Langevin equation of a fluid particle in wall-induced turbulence

We derive the Langevin equation describing the stochastic process of fluid particle motion in wall-induced turbulence (turbulent flow in pipes, channels, and boundary layers including the atmospheric surface layer). The analysis is based on the asymptotic behavior at a large Reynolds number. We use the Lagrangian Kolmogorov theory, recently derived asymptotic expressions for the spatial distribution of turbulent energy dissipation, and also newly derived reciprocity relations analogous to the Onsager relations supplemented with recent measurement results. The long-time limit of the derived Langevin equation yields the diffusion equation for admixture dispersion in wall-induced turbulence.     

应用谱理论研究压力脉动的湍流模式

本文应用谱分析理论研究了剪切湍流场中的压力脉动,包括功率谱、均方值等.通过对压力脉动Possion方程的Fourier变换,首先将压力脉动谱表示成速度脉动谱的形式.利用Navier-Stokes方程的形式解及准正态分布假设,可以进一步将压力脉动功率谱表达式中所包含的速度脉动的三阶相关与四阶相关表示成速度脉动的二阶相关（功率谱）.最后,引入高雷诺数流的速度脉动功率谱模型,导出了由湍动e₀,耗散ε,雷诺应力-iu_j>及时均速度梯度表示的压力脉动均方值的湍流模式,并同现有数据进行了比较.     

RLW—Burgers方程的精确解

借助未知函数的变换，ＲＬＷ－Ｂｕｒｇｅｒｓ方程和ＫｄＶ－Ｂｕｒｇｅｒｓ方程化为易于求解的齐次形式的方程，从而得到ＲＬＷ－Ｂｕｒｇｅｒｓ方程和ＫｄＶ－Ｂｕｒｇｅｒｓ方程的精确解。     

Distribution of resistive body-force in curved free-surface flow

The customary procedure for including resistive effects in turbulent hydraulic and stratified atmospheric flows is to integrate the empirically-known boundary shears over the entire wetted boundary of a thin fluid slab. A resistive body-force is then assumed to exist everywhere in each slab to replace the boundary shearing force. For the classical Saint-Venant model, this body-force can be shown to have a constant distribution in the vertical direction, and therefore can be evaluated for use in the momentum differential equation. In the newer Dressler theory, however, for unsteady flow over curved beds, it is proved here that a constant body-force distribution is not possible. We determine its variable distribution and its magnitude for use in the curved-flow equations. This vasriable distribution acts to produce an equal resultant in every thin layer of fluid parallel to the bed in an angular wedge over the curved channel bed. The new curved-flow equations are therefore extended to include resistive effects.     

一类非线性偏微分方程的四阶格子Boltzmann模型

通过Chapman-Enskog展开技术和多尺度分析,建立了一种新的D1Q4带修正项的四阶格子Boltzmann模型,一类非线性偏微分方程从连续的Boltzmann方程得到正确恢复．统一了KdV和Burgers等已知方程类型的格子BGK模型,还首次给出了组合KdV-Burgers,广义Burgers—Huxley等方程...     

Unsteady state mathematical model of chemically reactive pollutants from an instantaneous line source into a stable atmospheric boundary layer

A time dependent atmospheric model represented for chemically reactive primary pollutants emitted from an elevated line source into a stable atmospheric boundary layer over a surface terrain. The model obtained from an analytical solution of the atmospheric diffusion equation with the quadratic diffusion coefficient (exchange coefficient) and the variable wind velocity taken to be of three different types’ viz. constant, constant shear and parabolic functions of vertical height. The pollutants considered to be of chemically reactive primary pollutants emitted from a time-dependent line source of Instantaneous type. In order to facilitate the application of the model the results for the general situation that includes chemical reaction rate & time dependent source incorporated in the model.     

一类KdV-Burgers方程的奇摄动解与孤子解

讨论了一类具有大Reynolds数且弱频散性的KdV-Burgers方程,在数学上表示为一类奇摄动KdV-Burgers方程.KdV-Burgers方程中含有的非线性项与频散项互补作用形成稳定向前传播的孤立子.通过数学分析,描述了孤立子的传播途径和传播速度等物理量的发展变化规律.通过奇摄动展开方法,构造了该问题的渐近解...     

NONLINEAR STABILITY OF PLANAR SHOCK PROFILES FOR THE GENERALIZED KdV-BURGERS EQUATION IN SEVERAL DIMENSIONS

This paper is concerned with the nonlinear stability of planar shock profiles to the Cauchy problem of the generalized KdV-Burgers equation in two dimensions. Our analysis is based on the energy method developed by Goodman [5] for the nonlinear stability of scalar viscous shock profiles to scalar viscous conservation laws and some new decay estimates on the planar shock profiles of the generalized KdV-Burgers equation.     

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.     

On The Atmospheric Boundary Layer Flow Modelling

The paper presents a mathematical and numerical investigation of the flow in the atmospheric boundary layer (ABL) over complex topography. The flow is supposed to be viscous, incompressible, turbulent and stationary. Two different mathematical–numerical approaches are briefly mentioned. Both models have been used to simulate a flow and pollution dispersion over a complex surface coal field in the North Bohemia which is supposed to be partially covered by a high forest stand. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the dynamics in a transitional boundary layer

IntroductionIll 1883 Professor Osborne Reynolds published in Philosopl1ical Transactions of the RoyalSociety the outcomes of his flow visua1ization at Manchester. These had shown that whetherthe flow in a pipe was direct to sinuous (or, as nowadays we would say, laminar to turbulent)depended on its Reynolds number. Transition from Iaminar to turbuIent flow becomes animportant probIem i1l fluid mechanics, which has attracted the interest of investigators fOrmore than l00 years. The partic…     

Free boundary effects on stability of two phase planar fluid motion in annulus. Part I: Migration of the stable mode

We study the linearized stability of a planar dynamical model describing two-phase perfect fluid circulating around a circle with a sufficiently large radius within a central gravitational field. The model is associated with the spatial and temporal structure of the zonally averaged global-scale atmospheric longitudinal circulation around the Earth. Two cases are studied separately; in the first one, the simulations were carried out using the rigid lid approximation at the upper boundary of the outer atmospheric layer. In the second one, the free boundary nonlinear conditions (kinematic and dynamic) were assumed on the outer atmospheric layer. For the both cases, a certain family of steady, explicit solutions which have circular streamlines was considered. The governing equations were linearized at these solutions to find the typical wave numbers of the interfacial wave perturbation to the basic state at which the destabilizing effect of shear, which overcomes the stabilizing effect of stratification, occurs. It is shown that for the both cases, the model always have the same two potentially unstable wave modes while there always exist two wave modes which are stable for any wavelengths. The behavior of the stable and unstable modes were compared for the both cases to investigate the effects of the free boundary on the mixing process at the interface.     

Mathematical and Numerical Study of the 3D Atmospheric Boundary Layer Flows Including Pollution Dispersion

The paper presents a mathematical and numerical investigation of the atmospheric boundary layer (ABL) flow over 3D complex terrain part of which is represented by the real topography of the Krkonose mountains located in the Czech Republic. The flow is supposed to be turbulent, non‐stratified, viscous, incompressible and stationary. Two mathematical models have been formulated. The first model is based upon the RANS equations in the conservative form and the second one uses the Boussinesq approximation of RANS equations and takes the non‐conservative form. Also pollution dispersion over the complex 3D terrain has been considered in both models. The problem closure is achieved by an algebraic turbulence model and given boundary conditions.     

Interactive computing methods for aeroelastic analysis of turbomachinery

An interaction viscous‐inviscid method for efficiently computing steady and unsteady viscous flows is presented. The inviscid domain is modeled using a finite element discretization of the full potential equation. The viscous region is modeled using a finite difference boundary layer technique. The two regions are simultaneously coupled using the transpiration approach. A time linearization technique is applied to this interactive method. For unsteady flows, the fluid is assumed to be composed of a mean or steady flow plus a harmonically varying small unsteady disturbance. Numerically exact nonreflecting boundary conditions are used for the far field conditions. Results for some steady and unsteady, laminar and turbulent flow problems are compared to linearized Navier‐Stokes or time‐marching boundary layer methods. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Turbulent Boundary Layer Under the Influence of Adverse Pressure Gradient

The paper deals with the experimental analysis of turbulent boundary layer at the flat plate for large value of Reynolds number equal Re_θ ≈︁ 3000. The adverse pressure gradient generated by curvature of the upper wall corresponded to the case of pressure variation in axial compressor. The fully developed structure of turbulence was achieved by proper triggering of the boundary layer. The mean and turbulent flow-fields were investigated with the use of hot-wire technique while mean and instantaneous pressure fields were examined with piezoelectric transducers. The scaling and turbulence structure of fully developed turbulent boundary layer under the influence of adverse pressure gradient revealed the more pronounced contribution of outer region to the downstream development of turbulent boundary layer. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two-equation eddy viscosity models based on the Monin–Obukhov similarity theory

The present study is devoted for the development of two equation Reynolds-Averaged Navier–Stokes (RANS) closures for computational fluid dynamics (CFD) modelling of the atmospheric boundary layer. By using the inflow conditions based on the Monin–Obukhov similarity theory, the closure coefficients of the proposed models are derived from the analytical solutions of simplified turbulent transport equations. Modifications are conducted for three different turbulence models, which are standard $k-ϵ,$$k-\omega$ and Re-Normalisation Group (RNG) $k-ϵ$. Numerical experiments are performed for the homogeneous atmospheric boundary layer and the results are compared with the theoretical values in comparison to the standard versions of modified turbulence models. Developed models are implemented to open source CFD toolbox OpenFOAM.     

On the Turbulence Modelling of 3D-Atmospheric Boundary Layer Flow

The paper presents a mathematical and numerical investigation of the 3D–flow in the atmospheric boundary layer (ABL) over complex relief. The two–equation k - ε model is applied to account for the turbulence. The flow is also supposed to be viscous, incompressible and stationary. The boundary conditions are realized through the wall-functions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inflow Treatment for the Simulation of Subsonic Jets with Turbulent Nozzle Boundary Layers

The state of the boundary layer at the nozzle exit of a circular nozzle-jet configuration has an important influence on the development of the shear layer and the emitted sound. Of special interest is the acoustic near-field obtained when the nozzle exit boundary layer is fully turbulent. The turbulent inflow generation and the inflow boundary treatment are important issues to be addressed. We use the Synthetic Eddy Method (SEM) to generate a turbulent inflow which reproduces mean flow and Reynolds stress profiles of specified reference data. The spatially and temporally varying synthetic fluctuations are imposed in the simulation by a forcing term added to the governing equations which is active in a small region downstream of the inflow boundary. This forcing in combination with characteristic boundary conditions allows for passing of upstream-propagating acoustic waves and avoids an uncontrolled drift of mean-flow quantities. We employ this inflow boundary treatment for a subsonic nozzle-jet flow simulation at a Reynolds number of ∼ 9500 and Mach number of 0.9. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical Modelling of Atmospheric Flow over a Shelter-belt

The paper presents a mathematical and numerical study of the flow with pollution dispersion in the atmospheric boundary layer (ABL) over a simplified topography with a shelter-belt placed before the pollutant (coal dust) source. The flow is supposed to be viscous, incompressible, turbulent and stationary. A two different numerical models are briefly mentioned. The shelter-belt is supposed to be a solid and impermeable obstacle significantly changing the flow-field and hence it gives the possibility of influencing the level of the pollutant concentrations in the downstream region. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Soliton solutions of Burgers equations and perturbed Burgers equation

This paper carries out the integration of Burgers equation by the aid of tanh method. This leads to the complex solutions for the Burgers equation, KdV-Burgers equation, coupled Burgers equation and the generalized time-delayed Burgers equation. Finally, the perturbed Burgers equation in (1+1) dimensions is integrated by the ansatz method.