Dynamic Modeling and Three-Dimensional Motion Analysis of Underwater Gliders

For consideration of both the eccentric rotatable rigid body and the translational rigid body, the dynamic model of the underwater glider is derived. Dynamical behaviors are also studied based on the model and can be used as the guidance to underwater gliders design. Gibbs function of the underwater glider system is derived first, and then the nonlinear dynamic model is obtained by use of Appell equations. The relationships between dynamic behaviors and design parameters are studied by solving the dynamic m...     

On the application of a Boussinesq model to river flows including shocks

SERR-1D is a 4th-order finite volume 1D Boussinesq model including wave breaking energy dissipation through extra diffusive-like terms. This model has been primarily conceived to compute wave propagation in coastal areas and has been validated for breaking and non-breaking waves propagating over uneven bathymetries (Cienfuegos et al., 2005, 2006a, b, 2007). The present paper aims at investigating the ability of SERR-1D to simulate challenging fluvial hydraulic applications such as sudden gate operation in open channels generating short waves, dam-break flows and a steady hydraulic jump over a bump. The performance of the absorbing-generating boundary condition implemented in SERR-1D is first analysed in the context of fluvial applications where relatively short waves must be evacuated from the computational domain without producing spurious reflection. Next, by comparing numerical results to analytical and experimental dam-break test cases we show that the model is able to reproduce the overall features of these flows, but that additional care should be paid to the representation of energy dissipation and front speed in order to accurately represent bore dynamics.     

Higher-order Boussinesq-type equations for interfacial waves in a two-fluid system

Interfacial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. A set of higher-order Boussinesq-type equations in terms of the depth-averaged velocities accounting for stronger nonlinearity are derived. When the small parameter measuring frequency dispersion keeping up to lower-order and full nonlinearity are considered, the equations include the Choi and Camassa’s results (1999). The enhanced equations in terms of the depth-averaged velocities are obtained by applying the enhancement technique introduced by Madsen et al. (1991) and Schaffer and Madsen (1995a). It is noted that the equations derived from the present study include, as special cases, those obtained by Madsen and Schaffer (1998). By comparison with the dispersion relation of the linear Stokes waves, we found that the dispersion relation is more improved than Choi and Camassa’s (1999) results, and the applicable scope of water depth is deeper.     

On thermodynamics of fluids,solids and superconductors

We derive the relativistic Carnot-Clausius relation and the set of fundamental equations of the thermodynamic system with the aid of Neugebauer's variational principle for several media. Some equations are already well-known in the literature but here we obtain the full set from a uniform point of view.     

Wave crest and trough distributions in a broad-banded directional wave field

It is well established that the modulational instability enhances the probability of occurrence for extreme events in long crested wave fields. Recent studies, however, have shown that the coexistence of directional wave components can reduce the effects related to the modulational instability. Here, numerical simulations of the Euler equations are used to investigate whether the modulational instability may produce significant deviations from second-order statistical properties of surface gravity waves when short crestness (i.e., directionality) is accounted for. The case of a broad-banded directional wave field (i.e. wind sea) is investigated. The analysis is concentrated on the wave crest and trough distribution. For completeness a comparison with a unidirectional wave field is presented also. Results will show that the distributions based on second-order theory provide a good estimate for the simulated crest and trough height also at low probability levels.     

海浪感应电磁场的理论计算

根据麦克斯韦电磁理论,在地磁场中运动的海水将产生感应电磁场。利用一个简单的数学物理模型对感应电磁场在海水内部的分布进行了计算,结果表明海浪产生的电磁场明显依赖于海浪波动的周期及浪高。在100 m的海水深度内,海浪产生的磁感应强度的大小为纳特数量级,而电场强度的大小为几个微伏每米。在同一海水深度处,磁感应强度随海水波动的周期呈现近线性变化,而电场强度的大小有一个极值,该极值随海水深度的增加向长周期方向移动。海浪产生的电磁场是影响海洋电磁探测数据精度的主要噪声之一。     

Alternative forms of the higher-order Boussinesq equations: Derivations and validations

An alternative form of the Boussinesq equations is developed, creating a model which is fully nonlinear up to O(μ⁴) (μ is the ratio of water depth to wavelength) and has dispersion accurate to the Padé [4,4] approximation. No limitation is imposed on the bottom slope; the variable distance between free surface and sea bottom is accounted for by a σ-transformation. Two reduced forms of the model are also presented, which simplify O(μ⁴) terms using the assumption ε = O(μ^2/3) (ε is the ratio of wave height to water depth). These can be seen as extensions of Serre's equations, with dispersions given by the Padé [2,2] and Padé [4,4] approximations. The third-order nonlinear characteristics of these three models are discussed using Fourier analysis, and compared to other high-order formulations of the Boussinesq equations. The models are validated against experimental measurements of wave propagation over a submerged breakwater. Finally, the nonlinear evolution of wave groups along a horizontal flume is simulated and compared to experimental data in order to investigate the effects of the amplitude dispersion and the four-wave resonant interaction.     

Recent Advancement in Modeling Seafloor Dissipative Mechanism in Shallow Water

In this paper, the recent development in modeling seabed dissipative mechanisms in shallow water is reviewed. Specifically, laminar and turbulent boundary layer solutions as well as viscous mud flow solutions under transient waves are presented. These analytical solutions are compared with experimental data for both solitary waves and cnoidal waves. Very goed agreement is ohtained. The Boussinesq equations with boundary layer effects and the muddy seabed effects are also shown.     

Hyperbolic Mild Slope Equations with Inclusion of Amplitude Dispersion Effect: Random Waves

New hyperbolic mild slope equations for random waves are developed with the inclusion of amplitude dispersion. The frequency perturbation around the peak frequency of random waves is adopted to extend the equations for regular waves to random waves. The nonlinear effect of amplitude dispersion is incorporated approximately into the model by only considering the nonlinear effect on the carrier waves of random waves, which is done by introducing a representative wave amplitude for the carrier waves. The computation time is greatly saved by the introduction of the representative wave amplitude. The extension of the present model to breaking waves is also considered in order to apply the new equations to surf zone. The model is validated for random waves propagate over a shoal and in surf zone against measurements.