湍流边界层中固体小颗粒湍流运动的Lagrangian模型

给出了固体小颗粒在边界层中的Lagrangian运动方程,方程中包括受壁面影响的粘性阻力,Saffman升力及Magus升力等.使用频谱法,得到了颗粒响应流体的Lagrangian能谱的表达式,使用这些结果研究了各种响应特性.本文的结果清楚地表明了固体个颗粒在湍流扩散过程中,其湍流扩散是可能大于流体的.     

粉尘在湍流中随机扩散预报模型

本文将概率论和统计应用于环境保护工程，研究有重力作用的粉尘粒子在湍流中随机扩散，计及了气流速度的相关性，建立了粒子随机运动方程，利用Ｍｏｎｔｅ－Ｃａｒｌｏ方法构造出非线性方程的数值算法，推导出线性方程的解析解。经过实例计算表明，数值和解析联合算法的计算量小，预报精确度高，有较高的工程实用价值。     

沉淀固体微粒的湍流扩散

由于安装在玻璃粉末沉淀床上方的格栅的振动产生湍流运动。在格栅作用下,沉淀的部分玻璃粉末浮动上升,在格栅上方形成深度为D的湍流悬浮层,而其上部为一非湍流的静止的流体层。体积浓度的测量结果表明,在深度方向上仅有较弱的浓度梯度,并且在层外缘浓度迅速减小至零。基于浓度流量模型的理论分析与实验结果符合良好。     

不可压缩均匀各向同性湍流的统计理论

本文根据均匀各向同性湍流的涡旋结构理论,从Navier-Stokes方程出发,引进了准相似性条件,认为均匀各向同性湍流场在衰变过程中具有相似性,相似性尺度由表征湍流强弱的湍流脉动速度均方差q以及与特征涡旋尺度具有密切关系的湍流广义Taylor微尺度λ所决定,在对均匀各向同性湍流场计算中,假定湍流脉动在空间呈周期性,周期性尺度正比于λ。 本文对脉动速度等物理量用Fourier级数展开,将在物理空间上的计算转化到谱空间上,利用快速Fourier变换,采用前差格式和Leap-frog格式,对不同Reynolds数的均匀各向同性湍流场从衰变后期到前期进行了计算,得出了与实验较符合的结果。     

可压缩均匀各向同性湍流的直接数值模拟

采用8阶精度的中心差分格式及7阶精度的迎风偏斜格式对Re_l = 72~153, M_t= 0.2~0.7的均匀各向同性湍流进行了直接数值模拟, 建立了湍流数据库. 与他人的计算结果吻合十分理想, 说明方法的有效性. 数值结果表明, 采用适当的迎风型差分格式可以克服起动问题(start-up problem)对湍流Mach数的限制, 提高可计算的湍流Mach数, 是可压湍流直接数值模拟的有效方法. 分析了压缩性效应对湍流统计量的影响, 发现压缩性使得湍动能的衰减加快. 探讨了可压湍流中微激波产生的机理, 对流场进行了标度律分析. 发现在本文的Reynolds数和湍流Mach数条件下, 流场中扩展自相似性仍然成立, 同时发现压缩性对标度指数影响不大.     

悬浮固粒和密度界面上粒子覆盖层对湍流扩散的影响

本文实验研究了两层流体之间的密度界面上的粒子覆盖层和上层湍流混合层中的悬浮粒子对湍流扩散的影响。实验结果表明,其影响是显著的。湍流扩散距离D以时间t的k次幂变化:D=Bt^k,其中k与覆盖层的相对厚度(?)_p有关即(?)=0.200—0.130(?)_p;对于上层有悬浮粒子和纯两层流体,(?)_p为零,k为0.200,两者D的变化规律一样,只是有悬浮粒子的k值较纯两层流体的小。湍流的无量纲扩散速率可归结为E=KR_il^-n,这里n=1.5+0.93(?)_p,(?)_p越大E值下降越快。这说明覆盖层改变了扩散速率的指数变化律,对湍流扩散有较大的阻碍作用。悬浮粒子的作用只是减小K值,其E的变化规律同纯两层流体的一样。本文还对湍流混合和扩散机制作了讨论。     

线性密度分层流体中垂向湍流扩散的势能模型

本文研究在线性密度分层流体系统中垂向密度界面的无平均剪切湍流扩散规律,从分析湍流动能方程出发,提出一种湍流扩散的势能模型,得到湍流扩散距离随时间的变化以及无量纲扩散速率与当地Richardson数的关系.同时进行了实验检验,其结果与理论预测符合良好.     

颗粒湍能输运方程的两相湍流模型和平面闭式两相射流的数值模拟

在现有的两相湍流数值模拟中,对颗粒湍流普遍采用以局部追随概念为基础的代数模型,其预报结果在很多情况下与实验不符。本文提出了以颗粒湍能输运方程为基础的κ-ε-kκ两相湍流模型,并以平面闭式两相射流为例进行了数值模拟,预报结果与实验符合良好,表明此模型明显优于k-ε-A.P.的颗粒湍流代数模型。     

非均匀的有限信息扩散函数的探索及应用

小样本的信息处理和分析一直是金融、信息、地震灾害等众多领域中的热点问题．本文运用一维非均匀的有限信息扩散函数（GIDM）方法对小样本问题进行处理，并通过应用于一个实际问题来进行验证，首先根据非均匀信息扩散选取扩散函数，并利用McCormack方法求得其数值解。进而按照优化的准则优化后与大样本进行比较，取得了较理想的结果．     

两层流体系统中含有悬浮粒子无平均剪切湍流混合层的增长

本文对两层流体系统中含有粒子的无平均剪切湍流混合层的增长(扩散)行为,进行了实验研究和理论分析,并提出一个估计湍流混合层扩散速率的理论方法,即势能模型。这种模型还包含了纯两层流体的湍流扩散的结果。实验结果与该模型符合很好。混合层中含有粒子时扩散距离D随时间t的变化、无因次扩散速率E与Richardson数及Ri₁的关系均与纯两层流体的相同,但还与初始体积浓度(?)₀有关,D和E分别以的负1/5和负1次幂变化。     

Hexagonal Fourier-Galerkin Methods for the Two-Dimensional Homogeneous Isotropic Decaying Turbulence

In this paper, we propose two hexagonal Fourier-Galerkin methods for the direct numerical simulation of the two-dimensional homogeneous isotropic decaying turbulence. We first establish the lattice Fourier analysis as a mathematical foundation. Then a universal approximation scheme is devised for our hexagonal Fourier-Galerkin methods for Navier-Stokes equations. Numerical experiments mainly concentrate on the decaying properties and the self-similar spectra of the two-dimensional homogeneous turbulence at various initial Reynolds numbers with an initial flow field governed by a Gaussian-distributed energy spectrum. Numerical results demonstrate that both the hexagonal Fourier-Galerkin methods are as efficient as the classic square Fourier-Galerkin method, while provide more effective statistical physical quantities in general.     

The n-Wave Procedure and Dimensional Regularization for the Scalar Field in a Homogeneous Isotropic Space

We obtain expressions for the vacuum expectations of the energy–momentum tensor of the scalar field with an arbitrary coupling to the curvature in an N-dimensional homogeneous isotropic space for the vacuum determined by diagonalization of the Hamiltonian. We generalize the n-wave procedure to N-dimensional homogeneous isotropic space–time. Using the dimensional regularization, we investigate the geometric structure of the terms subtracted from the vacuum energy–momentum tensor in accordance with the n-wave procedure. We show that the geometric structures of the first three subtractions in the n-wave procedure and in the effective action method coincide. We show that all the subtractions in the n-wave procedure in a four- and five-dimensional homogeneous isotropic space correspond to a renormalization of the coupling constants of the bare gravitational Lagrangian.     

Representation of Isotropic Turbulence by Scalar Functions

The maximum number N(n) of scalar functions of wavevector needed to represent the general cumulant of order n of isotropic turbulence is determined. In addition to reproducing the known results that N(2) = 1, N(3) = 2, it is shown that N(4) = 4, N(5) = 4, N(6) = 9, etc.     

Hardy Spaces of Harmonic Functions on Homogeneous Isotropic Trees

A variational method for operator equations of the form Pu + δβ(u) ? f has been given in Dinca [1]. Here P is a (generally) nonlinear operator in a Hilbert space, β: H → ? ∞ is a convex, proper (β ≠ + ∞) and lower-semicontinuous functional and δβ(u) stands for the subdifferential of β at the point u. The present paper has two parts. The first part contents the main results of Dinca [1] without proofs. The second part discusses particular cases and applications to mechanics among which “the climatisation problem for non-linear elliptic equations” and its applications.     

Bergman Spaces and Carleson Measures on Homogeneous Isotropic Trees

Hastings studied Carleson measures for non-negative subharmonic functions on the polydisk and characterized them by a certain geometric condition relative to Lebesgue measure σ. Cima & Wogen and Luecking proved analogous results for weighted Bergman spaces on the unit ball and other open subsets of \(\mathbb {C}^{n}\). We consider a similar problem on a homogeneous tree, and study how the characterization and properties of Carleson measures for various function spaces depend on the choice of reference measure σ.     

SH Waves in a Homogeneous Transversely Isotropic Medium Generated by a Concentrated Force

SH waves in homogeneous, transversely isotropic media generated by a concentrated force are investigated. To this end, we construct the part of the Green tensor responsible for SH waves and derive its asymptotics at large distances from the source point. Bibliography: 7 titles.     

Asymptotics of the Wave Field in the Vicinity of the Symmetry Axis of a Transversely Isotropic Homogeneous Medium

Asymptotic formulas for the wave field, which describe the kiss singularity in a homogeneous transversely isotropic medium, are obtained. A physical interpretation of the results is presented. Bibliography: 10 titles.     

A Reversible Nearest Particle System on the Homogeneous Tree

We introduce a modified contact process on the homogeneous tree. The modification is to the death rate: an occupied site becomes vacant at rate one if the number of occupied id neighbors is at most one. This modification leads to a growth model which is reversible, off the empty set, provided the initial set of occupied sites is connected. Reversibility admits tools for studying the survival properties of the system not available in a nonreversible situation. Four potential phases are considered: extinction, weak survival, strong survival, and complete convergence. The main result of this paper is that there is exactly one phase transition on the binary tree. Furthermore, the value of the birth parameter at which the phase transition occurs is explicitly computed In particulars survival and complete convergence hold if the birth parameter exceeds 1/4. Otherwise, the expected extinction time is finite.     

Using the Evolution Operator Method to Describe a Particle in a Homogeneous Alternating Field

Using the evolution operator method, we construct coherent states of a nonrelativistic free particle with a variable mass M(t) and a nonrelativistic particle with a variable mass M(t) in a homogeneous alternating field. Under certain physical conditions, they can be regarded as semiclassical states of particles. We discuss the properties (in particular, the completeness relation, the minimization of the uncertainty relations, and the time evolution of the corresponding probability density) of the found coherent states in detail. We also construct exact wave functions of the oscillator type and of the plane-wave type for the considered systems and compute the quantum Wigner distribution functions for the wave functions of coherent and oscillator states. We establish the unitary equivalence of the problems of a free particle and a particle in a homogeneous alternating field.