Boltzmann statistical theory and asymptotics of the temperature distribution of spontaneous jets in the convective atmospheric surface layer

An ensemble of convective thermals is distinguished from the surface layer of penetrative turbulent convection over a heated horizontally uniform surface. A statistical model of the ensemble of convective thermals is developed that uses the idea of entropy in the Boltzmann-Jaynes form. The distribution of thermals by potential energies is shown to display an entropy maximum. On the basis of the Boltzmann distribution by potential energies, the temperature distribution of spontaneous jets is obtained and found to be consistent with known experimental data.     

Surface Elevation Distribution of Sea Waves Based on the Maximum Entropy Principle

A probability density function of surface elevation is obtained through improvement of the method introduced by Cieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distribution. The density function can be easily extended to higher order according to demand and is non-negative everywhere, satisfying the basic behavior of the probability. Moreover because the distribution is derived without any assumption about sea waves, it is found from comparison with several accepted distributions that the new form of distribution can be applied in a wider range of wave conditions. In addition, the density function can be used to fit some observed distributions of surface vertical acceleration although something remains unsolved.     

海洋的比熵和等熵分析

基于海水热力学局域平衡的假定及Feistel(2003,2005)给出的海水Gibbs热力学势函数表达式,利用全球海洋观测数据,计算了全球海洋网格域的比熵、位温、位密等热力学参数,分析了海水比熵的时-空分布格局及其与位温、位密以及中性面之间的关系。分析结果表明,海洋中的比熵与位温之间具有确定的解析关系,而海洋中的比熵与位密、中性面之间的分布则无明显的一致性;这一结论为文章进一步导出海洋内部近似稳态大尺度地转环流在等熵面上的流函数,证明等熵面与等密面的交线即物理海洋学上经典的动力计算方法中的Montgomery流函数,进而为海洋内部的准地转运动的等熵-等密分析提供了新的热力-动力学依据。     

用小波变换研究赤道西太平洋温度细结构

使用小波变换分析了赤道西太平洋暖池区的CTD资料的温度序列,表明垂向温度细结构具有自相似特征,有可能使用分数维模型来描述.计算了温度序列的奇异性指数及其概率分布,发现此分布具有近似普适的形式.非零概率的负指数意味着温度剖面可能存在奇异点.对经小波变换后的序列的周期性统计表明周期△和尺度α遵从幂律标度△～αβ,β≈1.这提示着细结构背后可能存在简单的二分串级机制.小波变换的振幅反映了温度脉动的强弱.据此可以确定脉动能量的垂向分布和能谱密度,和传统方法的比较表明小波能谱较为光滑,有利于精确测定谱斜率.     

Study of fine structure of temperature in the equatorial westernPacific Ocean with wavelet transform

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A static drilling riser model using free boundary conditions

A static three-dimensional analytical method for drilling risers experiencing large displacements and slip at the top joint is presented. The riser is described in cylindrical coordinates as a three-dimensional tensioned string, without bending or torsional stiffness. The vertical vessel displacement is not taken into account. The equilibrium configuration is obtained from the stationary condition of the total potential energy functional. Kinematic boundary conditions are introduced for the radial displacement only. The riser orientation at the top directly follows from the natural boundary conditions based on the variational treatment of the energy functional.     

Non-linear effects of the statistical model of shallow-water wind waves

This study deals with the non-linear effects of shallow-water wind waves. It is assumed that wind waves are an ergodic, random process, quasi-normal, stationary in time and homogeneous in space. The probability density function of sea surface oscillations is approximated by Gram-Charlier series in a modified form due to Edgeworth. Based on the above assumptions and on the fundamental statistical and stochastical laws the author has obtained the following characteristics: the probability density functions of wave heights, wave phases and velocity of the point mean wave height and mean wave length. The derived formulae are compared by the experimental data of the international expedition ‘Lubiatowo-74’. The analysis carried out has shown that real waves and the Gaussian model contradict considerably.     

一种新的非线性波浪周期概率分布

在最大熵原则的基础上,通过解一条件变分问题,导出一种新的适用于描述非线性波浪周期T统计分布的概率密度函数.这种概率分布有如下的优越性:(1)该分布的参数是由无因次周期的m(m为正数)阶分布矩得出,从而周期的信息熵达到最大,故适用于描述波浪周期的非线性;(2)该分布有4个参数,从而更能符合最大熵原则;(3)该分布形式简单...     

Statistics of fluctuations in high-frequency low-grazing-angle backscatter from a rocky sea bed

This paper examines the fluctuations in low-grazing-angle 100-kHz backscatter from a rocky limestone sea bed near Copenhagen, Denmark, at horizontal ranges up to 420 m. The sea-bed reverberation was characterized by strong short spatial-scale variations in scattering strength and statistical parameters. The measured areal backscatter strengths were in the range from -50 to -24 dB at grazing angles less than 3/spl deg/, showing a strong local variability and grazing-angle dependence definitely not in accordance with Lambert's law. The observed echo-amplitude distributions varied between log-normal and Rayleigh models, with more Rayleigh-like probability density functions having higher scintillation indices and skewness (approaching values of 1.0 and 0.63, respectively). The scintillation index and skewness parameters were found to increase mildly with both horizontal range and water-current magnitude. A simple model using the coherent superposition of multiple scatterers was proposed to explain the observed scattering statistics. This model is based on the assumption that the sea bed is effectively immobile, with water-borne scintillation and micro-multipaths providing fluctuations in scatterer phase. This simple model shows that echo-amplitude fluctuations can deviate from the Rayleigh model through two mechanisms: 1) decreasing the levels of water-borne phase fluctuation and 2) increasing the nonuniformity of the sea-bed scatterer amplitudes.     

A Semi-Analytical Method for the PDFs of A Ship Rolling in Random Oblique Waves

The PDFs (probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA (2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship''s manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas.     

Measuring information content from observations for data assimilations: connection between different measures and application to radar scan design

The previously derived formulations for using the relative entropy and Shannon entropy difference ( SD ) to measure information content from observations are revisited in connection with another known information measure—degrees of freedom for signal, which is defined as the statistical average of the signal part of the relative entropy. For a linear assimilation system, the statistical average of the relative entropy reduces to the SD . The formulations are extended for four-dimensional variational data assimilation (4DVar). The extended formulations reveal that the information content increases (or decreases) as the model error increase (or decrease) and/or become strongly (or weakly) correlated in 4-D space. These properties are also highlighted by illustrative examples, and the extended formulations are shown to be potential useful for designing optimum phased-array radar scan configurations to maximize the extractable information contents from radar observations by a 4DVar analysis system.     

渤海及黄海北部年极值冰厚概率分布的统计分析

采用渤海及黄海北部后报30a最大冰厚样本序列,采用平稳二项随机过程模型和组合概率分析方法,统计得到了年最大冰厚概率分布,估计了模型参数,并推算了不同重现期的极值冰厚.推算结果表明,该模型较好地刻划了该海域年最大冰厚的概率特性,为渤海海域平台结构设计和可靠性分析提供了重要的荷载基础.     

利用TOPEX卫星高度计资料分析东中国海的风、浪场特征

利用TOPEX卫星高度计和日本气象厅浮标观测资料,对东中国海的有效波高和风速进行比较,分析了卫星高度计资料的有效性。利用有效波高和风速的3种概率密度函数分布,结合TOPEX卫星高度计资料,并采用最大似然方法对统计分布参数进行估计,结果表明,有效波高的对数-正态概率密度分布与观测资料的直方图在有效波高的整个范围内符合较好,风速的直方图与Weibul概率密度分布符合较好。同时,分析了有效波高大于4 m的巨浪在东中国海的时空分布特征,表明巨浪多出现在冬、秋两季,平均有效波高最大值出现在夏季,且主要分布在东中国海东南部。     

Optimal Perturbations with Zero Potential Vorticity in the Eady Model

The problem of finding optimal perturbations, which are perturbations with a maximum ratio of the final energy to the initial energy, is considered in the Eady model of baroclinic instability. The solution to the problem uses explicit expressions for the energy functional, which are functions of parameters of an initial perturbation. For perturbations with zero potential vorticity, the basic parameters are the amplitudes of the initial buoyancy distributions at the boundaries of the atmospheric layer and a phase shift between these distributions. Dependences of the optimal phase shift and maximum energy ratio on the wave number and time optimization are determined using an analysis for extremum. The parameters of the optimal perturbations are compared with those of the growing normal modes. It is found that only one exponentially growing mode is an optimal perturbation.     

Wave energy assessment based on trivariate distribution of significant wave height,mean period and direction

Based on the Vine copula theory, a trivariate statistical model of significant wave height, characterized wave period and mean wave direction was constructed. To maintain the properties of the different types of variables, a special copula function was derived from the model developed by Johnson and Wehrly based on the maximum entropy principle. It was then combined with the Archimedean copulas to construct the proposed model. An effective algorithm for generating corresponding joint pseudo-random numbers was also developed. Statistical analysis of hindcast data for the significant wave height, mean wave period, and direction, which were collected from an observation point in the North Atlantic every three hours from 1997 to 2001, was performed. The marginal distributions of the significant wave height and mean wave period were fitted by a modified maximum entropy distribution, and the mean wave direction was fitted by a mixture of von Mises distributions. It was shown that the proposed model is a good fit for the data. The seasonal wave energy resources in the target area were assessed using the model estimates. Histograms of the directional wave energy, wave energy roses, and scatter and energy diagrams were presented.     

Nonlinear effects on the distribution of crest-to-trough wave heights

The statistical distribution of the crest-to-trough heights of narrowband nonlinear sea waves is derived in a semi-closed form. A quantitative comparison of the resulting density and exceedance probability distributions with those of the linear theory is given. It is shown that the nonlinearity of waves, even with steepnesses typical of extreme sea states, has an insignificant influence on the distribution of crest-to-trough heights.     

Effects of spectrum band width on the distribution of wave heights and periods

The statistical distribution of the crest-to-trough heights of narrowband nonlinear sea waves is derived in a semi-closed form. A quantitative comparison of the resulting density and exceedance probability distributions with those of the linear theory is given. It is shown that the nonlinearity of waves, even with steepnesses typical of extreme sea states, has an insignificant influence on the distribution of crest-to-trough heights.     

海浪的特征波陡

在现有的海浪要素统计分布的理论框架下具体地推导了二维海浪波良与波长的联合统计分布,波长统计分布以及波陡的统计分布,在此基础上对上特征波陡的定义及期 承风要素的变化规律做了较为细致的讨论。     

On several mechanisms of the formation of the compensated thermohaline inhomogeneities in the ocean

The process of the geostrophic adjustment in the stably stratified two-component medium is studied in the framework of a linear approximation. We demonstrate that, at the final stage of that process, a stationary trace is generated by the distribution of the temperature and salinity, whose horizontal inhomogeneities mutually compensate in the field of the density. The compensation level for the stationary thermohaline distributions forming during the geostrophic adjustment is estimated. The origination mechanism of compensated thermohaline inhomogeneities in hydrodynamically stable shear flows is examined. We show that, in such flows, the disturbances of the fields of buoyancy (density), pressure, and velocity damp with time, whereas the compensated disturbances of the fields of the temperature and salinity are carried off by the flow without damping. Based on the explicit solutions of the dynamic equations, it is shown that the evolution of the compensated distribution of the temperature and salinity in the shear flows usually results in the sharpening of the spatial gradients. This feature may be, among others, related to one of the factors of the origination of the fine structure of the ocean: the small-scale thermohaline inhomogeneities, which exist against the background of the smooth vertical distribution of the density.