非线性波波相互作用共轭源函数守恒量的分析

海浪组成波中的四波共振时满足谱作用量、谱能量及动量守恒，在变分同化所建立的波谱共轭方程中，对应于非线性波波相互作用源函数Boltzman积分形式，本文建立了其共轭源函数满足的守恒关系；实际海浪计算时广泛采用Hasselmann et al．(1985)的参数化方法，本文给出其综合作用表示式，证明也满足谱作用量、谱能量及动量守恒，并进一步导出了其共轭源函数中存在的守恒量。所有的共轭源函数守恒量只是对共轭算子而言的，对于共轭波谱则不存在相应的守恒关系。     

利用共轭方程研究海洋对于大气局域气温的作用

提出了利用共轭方程研究海洋对于局域大气平均气温的作用的方法。在现今海洋基本动力方程基础上导出了球坐标系下的海水温度共辊方程。分析了海水共轭温度的意义，其量值(或垂直梯度量值)表征了不同区域海洋对于局域气温的相应贡献，它在全球海洋中的分布对于局域气候形成与变化研究具有重要意义。     

海浪同化预报模型理论基础

将共轭变分同化方法应用于LAGFD－WAM海浪数值模式，导出了海浪谱能量平衡方程的共轭方程以及风输入、破碎、底摩擦、波波非线性相互作用和波流相互作用的相庆共轭源函数，建立了海浪同化模型，数值计算仍采用特征线嵌入计算格式，为合成孔径雷达波谱反演资料和卫星高度计有效波高资料同化奠定理论基础。     

海浪同化预报模型理论基础

将共轭变分同化方法应用于 LAGFD- WAM海浪数值模式 ,导出了海浪谱能量平衡方程的共轭方程以及风输入、破碎、底摩擦、波波非线性相互作用和波流相互作用的相应共轭源函数 ,建立了海浪同化模型 ,数值计算仍采用特征线嵌入计算格式 ,为合成孔径雷达波谱反演资料和卫星高度计有效波高资料同化奠定理论基础     

AKNS系统的2+1维一般化

讨论AKNS完全可积分系的一种2＋1维一般化。给出对应的Kdv方程及SineGordan方程的一种2＋1维一般化，导出其Hamilton形式。证明了经变量变换后，这类2＋1维完全可积分系可化为1＋1维已知可积分系。     

求解扩展的Sylvester共轭矩阵方程

研究扩展Sylvester共轭矩阵方程及更一般形式复矩阵方程的解,利用复矩阵的实形式方法得到求解方程的迭代算法.数值例子展示了该算法的有效性.     

地形坡度对斜压大气扰动的影响

本文推导出σ坐标系斜压大气的准地转位涡方程，该方程形式与Ｐ坐标系的准地转位涡方程非常相似，但本质不同，本文还用ＷＫＢ方法讨论了大地形坡度对斜压大气扰动发展的影响。指出：东西走向山脉的南坡有利于低层大气槽线呈西北－东南向的扰动发展，也有利于高层大气槽线呈东北－西南向的扰动发展     

关于鱼的生长方程的研究──Ⅱ.估计参数的一种新方法

目前描述鱼的体重生长的方程主要有（１）ｗ＝ｗ∞［１－ｅ＾－ｋ（ｔ－ｔ０）］＾３，和作者对该方程推广而导出的方程（２）ｗ＝ｗ∞［１－ｅ＾－ｋ（ｔ－ｔ０）］＾ｒ，本文对基于这两个方程的４种参数估计法，指出了其不足之处，并提出了一种估计参数的新方法－搜寻逼近法。该方法比前４种方法具有更好的拟合优度，通过实例计算得到进一步的证实。此外，还外鱼的样本资料的处理作了论述。这对更好的掌握鱼的生长规律，进而合理利     

半封闭海区潮波运动问题的构建

利用海底粘滞性条件,首先导出了海底摩擦与海面坡度之间的简单关系式,在此基础上导出了水平流通量与海面坡度的关系式。然后利用连续性方程进一步得到了海面升高即潮位所满足的二阶椭圆型方程,进而导出了以潮位形式给出的半封闭海区岸壁不可穿透条件。最终在给定半封闭海区开边界水位分布的条件下构建了完整的关于潮位分布函数的微分方程边值问题。初步讨论表明,海底摩擦矢量与水平流通量矢量并不在相反的方向上。     

一个新的破碎波统计模式

由运动方程和涡度方程所导得的两个首次积分估计给出了海波破碎的发生条件和破碎波的波面限制。由这两个条件所构造的新的破碎波统计模式，可导出海波的破碎面积率、破碎体积率和破碎能量损耗率的解析表达式，加之一个简单的白冠物理模型又导出了一个新的白冠覆盖率的解析表达式。     

球坐标系下MASNUM海浪数值模式的建立及其应用

为开展海浪对海洋上混合层的搅拌混合作用及其对海气界面通量的影响等研究,在LAGFD WAM区域海浪数值模式基础上建立了球坐标系下的全球海浪数值模式.重点导出了球坐标系下的海浪能量谱平衡方程及其复杂特征线方程,该组方程包含了背景流场对波动传播的调整、波动沿大圆传播的折射等.数值积分则采用复杂特征线嵌入计算格式.初步数值模拟结果表明,该海浪全球数值模式能够较为精确地刻画海浪的动力过程.     

A Eulerian–Lagrangian method for the simulation of wave propagation

A Eulerian–Lagrangian method (ELM) is employed for the simulation of wave propagation in the present research. The wave action conservation equation, instead of the wave energy balance equation, is used. The wave action is conservative and the action flux remains constant along the wave rays. The ELM correctly accounts for this physical characteristic of wave propagation and integrates the wave action spectrum along the wave rays. Thus, the total derivative for wave action spectrum may be introduced into the numerical scheme and the complicated partial differential wave action balance equation is simplified into an ordinary differential equation. A number of test cases on wave propagation are carried out and show that the present method is stable, accurate and efficient. The results are compared with analytical solutions and/or other computed results. It is shown that the ELM is superior to the first-order upwind method in accuracy, stability and efficiency and may better reflect the complicated dynamics due to the complicated bathymetry features in shallow water areas.     

A Eulerian–Lagrangian method for the simulation of wave propagation

A Eulerian–Lagrangian method (ELM) is employed for the simulation of wave propagation in the present research. The wave action conservation equation, instead of the wave energy balance equation, is used. The wave action is conservative and the action flux remains constant along the wave rays. The ELM correctly accounts for this physical characteristic of wave propagation and integrates the wave action spectrum along the wave rays. Thus, the total derivative for wave action spectrum may be introduced into the numerical scheme and the complicated partial differential wave action balance equation is simplified into an ordinary differential equation. A number of test cases on wave propagation are carried out and show that the present method is stable, accurate and efficient. The results are compared with analytical solutions and/or other computed results. It is shown that the ELM is superior to the first-order upwind method in accuracy, stability and efficiency and may better reflect the complicated dynamics due to the complicated bathymetry features in shallow water areas.     

利用海浪谱共轭方程进行东海敏感性区域分布研究

近岸局部范围内的波浪是由远处洋面上生成并传播过来的，它的生成发展源地(敏感性海域)对于所关注范围的波浪起决定性影响。共轭方程中的模式变量反映了物理参量的梯度变化，利用它可以达到精确确定敏感海域具体位置的目的。本文在LAGFD-WAM海浪模式基础上建立了海浪谱共轭方程，提出了通过在关注点邻域加一小扰动作为逆向积分海浪谱共轭方程的驱动项，来计算出梯度极值分布的思想。将这一思想应用于东中国海区域，通过一系列试验来确定舟山及长江口附近海域的敏感性区域位置。试验结果符合物理意义，梯度极值分布结果为下一步的多源卫星观测资料复合分析及最优实测方案设计奠定了基础。     

Euler–Lagrange equations for the spectral element shallow water system

We present the derivation of the discrete Euler–Lagrange equations for an inverse spectral element ocean model based on the shallow water equations. We show that the discrete Euler–Lagrange equations can be obtained from the continuous Euler–Lagrange equations by using a correct combination of the weak and the strong forms of derivatives in the Galerkin integrals, and by changing the order with which elemental assembly and mass averaging are applied in the forward and in the adjoint systems. Our derivation can be extended to obtain an adjoint for any Galerkin finite element and spectral element system.We begin the derivations using a linear wave equation in one dimension. We then apply our technique to a two-dimensional shallow water ocean model and test it on a classic double-gyre problem. The spectral element forward and adjoint ocean models can be used in a variety of inverse applications, ranging from traditional data assimilation and parameter estimation, to the less traditional model sensitivity and stability analyses, and ensemble prediction. Here the Euler–Lagrange equations are solved by an indirect representer algorithm.     

Extraction of Ocean Wave Spectra From Simulated Noisy Bistatic High-Frequency Radar Data

An algorithm is developed for the inversion of bistatic high-frequency (HF) radar sea echo to give the nondirectional wave spectrum. The bistatic HF radar second-order cross section of patch scattering, consisting of a combination of four Fredholm-type integral equations, contains a nonlinear product of ocean wave directional spectrum factors. The energy inside the first-order cross section is used to normalize this integrand. The unknown ocean wave spectrum is represented by a truncated Fourier series. The integral equation is then converted to a matrix equation and a singular value decomposition (SVD) method is invoked to pseudoinvert the kernel matrix. The new algorithm is verified with simulated radar Doppler spectrum for varying water depths, wind velocities, and radar operating frequencies. To make the simulation more realistic, zero-mean Gaussian noise from external sources is also taken into account     

Refraction-Diffraction Mathematical Model for Waves With Lateral Energy Transmission Mechanism and Its Verification

To solve problems concerning wave elements and wave propagation, an effective way is the wave energy balance equation, which is widely applied in oceanography and ocean dynamics for its simple computation. The present papaer advances wave energy balance equations considering lateral energy transmission and energy loss as the governing equation for the study of wave refraction-diffraction. For the mathematical model, numerical simulation is made by means of difference method, and the result is verified with two examples.     

利用波能平衡方程研究波浪折射——绕射的数学模型及数值模拟

波能平衡方程是研究风浪要素及波能传播问题的很有效的方法，计算较为简单，在海洋学及海岸动力学中得到广泛的应用。本文采用考虑波能侧向传递机制和耗损制约的波能平衡方程组作为研究波浪折射——绕射变形的控制方程。对数学模型用差分法进行了数值模拟，并用两个例题进行了验证     

New periodic wave solutions of a time fractional integrable shallow water equation

In this paper, author employed Jacobi elliptic function expansion method to build the new wave solutions of time fractional modified Camassa–Holm equation which is completely integrable dispersive shallow-water equation. In ocean engineering, Camassa–Holm equation is generally used as a tool in computer simulation of the water waves in shallow sees, coastal and harbors. The obtained solutions show that the Jacobi elliptic function expansion method (JEFEM) which based on Jacobi elliptic functions is an efficient, reliable, applicable and accurate tool for analytic approximation of a wide variety of nonlinear conformable time fractional partial differential equations.