任意截面直渠中先锋孤立子生成问题中的生成周期和振幅(英文)

借助任意截面直渠中的ｆＫｄＶ方程,理论上确定了先锋孤立子生成的平均特性。基于任意截面直渠中的ＡｆＫｄＶ方程,求得了先锋孤立子生成问题中的理论生成振幅和周期。作为例子,文中预报和比较了正方形和等腰三角形断面直渠中的生成周期和振幅。并且,理论研究也证实,对于正方形渠,当渠宽ｂ＝１时,所得的结果可退化为Ｘｕ［１］等人的结果。     

问题中的理论平均波阻(英文)

利用准三维的ｆＫｄＶ方程和四区间划分法,理论给出了任意截面的直渠道中先锋孤立子生成的理论平均波阻和区间平均能量的时间变化率。基于ｆＫｄＶ方程系数的正则性,文中结果是Ｘｕ等人结果的一个推广。对具有相同截面面积的正方形和等腰三角形截面的渠道及在不同强迫源和强迫源速度条件下,对理论平均波阻和平均生成能的时间变化率进行了数值比较和理论预报。比较指出,理论和数值结果吻合得很好。     

Generating Velocities in Precursor Soliton Generation in a Straight Channel with Arbitrary Cross Section

利用准三维的ｆＫｄＶ方程及四区间划分法,理论上求得了先锋孤立子生成诸速度—先锋孤立子的运动速度、压水区中流的速度及尾波列第一个跨零点的速度。所述理论是Ｘｕ等人的先锋孤立子生成理论的一个推广。作为应用的例子,运用作者得到的理论结果,对具有相同截面面积的等腰三角形和正方形截面的直渠中先锋孤立子生成的诸速度进行了理论预报和数值比较。比较指出,理论和数值结果吻合得很好。     

两层分层流体中初始内孤立波分裂的数值研究

本文导得了1个研究内波分裂的射线型二维KdV方程。利用这一方程的一维退化方程进行了实验室尺度下孤立子型内波分裂的数值研究。数值结果表明,深水区的初始内孤立波和实测的内孤立波(内潮)在通过陆坡区时都会产生分裂,并在陆架上(浅水区)生成一内孤立子波列。这表明在实际海洋条件下,深海区内潮的分裂是陆架上海洋内孤立子波包(或波列)生成的主要机制之一。     

侧边界对内长波传播影响的数值模拟

利用修正的非线性水平二维Lynett-Liu内长波数值模式,模拟了小振幅孤立子内波进出水道口的传播过程,及其穿过狭窄水道的衍射过程。通过分析孤立子内波垂向波形和水平二维纹理图像随水道口的形状及开阔水域宽度的变化．研究了侧边界对孤立子内波传播所产生的影响,并与卫星遥感图片进行了对比。     

先锋孤立子生成的理论平均波阻 Ⅱ.数值研究

基于fKdV方程系数的正则特性，以二维两层流的先锋孤立子生成问题为算例，用数值方法对本文部分（Ⅰ）中的理论平均波阻，能量劈分及能量劈分比进行检验。从理论与数值结果的比较知，理论与数值结果符合得很好。这表明本文部分（Ⅰ）中的理论平均波阻，能量劈分及能量劈分比可用于先锋孤立子生成参数的预报，也表明本文部分（Ⅰ）中的理论可推广应用于二维非线性强迫系统。     

南海北部陆坡内孤立波对桩柱作用力的极值推算

内孤立波的发生常伴随着大振幅波动和突发性强流,对桩柱等海中结构物产生强烈破坏作用。基于KdV方程和Morison公式,在忽略高阶模态的情况下,探讨内孤立波对桩柱的单位作用力、总作用力、剪力和弯矩的极值问题,并利用2016-07南海北部陆坡的实测资料对理论结果进行检验。结果表明:1)在内孤立波最大振幅所在的垂向剖面上,上层与下层各存在一个单位作用力极值,且二者方向相反,上层总作用力强于下层,最大剪力和弯矩分别发生于水平流速的转向层和海底;2)各水层中,沿着内孤立波的传播方向,所有作用力的数值均随时间的推移先递增后递减,存在正向或负向的最大值;3)全水层总作用力极值发生在半周期,其值与波动振幅和水平波速有关,其他作用力极值发生于最大振幅时刻之前,作用力极值与振幅和非线性波速正相关,与水平特征宽度负相关;4)单位作用力极值的时间提前量与振幅和水平特征宽度强相关,与非线性波速弱相关。     

海表外强迫效应对连续层化流体中先驱内孤立波生成的影响

移动的海面或海底强迫在共振条件下会向强迫上游周期性地生成内孤立波,这种内孤立波被称为先驱内孤立波。本文利用三维全非线性、全频散的非静力模型NHWAVE,模拟连续分层流体受到海面外强迫作用而产生的先驱内孤立波,研究了正负外强迫效应对先驱内孤立波生成过程和形态特征的影响。结果显示,负效应强迫作用下先驱内孤立波具有更长的生成周期,这与两层流体中的结论相同;在强迫区内部,正效应强迫使水体的等密度面维持较稳定的结构,而当强迫效应为负时,强迫区内水体的等密度面随时间起伏较大。在正负两种效应强迫作用下,流场均维持了逆时针的回流结构,不过在负效应强迫作用下,流场更为复杂。     

南极乔治王岛柯林斯冰帽小冰穹冰心地球化学初步研究

通过对南极乔治王岛柯林斯冰帽小冰穹冰心１００个样品的化学分析结果进行Ｒ型因子分析，将主要环境信息归结到四个因子上，解释总变量方差的９９．１７％．Ｆ１因子特征值为３．７７５，解释变量方差的４１．９５％，为Ｋ＋、Ｍｇ２＋、Ｃａ２＋、ＳＯ４２－组合，主要代表了陆源杂质的输入；Ｆ３因子特征值为３．３３８，解释变量方差的３７．０９％，为Ｎａ＋、Ｃｌ－、Ｂｒ－组合，代表了海源杂质的输入；Ｆ２因子特征值为１．０３０，解释变量方差的１１．４４％，代表ＮＨ４＋离子的输入；Ｆ４因子特征值为０．７８２，解释变量方差的８．６９％，代表ＮＯ３－离子的输入。通过考察代表不同环境的各因子的因子得分值随冰心深度的变化趋势，研究了可溶杂质输入随时间的变化关系。     

先锋孤立子生成的理论平均波阻(Ⅰ).理论

根据作者导得的AfKdV方程，理论上确定了先锋孤立子生成问题的理论平均波阻，能量劈分及能量劈分比。本文的能量劈分是确定先锋孤立子生成参数的理论基础。同时，本理论确定了现有理论中的自由未知参数问题，从而使先锋孤立子生成参数得到理论预报。     

Ricci孤立子的势函数

Bakry-Emery Ricci张量定义为Ricf=Ric+Hessf.特殊地,当光滑实值函数f为常数时,Bakry-Emery Ricci张量为Ricci张量,方程Ricf=ρg(ρ为常数)实际为梯度Ricci孤立子方程.本文应用Bakry-Emery Ricci张量与Riccati不等式来研究梯度Ricci孤立子...     

Solitons northeast of Tung-Sha Island during the ASIAEX pilot studies

In a recent study, satellite images have shown that internal solitons are active in the northern South China Sea (SCS). During the Asian Seas International Acoustic Experiment (ASIAEX) pilot studies, current profiler and thermistor chain moorings were deployed in the spring of 1999 and 2000 to investigate internal solitons northeast of Tung-Sha Island on the continental slope of the northern SCS. Most of the observed internal solitons were first baroclinic mode depression waves. The largest horizontal current velocity, vertical displacement, and temperature variation induced by the internal solitons were around 240 cm/s, 106 m, and 11/spl deg/C, respectively, while the estimated nonlinear phase speed was primarily westward at 152 /spl plusmn/ 4 cm/s. The observed internal solitons could be categorized as four types. The first type is the incoming wave from deep water and can be described reasonably well with the KdV equation. The second and third types are in the transition zone before and close to the turning point (where the upper and lower layer depths are equal), respectively. These two types of solitons were generally near the wave-breaking stage. The fourth type of soliton is a second baroclinic mode and probably was locally generated. The time evolutions are asymmetric, especially at the middle depths. A temperature kink following the main pulse of the soliton is often seen. Higher order nonlinear and shallow topographic effects could be the primary cause for these features. The appearance/disappearance of internal solitons coincides mostly with spring/neap tide. The internal soliton is irregularly seen during the neap tide period and its amplitude is generally small. The time interval between two leading solitons is generally around 12 h. The first baroclinic mode of the semidiurnal tide has a larger amplitude than the diurnal tide and could redistribute its energy into the soliton.     

超高速光孤子传输特性分析及数值模拟

通过数值解非线性耦合薛定谔方程 ,研究高速光孤子通信系统中高阶色散和偏振模色散对孤子传输的影响 ,并数值模拟孤子在单模光纤中的演变。研究结果表明 :偏振模色散导致孤子脉冲展宽、峰值功率下降、峰值点随传输距离漂移 ;高阶色散和偏振模色散使孤子加速展宽、脉冲沿出现非对称的振荡结构 ,脉冲峰值点随传输距离的漂移而发生改变     

Breaking solitary wave evolution over a porous underwater step

Solitary wave evolution over a shelf including porous damping is investigated using Volume-Averaged Reynolds Averaged Navier–Stokes equations. Porous media induced damping is determined based on empirical formulations for relevant parameters, and numerical results are compared with experimental information available in the literature. The aim of this work is to investigate the effect of wave damping on soliton disintegration and evolution along the step for both breaking and non-breaking solitary waves. The influence of several parameters such as geometrical configuration (step height and still water level), porous media properties (porosity and nominal diameter) or solitary wave characteristics (wave height) is analyzed. Numerical simulations show the porous bed induced wave damping is able to modify wave evolution along the step. Step height is observed as a relevant parameter to influence wave evolution. Depth ratio upstream and downstream of the edge appears to be the more relevant parameter in the transmission and reflection coefficients than porosity or the ratio of wave height–water depth. Porous step also modifies the fission and the solitary wave disintegration process although the number of solitons is observed to be the same in both porous and impermeable steps. In the absence of breaking, porous bed triggers a faster fission of the incident wave into a second and a third soliton, and the leading and the second soliton reduces their amplitude while propagating. This decrement is observed to increase with porosity. Moreover, the second soliton is released before on an impermeable step. Breaking process is observed to dominate over the wave dissipation at the porous bottom. Fission is first produced on a porous bed revealing a clear influence of the bottom characteristics on the soliton generation. The amplitude of the second and third solitons is very similar in both impermeable and porous steps but they evolved differently due to the effect of bed damping.     

Collisions Between Lumps/Rogue Waves and Solitons for A (3+1)-Dimensional Generalized Variable-Coefficient Shallow Water Wave Equation

In this paper, we investigate a (3+1)-dimensional generalized variable-coefficient shallow water wave equation, which can be used to describe the flow below a pressure surface in oceanography and atmospheric science. Employing the Kadomtsev-Petviashvili hierarchy reduction, we obtain the semi-rational solutions which describe the lumps and rogue waves interacting with the kink solitons. We find that the lump appears from one kink soliton and fuses into the other on the x−y and x−t planes. However, on the x−z plane, the localized waves in the middle of the parallel kink solitons are in two forms: lumps and line rogue waves. The effects of the variable coefficients on the two forms are discussed. The dispersion coefficient influences the speed of solitons, while the background coefficient influences the background’s height.

     

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.