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.

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.

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.

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.

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.

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.

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 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.

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.

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 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

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.

This study establishes a common coupled fixed point for two pairs of compatible and sequentially continuous mappings in the intuitionistic fuzzy metric space that satisfy the Ï• -contractive conditions. Many basic definitions and theorems have been used from some recent scientific papers about the binary operator, t-norm, t-conorm, intuitionistic fuzzy metric space, and compatible mapping for reaching to the paper's purpose.

Highlights

● Coupled Fixed Point Theorems

● Contractive Condition

● Intuitionistic Fuzzy Metric Spaces.

Ensuring accurate parameter identification and diving motion prediction of marine crafts is essential for safe navigation, optimized operational efficiency, and the advancement of marine exploration. Addressing this, this paper proposes an instrumental variable-based least squares (IVLS) algorithm. Firstly, aiming to balance complexity with accuracy, a decoupled diving model is constructed, incorporating nonlinear actuator characteristics, inertia coefficients, and damping coefficients. Secondly, a discrete parameter identification matrix is designed based on this dedicated model, and then a IVLS algorithm is innovatively derived to reject measurement noise. Furthermore, the stability of the proposed algorithm is validated from a probabilistic point of view, providing a solid theoretical foundation. Finally, performance evaluation is conducted using four depth control datasets obtained from a piston-driven profiling float in Qiandao Lake, with desired depths of 30 m, 40 m, 50 m, and 60 m. Based on the diving dynamics identification results, the IVLS algorithm consistently shows superior performance when compared to recursive weighted least squares algorithm and least squares support vector machine algorithm across all depths, as evidenced by lower average absolute error (AVGAE), root mean square error (RMSE), and maximum absolute error values and higher determination coefficient ($R^2$). Specifically, for desired depth of 60 m, the IVLS algorithm achieved an AVGAE of 0.553 m and RMSE of 0.655 m, significantly outperforming LS-SVM with AVGAE and RMSE values of 8.782 m and 11.117 m, respectively. Moreover, the IVLS algorithm demonstrates a remarkable generalization capability with $R^2$ values consistently above 0.95, indicating its robustness in handling varied diving dynamics.

Highlights

● Integration of measurement noise and nonlinear actuator traits refines dynamic environmental modeling.

● IVLS promotes noise-data independence, ensuring parameter convergence sans prior noise knowledge.

● Employing moderate depth data exemplifies successful marine craft motion modeling in real-world.

● Field data parameter identification and prediction are enhanced by superior IVLS over RWLS, LS-SVM.

Deep-sea submersibles are significant mobile platforms requiring multi-functional capabilities that are strongly determined by the constituent materials. Their cylindrical protective cover can be advanced by designing their sandwiched cellular materials whose physical properties can be readily parameterized and flexibly tuned. Porous honeycomb materials are capable of possessing tuned positive, negative, or zero Poisson's ratios (PPR, NPR, and ZPR), which is expected to produce distinct physical performance when utilized as a cellular core of cylindrical shells for the deep-sea submersibles. A novel cylindrical meta-structure sandwiched with the semi-re-entrant ZPR metamaterial has been designed as well as its similarly-shaped sandwich cylindrical shell structures with PPR and NPR honeycombs. The mechanical and vibroacoustic performance of sandwich cylindrical shells with cellular materials featuring a full characteristic range of Poisson's ratios are then compared systematically to explore their potential for engineering applications on submerged pressure-resistant structures. The respective unit cells are designed to feature an equivalent load-bearing capability. Physical properties of pressure resistance, buckling, and sound insulation are simulated, respectively, and the orders of each property are then generalized by systematic comparison. The results indicate that the PPR honeycomb core takes advantage of higher structural strength and stability while the ZPR one yields better energy absorption and sound insulation behavior. The NPR one yields moderate properties and has the potential for lower circumferential deformation. The work explores the application of cellular materials with varied Poisson's ratios and provides guidance for the multi-functional design of sandwich cylindrical meta-structures.

Highlights

● The properties of sandwich cylindrical shells with cellular materials with a full characteristic range of Poisson's ratios have been systematically compared.

● The PPR honeycomb core takes advantage of the highest structural strength and stability.

● The ZPR core yields the best energy absorption capability and sound insulation performance.

● The NPR honeycomb core yields moderate properties and has the potential for lower circumferential deformation.

The Cahn-Hilliard system was proposed to the first time by Chan and Hilliard in 1958. This model (or system of equations) has intrinsic participation energy and materials sciences and depicts significant characteristics of two phase systems relating to the procedures of phase separation when the temperature is constant. For instance, it can be noticed when a binary alloy (“Aluminum + Zinc” or “Iron + Chromium”) is cooled down adequately. In this case, partially or totally nucleation (nucleation means the appearance of nuclides in the material) is observed: the homogeneous material in the initial state gradually turns into inhomogeneous, giving rise to a very accurate dispersive microstructure. Next, when the time scale is slower the microstructure becomes coarse. In this work, to the first time, the unified method is presented to investigate some physical interpretations for the solutions of the Cahn-Hilliard system when its coefficients varying with time, and to show how phase separation of one or two components and their concentrations occurs dynamically in the system. Finally, 2D and 3D plots are introduced to add more comprehensive study which help to understand the physical phenomena of this model. The technique applied in this analysis is powerful and efficient, as evidenced by the computational work and results. This technique can also solve a large number of higher-order evolution equations.

Highlights

● Different wave structures for abundant solutions to the Chan–Hilliard system are investigated.

● Performance was done using the strategy of the unified method.

● Physical explanations are discussed for the obtained solutions.

The Schrodinger equation type nonlinear coupled Maccari system is a significant equation that flourished with the wide-ranging arena concerning fluid flow and the theory of deep-water waves, physics of plasma, nonlinear optics, etc. We exploit the enhanced tanh approach and the rational (G′/G) -expansion process to retrieve the soliton and dissimilar soliton solutions to the Maccari system in this study. The suggested systems of nonlinear equations turn into a differential equation of single variable through executing some operations of wave variable alteration. Thereupon, with the successful implementation of the advised techniques, a lot of exact soliton solutions are regained. The obtained solutions are depicted in 2D, 3D, and contour traces by assigning appropriate values of the allied unknown constants. These diverse graphical appearances assist the researchers to understand the underlying processes of intricate phenomena of the leading equations. The individual performances of the employed methods are praiseworthy which justify further application to unravel many other nonlinear evolution equations ascending in various branches of science and engineering.

Highlights

● We have obtained new solitons for the coupled nonlinear Maccari's system describing the motion of isolated waves in fluid-flow.

● This model describes propagation of solitons in the theory of deep-water waves.

● Abundant closed form wave solutions are successfully generated in terms of rational, trigonometric and hyperbolic functions.

● The acquired solutions alongside particular values of involved free parameters are figured out in 3D, 2D and contour profiles to depict diverse soliton patterns.

In this paper, the generalized dissipative Kawahara equation in the sense of conformable fractional derivative is presented and solved by applying the tanh-coth-expansion and sine-cosine function techniques. The quadratic-case and cubic-case are investigated for the proposed model. Expected solutions are obtained with highlighting to the effect of the presence of the alternative fractional-derivative and the effect of the added dissipation term to the generalized Kawahara equation. Some graphical analysis is presented to support the findings of the paper. Finally, we believe that the obtained results in this work will be important and valuable in nonlinear sciences and ocean engineering.

Highlights

● The conformable-time-fractional generalized dissipative Kawahara equation is presented and solved by using the tanh-coth-expansion and sine-cosine-function methods.

● The quadratic-case and cubic-case are investigated for the proposed model.

● The new solutions highlighted the effect of the presence of the alternative fractional-derivative and the effect of the added dissipation term to the generalized Kawahara equation.

● Some graphical analysis is presented to support the findings of the current work.

The fundamental objective of this paper is to study the effectiveness of magnetic field and gravity on an isotropic homogeneous thermoelastic structure based on four theories of generalized thermoelasticity. In another meaning, the models of coupled dynamic theory (CDT), Lord-Shulman (LS), Green-Lindsay (GL) as well as Green-Naghdi (GN II) will be taken in the consideration. Then, applying the harmonic method (normal mode technique), the solution of the governing equations and the expressions for the components of the displacement, temperature and (Mechanical and Maxwell's) stresses is taken into account and calculated numerically. The impacts of the gravity and magnetic field are illustrated graphically which are pronounced on the different physical quantities. Finally, the results of some research that others have previously obtained may be found some or all of them as special cases from this study.

Highlights

Investigate conducting thermoelectric materials as a new class of applicable thermoelectric solids. The result provides a motivation to investigate conducting thermoelectric materials as a new class of applicable thermoelectric solids. The results presented in this paper should prove useful for researchers in material science, designers of new materials, physicists as well as for those working on the development of magneto-thermo-elasticity and in practical situations as in geophysics, optics, acoustics, geomagnetic and oil prospecting etc. The used methods in the present article are applicable to a wide range of problems in thermodynamics and thermoelasticity.

This study looks at the mathematical model of internal atmospheric waves, often known as gravity waves, occurring inside a fluid rather than on the surface. Under the shallow-fluid assumption, internal atmospheric waves may be described by a nonlinear partial differential equation system. The shallow flow model's primary concept is that the waves are spread out across a large horizontal area before rising vertically. The Fractional Reduced Differential Transform Method(FRDTM) is applied to provide approximate solutions for any given model. This aids in the modelling of the global atmosphere, which has applications in weather and climate forecasting. For the integer-order value (α=1), the FRDTM solution is compared to the precise solution, EADM, and HAM to assess the correctness and efficacy of the proposed technique.

Highlights

● Under the shallow fluid assumption, the mathematical model of internal atmospheric waves is considered.

● In this model, waves are spread out across a large horizontal area before rising vertically.

● The fractional reduced differential transform method (FRDTM) is applied to find the approximate solution of time-fractional non-linear system of PDEs.

● The fractional solution provides a pragmatic look into the physical behaviour of internal waves, which can be helpful to refine climate and weather models.

● The obtained results have been compared with the numerical solution, EADM, and HAM for integer order to check the correctness and efficacy of the proposed technique.

The primary objective of this research problem is to analyze the Rayleigh wave propagation in homogeneous isotropic half space with mass diffusion in Three Phase Lag (TPL) thermoelasticity at two temperature. The governing equations of thermodiffusive elastic half space have been solved using the normal mode analysis in order to obtain the Rayleigh wave frequency equation at relevant boundary conditions. The variation of various parameters like non-dimensional speed, attenuation coefficient, penetration depth and specific loss corresponding to thermodiffusion parameter, relaxation time, wave number and frequency has been obtained. The effect of these parameters on Rayleigh wave propagation in thermoelastic half space are graphically demonstrated and variations of all these parameters have been compared within Lord-Shulman (L-S), Green-Nagdhi (GN-III) and Three Phase Lag (TPL) theory of thermoelasticity.

Highlights

● Rayleigh wave propagation in homogeneous isotropic half space with mass diffusion in Three Phase Lag thermoelasticity at two temperature.

● Normal mode analysis is used to obtain the Rayleigh wave frequency equation at relevant boundary conditions.

● Relevant cobalt material parameter has been considered to demonstrate the variation of various parameters of Rayleigh wave propagation.

● Variation of non-dimensional speed, attenuation coefficient, penetration depth and specific loss has been demonstrated graphically.

● Variation of parameters have been compared within Lord-Shulman (L-S), Green-Nagdhi (GN-III) and Three phase lag theory of thermoelasticity.

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.