Journal of Ocean Engineering and Science最新文献

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.

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.

In the frame of fully nonlinear potential flow theory, series solutions of interfacial periodic gravity waves in a two-layer fluid with free surface are obtained by the homotopy analysis method (HAM), and the related wave forces on a vertical cylinder are analyzed. The solution procedure of the HAM for the interfacial wave model with rigid upper surface is further developed to consider the free surface boundary. And forces of nonlinear interfacial periodic waves are estimated by both the classical and modified Morison equations. It is found that the estimated wave forces by the classical Morison equation are more conservative than those by the modified Morison’s formula, and the relative error between the total inertial forces calculated by these two kinds of Morison’s formulae remains over $25\%$ for most cases unless the upper and lower layer depths are both large enough. It demonstrates that the convective acceleration neglected in the classical Morison equation is rather important for inertial force exerted by not only internal solitary waves but also interfacial periodic waves. All of these should further deepen our understanding of internal periodic wave forces on a vertical marine riser.

This study presents a large family of the traveling wave solutions to the two fourth-order nonlinear partial differential equations utilizing the Riccati-Bernoulli sub-ODE method. In this method, utilizing a traveling wave transformation with the aid of the Riccati-Bernoulli equation, the fourth-order equation can be transformed into a set of algebraic equations. Solving the set of algebraic equations, we acquire the novel exact solutions of the integrable fourth-order equations presented in this research paper. The physical interpretation of the nonlinear models are also detailed through the exact solutions, which demonstrate the effectiveness of the presented method.The Bäcklund transformation can produce an infinite sequence of solutions of the given two fourth-order nonlinear partial differential equations. Finally, 3D graphs of some derived solutions in this paper are depicted through suitable parameter values.

Pressure hulls play an important role in deep-sea underwater vehicles. However, in the ultra-high pressure environment, a highly destructive phenomenon could occur to them which is called implosion. To study the characteristics of the flow field of the underwater implosion of hollow ceramic pressure hulls, the compressible multiphase flow theory, direct numerical simulation, and adaptive mesh refinement are used to numerically simulate the underwater implosion of a single ceramic pressure hull and multiple linearly arranged ceramic pressure hulls. Firstly, the feasibility of the numerical simulation method is verified. Then, the results of the flow field of the underwater implosion of hollow ceramic pressure hulls in 11000 m depth is analyzed. There are the compression-rebound processes of the internal air cavity in the implosion. In the rebound stage, a shock wave that is several times the ambient pressure is generated outside the pressure hull, and the propagation speed is close to the speed of sound. The pressure peak of the shock wave has a negative exponential power function relationship with the distance to the center of the sphere. Finally, it is found that the obvious superimposed effect between spheres exists in the chain-reaction implosion which enhances the implosion shock wave.

The ($2+1$)-dimensional Chaffee–Infante has a wide range of applications in science and engineering, including nonlinear fiber optics, electromagnetic field waves, signal processing through optical fibers, plasma physics, coastal engineering, fluid dynamics and is particularly useful for modeling ion-acoustic waves in plasma and sound waves. In this paper, this equation is investigated and analyzed using two effective schemes. The well-known tanh-coth and sine-cosine function schemes are employed to establish analytical solutions for the equation under consideration. The breather wave solutions are derived using the Cole–Hopf transformation. In addition, by means of new conservation theorem, we construct conservation laws (CLs) for the governing equation by means of Lie–Bäcklund symmetries. The novel characteristics for the ($2+1$)-dimensional Chaffee–Infante equation obtained in this work can be of great importance in nonlinear sciences and ocean engineering.

The main idea of this article is the investigation of atmospheric internal waves, often known as gravity waves. This arises within the ocean rather than at the interface. A shallow fluid assumption is illustrated by a series of nonlinear partial differential equations in the framework. Because the waves are scattered over a wide geographical region, this system can precisely replicate atmospheric internal waves. In this research, the numerical solutions to the fuzzy fourth-order time-fractional Boussinesq equation (BSe) are determined for the case of the aquifer propagation of long waves having small amplitude on the surface of water from a channel. The novel scheme, namely the generalized integral transform (proposed by H. Jafari [35]) coupled with the Adomian decomposition method (GIADM), is used to extract the fuzzy fractional BSe in $R,R^n$ and $\left(2nth\right)$-order including $gH$-differentiability. To have a clear understanding of the physical phenomena of the projected solutions, several algebraic aspects of the generalized integral transform in the fuzzy Caputo and Atangana-Baleanu fractional derivative operators are discussed. The confrontation between the findings by Caputo and ABC fractional derivatives under generalized Hukuhara differentiability are presented with appropriate values for the fractional order and uncertainty parameters $\wp \in [0,1]$ were depicted in diagrams. According to proposed findings, hydraulic engineers, being analysts in drainage or in water management, might access adequate storage volume quantity with an uncertainty level.