关于具二次约束最小二乘问题的敏度分析

本文系统地研究具二次约束最小二乘问题的敏度分析。首先给出长期方程唯一正根的上界和下界；然后证明割线法用于计算拉格朗日乘子时全局收敛；最后给出解的扰动界。     

An infinity of conservation laws of fKdV equation

An infinity of conservation laws of fKdV equation is derived in terms of the Miura and Gardner''s transform.The pseudo-mass and energy theorems are studied by the first two conservation laws.As a typical example,the theoretical mean wave resistance and the regional distribution of energy of the precursor soliton generation are determined by means of the first and the second conservation laws.     

Wave-Current Forces on Small Square Cylinders (Part I)

-Based on the extended Morison Equation and model tests, the in-line forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in detail in this paper. The hydrodynamic coefficient CD and Cu related to KC number and the effect of direction of wave incidence are also given, which can be used in engineering practice.     

考虑非线性弥散影响的波浪变形数学模型

提出了逼近Kirby和Dalrymple的非线性弥散关系的显式非线性弥散关系的表达式,该显式表达式与他们的非线性弥散关系的精度几乎完全相同.采用显式非线性弥散关系,结合含弱非线性效应的缓坡方程,得到考虑非线性弥散影响的波浪变形数学模型,并对该数学模型进行了数值验证.结果表明,考虑非线性弥散影响的波浪变形数学模型更为精确.     

A linear Boltzmann equation to model wave scattering in the marginal ice zone

We present a linear Boltzmann equation to model wave scattering in the Marginal Ice Zone (the region of ocean which consists of broken ice floes). The equation is derived by two methods, the first based on Meylan et al. [Meylan, M.H., Squire, V.A., Fox, C., 1997. Towards realism in modeling ocean wave behavior in marginal ice zones. J. Geophys. Res. 102 (C10), 22981–22991] and second based on Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136]. This linear Boltzmann equation, we believe, is more suitable than the equation presented in Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136] because of its simpler form, because it is a differential rather than difference equation and because it does not depend on any assumptions about the ice floe geometry. However, the linear Boltzmann equation presented here is equivalent to the equation in Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136] since it is derived from their equation. Furthermore, the linear Boltzmann equation is also derived independently using the argument in Meylan et al. [Meylan, M.H., Squire, V.A., Fox, C., 1997. Towards realism in modeling ocean wave behavior in marginal ice zones. J. Geophys. Res. 102 (C10), 22981–22991]. We also present details of how the scattering kernel in the linear Boltzmann equation is found from the scattering by an individual ice floe and show how the linear Boltzmann equation can be solved straightforwardly in certain cases.     

A General Linear Wave Theory for Water Waves Propagating over Uneven Porous Bottoms

Starting from the widespread phenomena of porous bottoms in the near shore region, considering fully the diversity of bottom topography and wave number variation, and including the effect of evanescent modes, a general linear wave theory for water waves propagating over uneven porous bottoms in the near shore region is established by use of Green‘s scond identity. This theory can be reduced to a number of the most typical mild-slope equations curreutly in use and provide a reliable research basis for follow-up development of nonlinear water wave theory involving porous bottoms.     

Hammerstein型非线性积分方程解的存在性

该文采用化为积分方程组的方法 ,利用锥上不动点指数计算 ,在不要求非线性项 f (x,u)非负的情况下 ,证明 Hammerstein型非线性积分方程 φ(x) =∫Gκ(x,y) f (y,φ(y) ) dy非平凡解和多解存在性的一些新的结果。此结果可用来证明非线性常微分方程两点边值问题解的存在性。     

Numerical modelling of deformation of multi-directional random waves over a varying topography

Two numerical formulations of the breaking phenomenon were implemented in a numerical model for random wave propagation based on the elliptic formulation of the mild-slope equation. The randomness of the wave field was simulated based on a spectral component method, in which the 3-D spectrum is discretised in components of equal energy. One of the breaking process formulations is based on the concept of breaking each independent spectral component. The other is based on the distribution of the local amount of energy dissipated through the independent spectral components. The model based on the concept of breaking each independent spectral component produces the best estimates of the wave field, when the numerical results are compared with laboratory data.     

水下滑翔器的运动建模与分析

介绍了水下滑翔器的工作机理，对其沉浮阶段的滑翔过程进行了动力学分析，推导了滑翔器在垂直剖面上的动力学方程。论文深入分析了水下滑翔器稳态时的运动规律，以水下滑翔器试验模型为例，推导了其稳态运动参数，通过线性化与适当的简化，得到模型在垂直剖面上的运动状态方程，讨论了系统的可控性与可观测性，为水下滑翔器系统的开发设计和控制提供了理论依据，具有重要的指导意义。     

Parabolic Wave Propagation Modelling in Orthogonal Coordinate Systems

This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild-slope equation in the orthogonal coordinate system. Two types of coordinate systems are studied: (a) a general form of orthogonal coordinate system and (b) the conformal system, a special form of orthogonal coordinate system. Two typical examples, namely, expanded breakwaters and a circular channel, are studied to validate the model. First, the examples are studied by use of the general orthogonal coordinates. Then the same examples are computed by use of the confonnal system. The computational results show that the confonnal coordinate system generally gives better predictions than the general orthogonal system. A numerical technique for generating the conformal grid is combined with the numerical model to improve the practicability of the model. The comparison between the result from the numerical grid system and that from the analytical grid system shows that reliable computational results can be obtained by use of the numerical confonnal grid system.