一些有关特殊组合数的恒等式

在Faàdi Bruno公式和Lagrange反演公式的基础上,得到一些有关Bell数和第二类Stirling数的恒等式。     

有效声速泰勒级数逼近的适用条件

在水下高精度声学定位和声纳水深测量中,需要高精度的有效声速参量。在实际中,精确计算有效声速需要声线跟踪算法,但计算成本较高。有效声速的泰勒级数逼近作为一种有效声速的近似逼近方法,可避免大量计算成本。讨论了有效声速泰勒级数逼近公式的不同阶数逼近情况,特别是给出了两类有效声速泰勒级数逼近公式的适用条件,以及他们随高度增大适用性和逼近精度的变化。研究表明,当声速剖面稀疏时,宜采用谐波平均声速下的泰勒级数改正公式;当高度角小于50°时,有效声速泰勒级数逼近精度出现明显的衰减。     

扁球重力场的水准面方程和重力公式

文章论述了扁球水准面方程和重力公式的级数表示方法。论证了它们和重力位函数的级数展开精度的关系,指出水准面方程和重力公式应取决于重力位的级数展开精度,推导重力公式时必须与重力位保持精度一致.否则将出现矛盾和错误。 文章还讨论了扁球水准面形状与正常位系数的关系,指出水准面的中纬度隆起与J_4有关(见文中(17)式),因此Bruns扁球不存在=45°处隆起的问题,Bruns正常重力公式中也不应出现β_1sin~2项,从而对一类正常重力公式的正确性提出了疑问。     

辅助纬度反解公式的Lagrange级数法推演

对地图投影理论中经常遇到的等距离纬度、等量纬度和等面积纬度的反解公式进行了新的研究。利用Lagrange级数公式,借助计算机代数系统强大的数学分析功能,全面给出了这些纬度用椭球偏心率幂级数形式表示的反解公式。与以往数值形式表示的反解展开式不同,这些反解公式是以符号形式给出。研究表明计算机代数系统的应用不但极大地提高了公式推演的效率和准确度,而且反解系数从此可以表示为更简单和更便于记忆的符号形式。     

Stirling数的概率表示的新应用

运用两类Stirling数的概率表示得到两类Stirling数的一些特殊值,证明并得到了一些有关两类Stirling数的新的递推公式和恒等式,从而丰富发展了孙平、王天明关于“Stirling数的概率表示和应用”中的内容。     

错排数的概率表示的新应用

利用孙平和王天明给出的错排数的概率表示,得到有关错排数的递推公式新的证明方法,并得到有关错排数的一些新结果.     

三轴椭球表面积的近似计算

推导出了一组三轴椭球表面积近似计算的级数展开公式,并对应地给出了三轴椭球退化为扁椭球和旋转椭球时的表面积公式。该组公式通过引入偏心率、第三扁率等扁率,使公式结构上更为简洁,具有对称性,进一步完善了椭球表面积的计算理论。验算分析表明,相比于传统的近似公式,给出的近似计算公式的精度显著提高,具有实用价值。     

数学形态学的合并综合算子研究

针对当前地图综合算子的研究难点,引入了数学形态学相关理论,建立了基于形态学的合并综合算子模型.并利用建立的合并算子,结合矢量数据模型和栅格数据模型的相互转化,进行了街区的合并实验,取得了较好的效果.     

有限水深中零航速浮体波浪力计算奇点积分的数值处理方法

使用三维源汇分布法Ⅲ计算有限水深中零航速浮体所受到的波浪力,对两种不同形式的格林函数中所共同存在的奇点问题分别进行了处理。公式推导表明,使用级数形式的格林函数可以使计算更加快捷。最后,对不同尺度的圆柱体进行了验算,在对计算结果与解析解进行了比较之后,工程计算也证明选择格林函数级数计算公式是更令人满意的方案。     

浮冰在规则波和双色波下的运动特性研究

为研究浮冰在波浪下的运动特性,以单个聚氯乙烯（PVC）塑料圆板模拟浮冰,进行了一系列波浪试验研究。在规则波试验基础上,同时研究了双色波条件下的浮冰运动特性。结果显示：规则波条件下浮冰运动幅频响应算子首先随无量纲波长的增大而增大,当无量纲波长大于4.0后,运动幅频响应算子随无量纲波长的变化不明显,且趋于一定值;在双色波条件下,对应频率组成成分的浮冰运动幅频响应算子与规则波条件下随波长的变化规律一致。根据部分规则波试验结果提出预测浮冰慢漂速度的经验公式,并用已有的试验和余下的规则波与双色波试验结果进行验证。结果表明,经验公式对规则波和双色波条件下的浮冰慢漂速度的误差在20%以内,预测结果吻合较好。     

Outer wave number spectrum and statistical distribution of apparent wave number vector

Based on the ray theory and Longuet-Higgins’s linear model of sea waves, the joint distribution of wave envelope and apparent wave number vector is established. From the joint distribution, we define a new concept, namely the outer wave number spectrum, to describe the outer characteristics of ocean waves. The analytical form of the outer wave number spectrum, the probability distributions of the apparent wave number vector and its components are then derived. The outer wave number spectrum is compared with the inner wave number spectrum for the average status of wind-wave development corresponding to a peakness factor P = 3. Discussions on the similarity and difference between the outer wave number spectrum and inner one are also presented in the paper.     

沉积物中水合物含气量测定方法

建立了沉积物中水合物含气量的测定方法;测定了人工松散沉积物中甲烷水合物、南海神狐海域及祁连山冻土区天然气水合物样品的含气量;计算了样品的表观水合指数(水与气体的摩尔比);探讨了水合物含气量的影响因素.测试结果表明,人工甲烷水合物样品表观水合指数与晶体水合指数相近,样品中水合物的浓度大,含气量较高;南海神狐海域及祁连山冻...     

鹰爪虾染色体数目与核型的研究

于１９９０年,１９９４年,１９９７年每年４－７月,在青岛石老人沿海采集爪虾样品,以精巢,胚胎及无节幼体为材料进行染色体的数目及核型的研究。染色体的制备均采用干法,用Ｏｌｙｍｐｕｓ显微镜进行观察,依据Ｌｅｖａｎ等的分类标准进行核型分析。     

安全管道判断算法及其优化

结合射线法和环绕计数法的优点,提出了有向穿越计数算法,该算法更加高效且容易实现,可作为安全管道判断的首选方法。对3种特定类型的安全管道进行了有针对性的优化,其中单调多边形管道的时间复杂度提升到了O(log n)级别;通过建立基于概率分布的简单外部或内部边界,在绝大多数情况下只需一次判断,优化了平均时间复杂度;通过改变顶点排列顺序,将有向穿越计数算法扩展到环形管道。     

Characteristics of Parameters for Local Scour Depth around Submarine Pipelines in Waves

The purpose of this study is to investigate the characteristics of parameters for local scour depth around submarine pipes due to waves. Because it is impossible to consider all the factors that influence the scour, it is reasonable to investigate the correlations between parameters and scour. The experimental works about scour were performed for the conditions of 40, 60, 90 m pipe diameter, various wave periods, and wave height in the case of horizontal bed and 1/10 slope bed, respectively. Analyzing the results of experiments, the Reynolds number, Shields parameter, Keulegan-Carpenter number, Ursell number, and Modified Ursell number were estimated. The correlations between the relative scour depth, which is the maximum equilibrium local scour depth divided by the pipe diameter, and 5 parameters were analyzed. It was shown that there was hardly any correlation with the Reynolds number. In the case of a horizontal bed, the Keulegan-Carpent number had the highest correlation, but in the case of the slope bed the correlation was greatly reduced. The modified Ursell number showed a high correlation regardless of the type of bed.     

Sediment movement under unidirectional flows: an assessment of empirical threshold curves

A selection of threshold data sets from previous investigations is used to re-examine, selectively, some of the empirical curves that are most commonly used for the prediction of sediment threshold. Simple analytical formulae are derived describing single line curves for mean threshold values and envelopes for the initial movement of discrete particles and the commencement of mass sediment transport phases of the critical condition.The complexity of factors governing the prevailing conditions at threshold, together with the randomness of events, limits deterministic solutions; however, the curves provide an approach that can be used readily in practical applications. In contrast, the envelope presentation is more of a stochastic approach to the definition of threshold. It recognises that there is no definitive threshold condition under which a particular particle size can be displaced, but rather that a range of threshold values exist.The empirical threshold relationships were derived on the basis of a relatively large amount of data. However, the sources utilised have interpreted the ‘critical condition’ in various ways, implying that the formulae must be treated with caution in applications.     

海洋盐指演化过程的数值模拟

盐指现象的数值模拟研究对理解小尺度海洋动力学过程具有十分重要的意义。本文建立了二维方腔模型,通过有限体积法求解控制方程,对盐指现象的演化过程进行了模拟计算和数值分析,在热瑞利数为(1.12～2.24)×107的变化范围内,展示并对比了不同粘滞系数、热瑞利数和盐瑞利数情况下的盐指现象,发现随着粘滞系数的增加,盐指的演变速率变慢,生成数目减少;热瑞利数的增加对盐指的演变速率具有抑制作用,而盐瑞利数的增加则对其具有促进作用。     

山东沿海浮游植物的同化系数

应用~(14)C示踪的方法,对山东沿海的13个海区浮游植物的同化系数进行了比较全面的测定和计算。指出不同海区和不同季节同化系数存在着明显的变化。提出不同海区季和年平均值的变化范围,以及垂直变化规律的特点。     

Reynolds number dependence of mixing in a lock-exchange system from direct numerical and large eddy simulations

Turbulent mixing of water masses of different temperatures and salinities is an important process for both coastal and large-scale ocean circulation. It is, however, difficult to capture computationally. One of the reasons is that mixing in the ocean occurs at a wide range of complexity, with the Reynolds number reaching , or even higher.In this study, we continue to investigate whether large eddy simulation (LES) can be a reliable computational tool for stratified mixing in turbulent oceanic flows. LES is attractive because it can be times faster than a direct numerical simulation (DNS) of stratified mixing in turbulent flows. Before using the LES methodology to compute mixing in realistic oceanic flows, however, a careful assessment of the LES sensitivity with respect to Re needs to be performed first. The main objectives of this study are: (i) to investigate the performance of different LES models at high Re, such as those encountered in oceanic flows; and (ii) to study how mixing varies as a function of Re. To this end, as a benchmark we use the lock-exchange problem, which is described by unambigous and simple initial and boundary conditions. The background potential energy, which accurately quantifies irreversible mixing in an enclosed system, is used as the main criterion in a posteriori testing of LES.This study has two main achievements. The first is that we investigate the accuracy of six combinations of two different classes of LES models, namely eddy-viscosity and approximate deconvolution types, for 3×10³Re3×10⁴, for which DNS data is computed. We find that all LES models almost always provide significantly more accurate results than cases without LES models. Nevertheless, no single LES model that is persistently superior to others over this Re range could be identified. Then, an ensemble of the four best performing LES models is selected in order to estimate mixing taking place in this system at Re=10⁵ and 10⁶, for which DNS is presently not feasible. Thus the second achievement of this study is to quantify mixing taking place in this system over an Re range that changes by three orders of magnitude. We find that the background potential energy increases by about 67% when Re is increased from Re=10³ to Re=10⁶, within the computation period, with the most significant increase taking place from Re=3×10³ to Re=10⁵.     

海浪外观统计与内部结构关系的数值研究

基于数值模拟的三维随机海面,从时间域和空间域两个角度对海浪的外观特征和内部结构间的关系进行了研究,得出了一些在工程应用上有参考价值的结果.文章认为,将波面看作是若干随机正弦波叠加的海浪结构模型,用于描述平稳、均匀和窄谱的海况时,其频谱分析结果与外观统计结果基本上是一致的;但是,当海面处于谱宽度较大的风浪或混合浪状态时,一些频谱分析结果必须经过修正才能应用.同一海况下,海面波动的时间过程和沿主波向的空间分布是明显不同的.当海面有突发性大浪时,外频谱能够很好地反映不平稳海况,而频谱则把这种不平稳性平滑了.文章着重讨论了波长和波陡的计算、频谱和外频谱的差异.