that tiny numerical noises of the DNS result are quickly enlarged to a macroscopic level so that the DNS results are quickly polluted badly.

● Detailed comparisons between the CNS and DNS reveal that artificial numerical noises lead to large deviations of the turbulent flow even in long-term statistics.

Real-time predicting of stochastic waves is crucial in marine engineering. In this paper, a deep learning wave prediction (Deep-WP) model based on the ‘probabilistic' strategy is designed for the short-term prediction of stochastic waves. The Deep-WP model employs the long short-term memory (LSTM) unit to collect pertinent information from the wave elevation time series. Five irregular long-crested waves generated in the deepwater offshore basin at Shanghai Jiao Tong University are used to validate and optimize the Deep-WP model. When the prediction duration is 1.92s, 2.56s, and, 3.84s, respectively, the predicted results are almost identical with the ground truth. As the prediction duration is increased to 7.68s or 15.36s, the Deep-WP model's error increases, but it still maintains a high level of accuracy during the first few seconds. The introduction of covariates will improve the Deep-WP model's performance, with the absolute position and timestamp being particularly advantageous for wave prediction. Furthermore, the Deep-WP model is applicable to predict waves with different energy components. The proposed Deep-WP model shows a feasible ability to predict nonlinear stochastic waves in real-time.

Highlights

● A deep learning wave prediction (Deep-WP) model is proposed for stochastic waves.

● The model is based on an effective 'probabilistic' strategy.

● Three covariates are introduced, successfully improving the prediction accuracy.

● The model's performance is validated by experimental measurements.

In this article, the fractional diffusion-advection equation with resetting is introduced to promote the theory of anomalous transport. The fractional equation describes a particle's non-diffusive motion performing a random walk and is reset to its initial position. An analytical method is proposed to obtain the solution of the fractional equation with resetting via Fourier and Laplace transformations. We study the influence of the fractional-order and resetting rate on the probability distributions, and the mean square displacements are analyzed for different cases of anomalous regimes.

Highlights

● The fractional diffusion-advection equation has been solved in the case of resetting assumption.

● The probability distribution functions (non-Maxwellian distributions) of the analytical solutions have been illustrated.

● The mean square displacement (MSD) analysis has been studied to determine the mode of displacement of particles followed over time (freely diffusing, transported, bound and limited in its movement).

In the organizational setting of marine engineering, a significant number of information security incidents have been arised from the employees' failure to comply with the information security policies (ISPs). This may be treated as a principal-agent problem with moral hazard between the employer and the employee for the practical compliance effort of an employee is not observable without high cost-. On the other hand, according to the deterrence theory, the employer and the employee are inherently self-interested beings.It is worth examining to what extent the employee is self-interested in the marine ISPs compliance context. Moreover, it is important to clarify the proper degree of severity of punishment in terms of the deterrent effect. In this study, a marine ISPs compliance game model has been proposed to evaluate the deterrence effect of punishment on the non-compliance behavior of employee individuals. It is found that in a non-punishment contract, the employee will decline to comply with the marine ISPs; but in a punishment contract, appropriate punishment will lead her to select the marine ISPs compliance effort level expected by the employer, and cause no potential backfire effect.

The paper investigates the multiple rogue wave solutions associated with the generalized Hirota-Satsuma-Ito (HSI) equation and the newly proposed extended (3 + 1)-dimensional Jimbo-Miwa (JM) equation with the help of a symbolic computation technique. By incorporating a direct variable transformation and utilizing Hirota’s bilinear form, multiple rogue wave structures of different orders are obtained for both generalized HSI and JM equation. The obtained bilinear forms of the proposed equations successfully investigate the 1st, 2nd and 3rd-order rogue waves. The constructed solutions are verified by inserting them into original equations. The computations are assisted with 3D graphs to analyze the propagation dynamics of these rogue waves. Physical properties of these waves are governed by different parameters that are discussed in details.

In the fields of oceanography, hydrodynamics, and marine engineering, many mathematicians and physicists are interested in Burgers-type equations to show the different dynamics of nonlinear wave phenomena, one of which is a (3+1)-dimensional Burgers system that is currently being studied. In this paper, we apply two different analytical methods, namely the generalized Kudryashov (GK) method, and the generalized exponential rational function method, to derive abundant novel analytic exact solitary wave solutions, including multi-wave solitons, multi-wave peakon solitons, kink-wave profiles, stripe solitons, wave-wave interaction profiles, and periodic oscillating wave profiles for a (3+1)-dimensional Burgers system with the assistance of symbolic computation. By employing the generalized Kudryashov method, we obtain some new families of exact solitary wave solutions for the Burgers system. Further, we applied the generalized exponential rational function method to obtain a large number of soliton solutions in the forms of trigonometric and hyperbolic function solutions, exponential rational function solutions, periodic breather-wave soliton solutions, dark and bright solitons, singular periodic oscillating wave soliton solutions, and complex multi-wave solutions under various family cases. Based on soft computing via Wolfram Mathematica, all the newly established solutions are verified by back substituting them into the considered Burgers system. Eventually, the dynamical behaviors of some established results are exhibited graphically through three - and two-dimensional wave profiles via numerical simulation.

The Tension Leg Platform (TLP) is a hybrid, compliant platform designed to sustain springing and ringing responses that are correlated to short-period motion. Since the period of short-period motion is within the wave energy concentration region, TLPs may experience sensitive short-period motion, such as resonance and green water, that usually cause serious damage to TLPs. In this study, a precontrol methodology is presented as a solution to prevent TLP-sensitive short-period motion. By applying the precontrol methodology, the parameters of TLP can be predetermined, allowing TLP motion performance to meet the requirements of short-period motion before sensitive motions actually occur. For example, the damping coefficient should be less than 4.3, the tendons' stiffness should be larger than 0.91 × 10⁸, and the dimensionless draft should be less than 0.665. The development of a precontrol methodology is based on a solid theoretical foundation. First, a series of simple and high-fidelity numerical models are proposed to simulate the natural period of roll, natural period of heave, and green water height. Second, a constraint regime is generated based on the numerical models and the sensitive motion range of short-period motion. The constraint regime is divided into two parts: the control range (corresponding to sensitive short-period motion) and the feasible range (the complementary set of control ranges in the whole parameter constraint domain). Finally, TLP parameters are derived from the calculated feasible range. The precontrol methodology goes beyond the conventional approach of real-time control by changing the control from a remedial action to a preventive action.

Highlights

This work proposes a precontrol methodology to constrain the short-period motion of Tension Leg Platform (TLP) to prevent the occurrence of sensitive short-period motion in advance with simple and high-fidelity numerical models developed. The precontrol methodology goes beyond the conventional approach of real-time control by changing the control from a remedial action to a preventive action.

This work develops simple and high-fidelity numerical models for TLP's short-period motion: natural period of roll motion model based on stability theory and green water height model based on wave height spectral distribution in body coordinate system.

In this paper, an experimental investigation on the wave loads and structural motions of two semi-fixed semi-immersed horizontal cylinders type rafts in the free surface zone is conducted. The physical models are tested at the 1:4.5 scale and exposed to a range of regular and irregular waves in a wave flume at Queen's University Belfast. The physical models and experimental setup are discussed alongside an investigation of the hydrodynamic phenomena, surge forces, and dynamic responses that each structure exhibits in the coastal wave climates. Furthermore, an investigation into the wave attenuation by both models is carried out. The results show that the surge forces have a positive correlation with wave steepness for both models. Hydrodynamic phenomena such as wave runup and overtopping, radiative damping and reflected waves, constructive interference, diffraction and flow separation were identified during the experiments. A negative mean heave displacement is observed during the monochromatic sea states which could result in impact loading and submergence of the superstructure components and photovoltaic panels at full-scale. The results presented in this paper may be used to calibrate and verify numerical models that calculate the global responses and hydrodynamic forces. It may also benefit the design processes of geometrically similar floating solar technologies by providing data on surge loads, motion responses and hydrodynamic observations.

Highlights

● An experimental investigation of two scaled and simplified floating photovoltaic structures in a wave flume environment.

● The dynamic responses, surge forces, wave attenuation and hydrodynamic phenomena were recorded using various instruments.

● A negative mean heave displacement is observed during the monochromatic sea states which could result in impact loading.

The real-time prediction of a floating platform or a vessel is essential for motion-sensitive maritime activities. It can enhance the performance of motion compensation system and provide useful early-warning information. In this paper, we apply a machine learning technique to predict the surge, heave, and pitch motions of a moored rectangular barge excited by an irregular wave, which is purely based on the motion data. The dataset came from a model test performed in the deep-water ocean basin, at Shanghai Jiao Tong University, China. Using the trained machine learning model, the predictions of 3-DoF (degrees of freedom) motions can extend two to four wave cycles into the future with good accuracy. It shows great potential for applying the machine learning technique to forecast the motions of offshore platforms or vessels.

Highlights

● The real-time prediction of the motion of a floating platform in irregular wave.

● A machine learning technique is applied to predict the surge, heave, and pitch motions of a moored barge, which is purely based on the motion data.

● The dataset was generated from a model test performed in the deep-water ocean basin.

● The predictions of motions are validated by experimental measurements.

In this article, we suggest a new form of modified Kudryashov's method (NMK) to study the Dual-mode Sawada Kotera model. We know very well that the more the solutions depend on many constants, the easier it is to study the model better by observing the change in the constants and what their impact is on the solutions. From this point of view, we developed the modified Kudryashov method and put it in a general form that contains more than one controllable constant. We have studied the model in this way and presented figures showing the correctness of what we hoped to reach from the proposed method. In addition to the results we reached, they were not sufficient, so we presented an extensive numerical study of this model using the finite differences method. We also came up with the local truncation error for the difference scheme is h6k2(1+k2). In addition, the analytical solutions we reached were compared with the numerical solutions, and we presented many forms that show that the results we reached are a clear contribution to this field.

Highlights

● We suggest a new form of modified Kudryashov's method (NKM) to study the Dual-mode Sawada Kotera model.

● We know very well that the more the solutions depend on many constants, the easier it is to study the model better by observing the change in the constants and what their impact is on the solutions.

● From this point of view, we developed the modified Kudryashov method and put it in a general form that contains more than one controllable constant.

● We have studied the model in this way and presented figures showing the correctness of what we hoped to reach from the proposed method.

● In addition to the results we reached, they were not sufficient, so we presented an extensive numerical study of this model using the finite differences method.

● We also came up with the local truncation error for the difference scheme is $h^6{k}^2(1+k^2)$ .

● In addition, the analytical solutions we reached were compared with the numerical solutions, and we presented many forms that show that the results we reached are a clear contribution to this field.

The dynamics of atmosphere and ocean can be examined under different circumstances of shallow water waves like shallow water gravity waves, Kelvin waves, Rossby waves and inertio-gravity waves. The influences of these waves describe the climate change adaptation on marine environment and planet. Therefore, the present work aims to derive symmetry reductions of Broer-Kaup-Kupershmidt equation in shallow water of uniform depth and then a variety of exact solutions are constructed. It represents the propagation of nonlinear and dispersive long gravity waves in two horizontal directions in shallow water. The invariance of test equations under one parameter transformation leads to reduction of independent variable. Therefore, twice implementations of symmetry method result into equivalent system of ordinary differential equations. Eventually, the exact solutions of these ODEs are computed under parametric constraints. The derive results entail several arbitrary constants and functions, which make the findings more admirable. Based on the appropriate choice of existing parameters, these solutions are supplemented numerically and show parabolic nature, intensive and non-intensive behavior of solitons.

Highlights

● Lie symmetry classification of Broer-Kaup-Kupershmidt equation in shallow water.

● The system describes the propagation of nonlinear and dispersive long gravity waves in two horizontal directions in shallow water.

● Symmetry reductions and invariant solutions are carried out.

● The obtained solutions are analyzed graphically.

● The solutions show parabolic nature, multi soliton, soliton fission phenomena.

This paper extracts some analytical solutions of simplified modified Camassa-Holm (SMCH) equations with various derivative operators, namely conformable and M-truncated derivatives that have been recently introduced. The SMCH equation is used to model the unidirectional propagation of shallow-water waves. The extended rational sine−cosine and sinh−cosh techniques have been successfully implemented to the considered equations and some kinds of the solitons such as kink and singular have been derived. We have checked that all obtained solutions satisfy the main equations by using a computer algebraic system. Furthermore, some 2D and 3D graphical illustrations of the obtained solutions have been presented. The effect of the parameters in the solutions on the wave propagation has been examined and all figures have been interpreted. The derived solutions may contribute to comprehending wave propagation in shallow water. So, the solutions might help further studies in the development of autonomous ships/underwater vehicles and coastal zone management, which are critical topics in the ocean and coastal engineering.

Highlights

● Simplified modified Camassa-Holm equation with conformable and M- fractional derivative order is investigated.

● The novel solutions of considered equations are obtained analytically.

● The solutions of the conformable and $M-$ truncated model are graphically compared in the figures for different values of $\alpha$ and $\beta$ that are in order of the derivative operator.

● The considered method suggests trigonometric functions producing dark, singular, and trigonometric solitons etc.

In this paper, the q-deformed Sinh-Gordon equation is solved analytically using a new general form based on the extended tanh approach. The numerical solutions of the equation is obtained using a b-spline finite element method. Also, we present numerous figures to demonstrate the various solitons propagation patterns. This type of equation has not been previously dealt with in such ways, whether analytical or numerical. This study is very useful in studying several physical systems that have lost their symmetry.

Highlights

● The q-deformed Sinh-Gordon equation was investigated analytically using the new general form of the extended tanh approach and numerically using a b-spline finite element method in this paper.

● We also present numerous figures to demonstrate the various solitons propagation patterns.

● This type of equation has not been previously dealt with in such ways, whether analytical or numerical.

● We believe that this study will be very useful in studying physical systems that have lost their symmetry.

A linear electrohydrodynamic Kelvin-Helmholtz instability of the interface between two viscoelastic Rivlin-Ericksen fluids enclosed by two concentric horizontal cylinders has been studied via the viscoelastic potential flow theory. The dispersion equation of complex coefficients for asymmetric disturbance has been obtained by using normal mode technique. the stability criteria are analyzed theoretically and illustrated graphically. The imaginary part of growth rate is plotted versus the wave number. The influences of dynamic viscoelastic, uniform velocities, Reynolds number, electric field, dynamic viscosity, density fluids ratio, dielectric constant ratio and inner fluid fraction on the stability of the system are discussed. The study finds its significance in Ocean pipelines to transfer oil or gas such as Eastern Siberia-Pacific Ocean oil pipeline.

Highlights

● The linear electrohydrodynamic Kelvin-Helmholtz instability analysis of two viscoelastic Rivlin-Ericksen fluids has been studied via the viscoelastic potential flow theory.

● The dispersion equation of complex coefficients has been obtaind by using normal mode technique.

● The effect of various parameters on the stability of the system are discussed.

● some limiting cases are considered and recovered previous works.

Ship-hull design is a complex process because the any slight local alteration in ship hull structure may significantly change the hydrostatic and hydrodynamic performances of a ship. To find the optimum hull shape under the design requirements, the state-of-art of ship hull design combines computational fluid dynamics computation with geometric modeling. However, this process is very computationally intensive, which is only suitable at the final stage of the design process. To narrow down the design parameter space, in this work, we have developed an AI-based deep learning neural network to realize a real-time prediction of the total resistance of the ship-hull structure in its initial design process. In this work, we have demonstrated how to use the developed DNN model to carry out the initial ship hull design. The validation results showed that the deep learning model could accurately predict the ship hull’s total resistance accurately after being trained, where the average error of all samples in the testing dataset is lower than 4%. Simultaneously, the trained deep learning model can predict the hip’s performances in real-time by inputting geometric modification parameters without tedious preprocessing and calculation processes. The machine learning approach in ship hull design proposed in this work is the first step towards the artificial intelligence-aided design in naval architectures.

The sea surface reconstructed from radar images provides valuable information for marine operations and maritime transport. The standard reconstruction method relies on the three-dimensional fast Fourier transform (3D-FFT), which introduces empirical parameters and modulation transfer function (MTF) to correct the modulation effects that may cause errors. In light of the convolutional neural networks’ (CNN) success in computer vision tasks, this paper proposes a novel sea surface reconstruction method from marine radar images based on an end-to-end CNN model with the U-Net architecture. Synthetic radar images and sea surface elevation maps were used for training and testing. Compared to the standard reconstruction method, the CNN-based model achieved higher accuracy on the same data set, with an improved correlation coefficient between reconstructed and actual wave fields of up to 0.96-0.97, and a decreased non-dimensional root mean square error (NDRMSE) of around 0.06. The influence of training data on the deep learning model was also studied. Additionally, the impact of the significant wave height and peak period on the CNN model’s accuracy was investigated. It has been demonstrated that the accuracy will fluctuate as the wave steepness increases, but the correlation coefficient remains above 0.90, and the NDRMSE remains less than 0.11.

In this research work, we present proof of the existence and uniqueness of solution for a novel method called tempered fractional natural transforms (TFNT) and give error estimates. This efficient method is applied to models, such as the time-space tempered fractional convection-diffusion equation (FCDE) and tempered fractional Black-Scholes equation (FBSE). We obtain exact solutions for these models using our methodology, which is very important for knowing the wave behavior in ocean engineering models and for the studies related to marine science and engineering. Finding exact solutions to tempered fractional differential equations (TFDEs) is far from trivial. Therefore, the proposed method is an excellent addition to the myriad of techniques for solving TFDE problems.

In this paper, the higher dimensional generalized Korteweg-de-Varies-Zakharov-Kuznetsov (gKdV-ZK) equation is under investigation. This model is used in the field of plasma physics which describes the effects of magnetic field on the weak ion-acoustic wave. We have applied two techniques, called as ϕ⁶-model expansion method and the Hirota bilinear method (HBM) to explore the diversity of wave structures. The solutions are expressed in the form of hyperbolic, periodic and Jacobi elliptic function (JEF) solutions. Moreover, the solitary wave solutions are also extracted. A comparison of our results to well-known results is made, and the study concludes that the solutions achieved here are novel. Additionally, 3-dimensional and contour profiles of achieved outcomes are drawn in order to study their dynamics as a function of parameter selection. On the basis of the obtained results, we can assert that the proposed computational methods are straightforward, dynamic, and well-organized, and will be useful for solving more complicated nonlinear problems in a variety of fields, particularly in nonlinear sciences, in conjunction with symbolic computations. Additionally, our discoveries provide an important milestone in comprehending the structure and physical behavior of complex structures. We hope that our findings will contribute significantly to our understanding of ocean waves. This study, we hope, is appropriate and will be of significance to a broad range of experts involved in ocean engineering models.

Nowadays seakeeping is mostly analyzed by means of model testing or numerical models. Both require a significant amount of time and the exact hull geometry, and therefore seakeeping is not taken into account at the early stages of ship design. Hence the main objective of this work is the development of a seakeeping prediction tool to be used in the early stages of ship design.

This tool must be fast, accurate, and not require the exact hull shape. To this end, an artificial intelligence (AI) algorithm has been developed. This algorithm is based on Artificial Neural Networks (ANNs) and only requires a number of ship coefficients of form.

The methodology developed to obtain the predictive algorithm is presented as well as the database of ships used for training the ANN. The data were generated using a frequency domain seakeeping code based on the boundary element method (BEM). Also, the AI predictions are compared to the BEM results using both, ship hulls included and not included in the database.

As a result of this work it has been obtained an AI tool for seakeeping prediction of conventional monohull vessels

Highlights

● Application of Artificial Neural Networks (ANNs) to predict seakeeping of monohulls in early ship design stages.

● High accuracy achieved by ANNs compared with traditional solvers.

● Methodology based on data augmentation, numerical computation, and ANN competition is applied.

● Fast computation method is developed achieving instant computation of seakeeping of monohulls.

● No need of hull shapes for computing seakeeping.

In order to meet the demand of high-precision heading angle transmission in the transfer alignment of inertial navigation system on moving base, the analytical function relationship between the hull deformation and the turning angular velocity and angular acceleration was derived by using the classical beam theory based on the analysis of the equivalent load exerted by the hydrodynamic force and inertia force on the hull structure during the turning process under the combined action of the steering rudder moment and wave force. The objective law between the angular motion and the azimuth deformation angle of the hull under the combined action of maneuvering and sea waves was revealed. Finally, the correction coefficients were determined according to the left turn and right turn motions of the hull by using the measured data of the ship in the sea trial during the S-shape maneuvering navigation, and the azimuth deformation angle correction was completed. The results indicated that the application of the Qu's bending deformation correction formula could greatly reduce the influence of the hull flexural deformation on the heading angle accuracy, meet the needs of high-precision heading angle transmission, and fully verify the correctness of the hull azimuth deformation law and the heading angle transmission error correction theory. This theory and method provided technical support for establishing high-precision distributed digital reference in the field of transfer alignment of inertial navigation on moving base and the application of heading angle transfer of other shipborne equipment.

The simplified modified Camassa-Holm (SMCH) equation is an important nonlinear model equation for identifying various wave phenomena in ocean engineering and science. The new auxiliary equation (NAE) method has been applied to the SMCH equation. Base on the method, we have obtained some novel analytical solutions such as hyperbolic, trigonometric, exponential, and rational function solutions of the SMCH equation. For appropriate values of parameters, three dimensional (3D) and two dimensional (2D) graphs are designed by Mathematica. The stability of the model is also discussed in this manuscript. The dynamic and physical behaviors of the solutions derived from the SMCH equation have been extensively discussed by these plots. All our solutions are indispensable for understanding the nonlinear phenomena of dispersive waves that are important in ocean engineering and science. In addition, our results are essential to clarify the various oceanographic applications containing ocean gravity waves, offshore rig in water, energy associated with a moving ocean wave and numerous other related phenomena. Finally, the obtained solutions are helpful for studying wave interactions in many new structures and high-dimensional models.

The study of internal atmospheric waves, also known as gravity waves, which are detectable inside the fluid rather than at the fluid surface, is presented in this work. We have used the time-fractional and fuzzy-fractional techniques to solve the differential equation system representing the atmospheric internal waves model. The q-Homotopy analysis Shehu transform technique (q-HAShTM) is used to solve the model. The method helps find convergent solutions since it helps solve nonlinearity, and the fractional derivative can be easily computed using the Shehu transform. Finally, the obtained solution is compared for the particular case of α=1 with the HAM solution to explain the method's accuracy.

As the Arctic Channel continues to be developed, collisions between polar navigation vessels and sea ice are inevitable, which will directly affect structural safety and vibration comfort. However, the numerical analysis method of ship-ice collision-induced vibration is not perfect, and the effect of fluid coupling is not typically considered. In this paper, a simplified numerical analysis method for ship-ice collision-induced vibration is proposed, in which a reliable ice load is obtained by first performing ship-ice-water-air coupled collision calculations, followed by ship-ice-water coupled vibration calculations to obtain the vibration response of the structure. In addition, this paper investigates the full coupling method and the modeling ranges and meshing sizes involved in the analysis ship-ice collision-induced vibration, and the computational efficiencies of the traditional ALE algorithm and S-ALE algorithm are compared. The results indicate that the simplified simulation analysis method and gradient meshing model improve the calculation accuracy and efficiency in ship-ice collision and vibration response analysis. Moreover, the modeling range of the water and air models cannot be less than 6 times the ship width, 2 times the ship length, and 1 times the ship depth, and the S-ALE algorithm saves 47.86% time compared to the ALE algorithm. The research results in this paper can provide a reference for the numerical simulation of ship-ice collision-induced vibration.

Highlights

● A simplified numerical analysis method for ship-ice collision induced vibration based on ship-ice water-air coupling.

● Computational process and modeling method for ship-ice-water-air full coupling collision analysis.

● Computational process and modeling method for ship-water-air full coupling vibration analysis.

● A highly efficient S-ALE coupling algorithm for large-scale fluid-structure coupling problems.

Computational Fluid Dynamics (CFD) investigations into water entry problems of a rigid flat plate with air pockets were systematically conducted. The Volume of Fluid (VOF) model was utilised to capture localised slamming phenomena that occur during, and post-impact events. The model's geometry was modified to include a pocket on the slamming impact surface to investigate the effect of air entrapment on the magnitude and distribution of slamming forces and pressures. A parametric study was conducted on the geometric parameters of the modelled pocket by altering its area, depth, and volume to examine the response of slamming force and pressure loading under several impact velocities. The numerical results of slamming forces and pressures were in good agreement with experimental drop test measurements (with relative error of -6% and 7% for the magnitude of slamming force and pressure, respectively). The numerical results proved that the peak pressure is proportional to the magnitude of impact velocity squared (p_max∝v²).

Highlights

● Demonstration of CFD capability of replicating experimental drop tests of a flat plate.

● The concept of embedded pockets on flat plate enabled a quantitative assessment of the effect of air entrapment.

● Pocket depth significantly affected the magnitudes of slamming forces and pressures.

There are increasing focuses on developing cost-effective floating wind turbines, for which efficient stress analysis methods are needed for floater structural design. Most of the today's studies focus on global analysis methods in which the floater is assumed as a rigid body or multiple rigid bodies and the stress distributions in the floater cannot be directly obtained. As part of the COWI Fonden funded EMULF project, a summary about the methodology, the numerical modeling procedure and the verification for stress response analysis of a semi-submersible floater for a 15MW wind turbine is presented. This analysis procedure includes the regeneration of the hydrodynamic pressure loads on the external wet surface of the floater due to wave diffraction, radiation and hydrostatic pressure change, and the application of these pressure loads, together with the time-varying gravity due motions, the inertial loads and the forces/moments at the boundaries (i.e. tower bottom and mooring line fairleads) of the floater to obtain the deformation and the stresses of the floater in the time domain. The analysis procedure is implemented in a developed MATLAB code and the DNV software package. The importance of the different hydrodynamic pressure components was discussed considering representative sea states. A verification of the obtained stress time series and statistics using this method against the regeneration from a linear frequency-domain approach was made considering irregular wave actions only, and a very good agreement was obtained. The developed methodology can provide an efficient solution for structural design analysis of floating wind turbines.

Highlights

● A methodology for floater stress analysis based on the global coupled wind and wave induced load and response analysis results for a floating wind turbine is proposed.

● Regeneration of hydrodynamic pressure time series due to the global motions of the floating wind turbine and projection to a structural analysis model are made.

● Validation of the proposed procedure for time-domain stress analysis of the floater against the frequency-domain approach for wave-only cases show a very good agreement.

The mathematical model of imbibition phenomenon through homogeneous as well as heterogeneous porous media is presented in this study. Various types of porous materials including Fragmented Mixture, Touchet silt loam, and Glass Beads are investigated and discussed in terms of the relative permeability, capillarity, and heterogeneity of the material on saturation rate of a reservoir. In the present model, the comparison of saturation level for different time and distance level have been discussed between homogeneous and heterogeneous porous medium for various types of sands. The reduced differential transform method (RDTM) is used to obtain approximate analytical solution of the proposed model. Numerical and graphical results are presented for a wide range of time and distance.

Highlights

● Here Purcell relative permeability model of imbibition phenomenon in double phase fluid flow in porous media is discussed

● The imbibition phenomenon is one of the useful phenomena occurs in secondary oil recovery process in Petroleum Engineering

● This study proposes the effect of heterogeneity on saturation rate for various types of porous materials

● The effect of capillary pressure and relative permeability on saturation rate are analysed for various porous materials Reduced differential transform method is used to obtain saturation rates for different distance and time levels

The production of renewable energy is key to satisfying the increasing demand for energy without further increasing pollution. Harnessing ocean energy from waves has attracted attention due to its high energy density. This study compares two generations of floating heaving point absorber WEC, WaveEL 3.0 and WaveEL 4.0, regarding their power performance and mooring line fatigue characteristics, which are essential in, e.g., LCoE calculations. The main differences between the two WECs are the principal dimensions and minor differences in their geometries. The DNV software SESAM was used for simulations and analyses of these WECs in terms of buoy heave motion resonances for maximising energy harvesting, motion characteristics, mooring line forces, fatigue of mooring lines, and hydrodynamic power production. The first part of the study presents results from simulations of unit WEC in the frequency domain and in the time domain for regular wave and irregular sea state conditions. A verification of the two WECs’ motion responses and axial mooring line forces is made against measurement data from a full-scale installation. In the second part of the study, the influence of interaction effects is investigated when the WECs are installed in wave parks. The wave park simulations used a fully-coupled non-linear method in SESAM that calculates the motions of the WECs and the mooring line forces simultaneously in the time domain. The amount of fatigue damage accumulated in the mooring lines was calculated using a relative tension-based fatigue analysis method and the rainflow counting method. Several factors that influence the power performance of the wave park and the accumulated fatigue damage of the mooring lines, for example, the WEC distance of the wave park, the sea state conditions, and the direction of incoming waves, are simulated and discussed. The study's main conclusion is that WaveEL 4.0, which has a longer tube than WaveEL 3.0, absorbs more hydrodynamic energy due to larger heave motions and more efficient power production. At the same time, the accumulated fatigue damage in the moorings is lower compared to WaveEL 3.0 if the distance between the WECs in the wave park is not too short. Its motions in the horizontal plane are larger, which may require a larger distance between the WEC units in a wave park to avoid losing efficiency due to hydrodynamic interaction effects.

Highlights

● Two heaving-point absorbers of similar type are compared to demonstrate how the hydrodynamic power performance is affected due to scale and geometry changes of the WEC's buoy.

● A verification of the WEC models is presented based on measurement data made on installed full-scale prototype WEC.

● Several factors that influence the power performance of the wave park and the accumulated fatigue damage of the mooring lines, for example, the WEC distance of the wave park, the sea state conditions, and the direction of incoming waves, are simulated and discussed.

● A sensitivity study of the WEC distance of wave parks shows how interaction effects between the WECs either empower or reduce hydrodynamic power production.

Vessel-shaped fish cages are promising large aquaculture structures developed in recent years, with an overall length of nearly 400 m. In this paper, a coupled hydroelasticity model of a vessel-shaped fish cage is used to calculate the motion and structural response in the time domain. First, the floating body of the cage is discretized into a multimodule system to calculate the frequency-domain hydrodynamic loads. Then, the multimodule system is connected by equivalent elastic beams to consider the hydroelastic behavior in the time domain. The hydrodynamic loads of the multimodule system are transformed from the frequency-domain loads. Moreover, based on the velocity field transfer functions and the motion of the multimodule system, coupling wave fields considering incident, diffraction and radiation waves are built and used to calculate the loads on the net and steel frame. By iterating the motion response of the multimodule system and the hydrodynamic loads on the net and steel frame in the time domain, the balanced hydroelasticity response of the whole cage is finally obtained. The results show that the hydroelasticity effects have a significant influence on the vertical displacement and cross-sectional load effects of the vessel-shaped fish cage.

Highlights

● A novel time-domain method used in hydroelastic analysis of a vessel-shaped fish cage is proposed.

● The influence of the elasticity of the main structure on the motion response and cross-sectional load effect of the vessel-shaped fish cage is analyzed carefully.

● Hydroelastic analysis of the vessel-shaped fish cage is achieved considering the influence of the floating body to the wave field.

Having estimates of wave climate parameters and extreme values play important roles for a variety of different societal activities, such as coastal management, design of inshore and offshore structures, marine transport, coastal recreational activities, fisheries, etc. This study investigates the efficiency of a state-of-the-art spatial neutral gas clustering method in the classification of wind/wave data and the evaluation of extreme values of significant wave heights (Hs), mean wave direction (MWD) and mean wave periods (T0) for two 39-year time periods; from 1979 to 2017 for the present climate, and from 2060 to 2098, for a future climate change scenario in the Northwest Atlantic. These data were constructed by application of a numerical model, WAVEWATCHIII^TM (hereafter, WW3), to simulate the wave climate for the study area for both present and future climates. Data from the model was extracted for the wave climate, in terms of the wave parameters, specifically Hs, MWD and T0, which were analyzed and compared for winter and summer seasons, for present and future climates. In order to estimate extreme values in the study area, a Natural Gas (hereafter, NG) clustering method was applied, separate clusters were identified, and corresponding centroid points were determined. To analyze data at each centroid point, time series of wave parameters were extracted, and using standard stochastic models, such as Gumbel, exponential and Weibull distribution functions, the extreme values for 50 and 100-year return periods were estimated. Thus, the impacts of climate change on wave regimes and extreme values can be specified.

Highlights

● Using GeoSOM clustering method, neural gas technique in clustering.

● Wave patterns for the present and future climates are somewhat similar.

● Determining areas with notable changes for the present and future climates.

● In the future, some areas are expected to experience notable reductions in sea ice.

With the increase of heat transfer problems in marine vehicles and submerged power stations in oceans, the search for an efficient finned-tube heat exchanger has become particularly important. The purpose of the present investigation is to analyze and compare the thermal exchange and flow characteristics between five different fin designs, namely: a concentric circular finned-tube (CCFT), an eccentric circular finned-tube (ECFT), a perforated circular finned-tube (PCFT), a serrated circular finned-tube (SCFT), and a star-shaped finned-tube (S-SFT). The fin design and spacing impact on the thermal-flow performance of a heat exchanger was computed at Reynolds numbers varying from 4,300 to 15,000. From the numerical results, and when the fin spacing has been changed from 2 to 7 mm, an enhancement in the Colburn factor and a reduction in the friction factor and fin performances were observed for all cases under study. Three criteria were checked to select the most efficient fin design: the performance evaluation criterion P_EC, the global performance criterion G_PC, and the mass global performance criterionMGPC. Whatever the value of Reynolds number, the conventional CCFT provided the lowest performance evaluation criterion P_EC, while the SCFT gave the highest amount of P_EC. The most significant value of G_PC was reached with the ECFT; however, G_PC remained almost the same for CCFT, PCFT, SCFT, and S-SFT. In terms of the mass global performance criterion, the S-SFT provides the highest MGpcas compared with the full fins of CCFT (41-73% higher) and ECFT (29-54% higher). Thus, the heat exchanger with S-SFT is recommended to be used in the cooling of offshore energy systems.

The loading method of the external excitations generated by the equipment directly affects the predicted result of the mechanical noise which should be the same under different excitation forms for the given equipment. In this paper, general load criteria are proposed to define forces/moments as the standard form and convert other forms of loads in the low-frequency domain. As the most typical form to characterize equipment excitation, acceleration load loading methods for different conditions are investigated. The equivalent formula between ideal accelerations and generalized forces establishes the first load criterion. The second load criterion is proposed to address the issue of an average acceleration loading, in which the phase and amplitude distribution are both absent, and cannot apply to the load identification. The upper and lower limits of the mechanical noise can be determined by the vibroacoustic transfer function of the three load models, and the energy-averaged value is used to represent the mechanical noise. Furthermore, the third criterion is used to handle the case where the acceleration load is given by the results of a bench test. According to the equipment source descriptor invariance, the conversion method is achieved between the bench test and the real ship based on the transfer function of a load model, and the mechanical noise is predicted by an equivalent energy method. Finally, a three-parameter method to quantitatively evaluate the well-fitting of experimental and numerical results, and the load criteria are well validated by underwater acoustic experiments of an experimental model.

The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a micropolar double porous thermoelastic material with voids (MDPTMWV) by virtue of Eringen's theory of nonlocal elasticity. Moore-Gibson-Thompson (MGT) heat equation is introduced to the considered model in the context of memory-dependent derivative and variable conductivity. By employing the normal mode technique, the non-dimensional coupled governing equations of motion are solved to determine the analytical expressions of the displacements, temperature, void volume fractions, microrotation vector, force stress tensors, and equilibrated stress vectors. Several two-dimensional graphs are presented to demonstrate the influence of various parameters, such as kernel functions, thermal conductivity, and nonlocality. Furthermore, different generalized thermoelasticity theories with variable conductivity are compared to visualize the variations in the distributions associated with the prior mentioned variables. Some particular cases are also discussed in the presence and absence of different parameters.

This article considers time-dependent variable coefficients (2+1) and (3+1) -dimensional extended Sakovich equation. Painlevé analysis and auto-Bäcklund transformation methods are used to examine both the considered equations. Painlevé analysis is appeared to test the integrability while an auto-Bäcklund transformation method is being presented to derive new analytic soliton solution families for both the considered equations. Two new family of exact analytical solutions are being obtained successfully for each of the considered equations. The soliton solutions in the form of rational and exponential functions are being depicted. The results are also expressed graphically to illustrate the potential and physical behaviour of both equations. Both the considered equations have applications in ocean wave theory as they depict new solitary wave soliton solutions by 3D and 2D graphs.

A soliton is a packet of self-reinforcing waves that maintains its structure when moving at a constant speed. Solitons are caused by the cancellation of the medium's nonlinear and dispersive effects. In plasmas, the bilinear form of Hirota will be utilized to investigate the (2+1)-dimensional Korteweg-de Vries equation with electrostatic wave potential. Solutions for complexiton lump interaction have been developed. To throw further light on the physical qualities of the recorded data, certain 3-dimensional and contour plots are presented to illustrate the interaction elements of these solutions.

Highlights

● The (2+1)-dimensional Korteweg-de Vries equation with electrostatic wave potential in plasmas.

● New lump interaction complexitons are successfully constructed.

● Numerical simulation of the presented results are presented.

In this paper, the (3+1 )-dimensional nonlinear evolution equation is studied analytically. The bilinear form of given model is achieved by using the Hirota bilinear method. As a result, the lump waves and collisions between lumps and periodic waves, the collision among lump wave and single, double-kink soliton solutions as well as the collision between lump, periodic, and single, double-kink soliton solutions for the given model are constructed. Furthermore, some new traveling wave solutions are developed by applying the exp(−ϕ(ξ)) expansion method. The 3D, 2D and contours plots are drawn to demonstrate the nature of the nonlinear model for setting appropriate set of parameters. As a result, a collection of bright, dark, periodic, rational function and elliptic function solutions are established. The applied strategies appear to be more powerful and efficient approaches to construct some new traveling wave structures for various contemporary models of recent era.

Highlights

● The Hirota bilinear method and the $\exp (-\varphi (\xi \left)\right)$ expansion technique are used to generate some new solitary wave solutions.

● The collision among lump wave and single, double-kink soliton solutions as well as the collision between lump, periodic, and single, double-kink soliton solutions of the given model are also constructed.

The system of (1+1 )-coupled Drinfel'd-Sokolov-Wilson equations describes the surface gravity waves travelling horizontally on the seabed. The objective of the present research is to construct a new variety of analytical solutions for the system. The invariants are derived with the aid of Killing form by using the optimal algebra classification via Lie symmetry approach. The invariant solutions involve time, space variables, and arbitrary constants. Imposing adequate constraints on arbitrary constants, solutions are represented graphically to make them more applicable in designing sea models. The behavior of solutions shows asymptotic, bell-shaped, bright and dark soliton, bright soliton, parabolic, bright and kink, kink, and periodic nature. The constructed results are novel as the reported results [26,28,29,30,33,38,42,49] can be deduced from the results derived in this study. The remaining solutions derived in this study, are absolutely different from the earlier findings. In this study, the physical character of analytical solutions of the system could aid coastal engineers in creating models of beaches and ports.

Highlights

● System of coupled Drinfel'd-Sokolov-Wilson equations describes waves travelling horizontally on the seabed.

● The killing form is used to get the invariants.

● One dimensional optimal sub algebras are classified and analytical solutions are attained via one parameter Lie symmetry analysis.

● The solutions are asymptotic, bell-shaped, bright and dark soliton, bright soliton, parabolic, bright and kink, kink, and periodic in nature.

By taking advantage of three different computational analytical methods: the Lie symmetry analysis, the generalized Riccati equation mapping approach, and the modified Kudryashov approach, we construct multiple new analytical soliton solutions to the nonlinear convection-diffusion-reaction equation (NCDR) with power-law nonlinearity and density-dependent diffusion. Lie symmetry analysis is one of the powerful techniques that reduce the higher-order partial differential equation into an ordinary differential equation by reduction of independent variables. By the Lie group technique, we obtain one-parameter invariant transformations, determining equations and corresponding vectors for the considered convection-diffusion-reaction equation. By treating the parameters of the governing equation as constants, the applied methods yield a variety of new closed-form solutions, including inverse function solutions, periodic solutions, exponential function solutions, dark solitons, singular solitons, combo bright-singular solitons, and the combine of bright-dark solitons and dark-bright solitons. Moreover, using the Bäcklund transformation of the generalized Riccati equation and modified Kudryashov method, we can construct multiple solitons and other solutions of the considered equation. The obtained new solutions of this work demonstrate that the used approaches are powerful and effective in dealing with nonlinear equations, and that these solutions are required to explain many biological and physical phenomena. Comparing our obtained solutions of this paper with the ones obtained in the literature, we see that our solutions are new and not reported elsewhere. These newly formed soliton solutions will be more beneficial in the various disciplines of ocean engineering, plasma physics, and nonlinear sciences.

In this article, non-linear time-fractional diffusion equations are considered to describe oil pollution in the water. The latest technique, fractional reduced differential transform method (FRDTM), is used to acquire approximate solutions of the time fractional-order diffusion equation and two cases of Allen-Cahn equations. The acquired results are collated with the exact solutions and other results from literature for integer-order α, which reveal that the proposed method is effective. Hence, FRDTM can be employed to obtain solutions for different types of nonlinear fractional-order IVPs arising in engineering and science.

In the field of maritime transport, motion and energy, the dynamics of deep-sea waves is one of the major problems in ocean science. A mathematical modeling of dynamics of solitary waves in deep sea under the two-layer stratification leads to NLS equation, and consequently, the interaction two of them can be formulated by coupled NLS equation. In this work, extended auxiliary equation and the exp(−Ï-(χ)) -expansion methods are employed to make the optical solutions of the Manakov model of coupled NLS equation. The methods used in this paper, in addition to providing the analysis of individual wave solutions, also provide general optical solutions. Some previously known solutions can be obtained by some special selections of parameters obtained by solving systems of algebraic equations. At this stage, it is more practical and convenient to apply methods with a symbolic calculation system.

Highlights

● Construction of optical soliton solutions Manakov model of coupled nonlinear Schrodinger equation.

● Applications of extended auxiliary equation methods.

● Hyperbolic, complex trigonometric, trigonometric and rational solutions.

● 3D, contour and 2D graphics for the solutions.