Physical Modelling of Point Source Dispersion Inside Atmospheric Boundary Layer

One of the most important problems in the turbulence theory is the process of turbulent mixing. Although many theoretical and experimental studies on the structure functions of a passive scalar as well as the probability density functions of its increment and gradient in a turbulent fluid have been published so far, the instantaneous feature of an advected scalar has not been explored very well. There are only a few experimental studies on a scalar concentration fluctuation analysis in turbulent flows. In this study the time‐series of both longitudinal velocity component and concentration analysis are to be presented. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

具有转向点的一类奇摄动边值问题解的多重边界层现象

本文讨论如下边值问题：x=0是转向点（c（0）=0），而在x=－1处出现多重边界层现象．对不同层次采用不同的伸长变量，构造具有不同量级的边界层校正项，得到关于解的一致有效的渐近展开式和有关的余项估计．     

Self-Similar "Stagnation Point" Boundary Layer Flows with Suction or Injection

Multiple solutions are reported for the two-dimensional boundary layer flow of a viscous fluid near a permeable wall through which fluid is uniformly withdrawn. In the limit of large wall suction, three flows of similarity form are found: the first is the well-known monotonic solution of Terrill; the second exhibits flow reversal, with the streamlines being separated into three distinct cells; the third also exhibits flow reversal, but has multiple cells only when the fluid withdrawal speed is less than some threshold. The wall injection problem is also briefly studied, only Terrill's branch of solutions being found. Numerical and asymptotic solutions are presented and compared; the large-suction asymptotics of the third solution branch are found to be rather subtle.     

滑移垂直壁面驻点附近的混合对流边界层流动

就粘性不可压缩流体,研究垂直壁面的滑移,对壁面驻点附近稳定混合对流边界层流动的影响.假定表面温度和外部流动速度与到驻点的距离呈线性变化.首先,将偏微分的控制方程,转变为常微分方程组,然后应用打靶法进行数值求解.对不同数值的控制参数,按分顺流和逆流两种情况,分析和讨论了流动特性和热传导特征.结果表明,逆流时,在浮力参数的某一范围内出现双解;顺流时,解是唯一的.一般而言,速度滑移导致壁面热传导率增大,而热滑移使之减小.     

关于边界层方法

本文指出传统的边界层方法(包括匹配法和Vi?ik—Lyusternik方法)的不足:不能作出边界层项的渐近展开式.提出多重尺度构造边界层项的方法,得到符合实情的结果.又与Levinson所用的方法比较,本方法能更简单地导出后一方法给出的边界层项的渐近展开式.又应用此方法研究现有的关于奇异摄动的某些成果,指出这些成果的局限性,并在一般情况下作出解的渐近展开式.     

Turbulent Entrainment in the Atmospheric Boundary Layer

Turbulent entrainment – the process by which turbulence inside of the atmospheric boundary layer entrains air from the free troposphere above it – has been investigated using direct numerical simulations in two configurations, one without a cloud and one with a cloud. With the first configuration, we have learned that the entrainment zone in a convective boundary layer growing into a linearly stratified troposphere is better described in terms of a two-layer structure, with different characteristic scales associated with each of the two sub-layers. With the second configuration, we have explained how wind shear across the entrainment zone capping a stratocumulus cloud can render evaporative cooling as important as radiative cooling in driving convective motions. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonmonotone Interior Layer Solutions for Singularly Perturbed Semilinear Boundary Value Problems with a Turning Point

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Boundary Layer Solution of the Boltzmann Equation for Specular Boundary Condition

In the paper, we establish the existence of steady boundary layer solution of Boltzmann equation with specular boundary condition in L_x,v²∩L_x,v^∞in half-space. The uniqueness, continuity and exponential decay of the solution are obtained, and such estimates are important to prove the Hilbert expansion of Boltzmann equation for half-space problem with specular boundary condition.     

边界层流中当地感受性过程的数值研究

边界层流中当地感受性问题的研究对层流向湍流转捩过程的预测与控制起着非常关键的作用,尤其是对边界层内诱导产生三维Tollmien-Schlichting(T-S)波成因过程的探讨具有更加重要的理论意义.采用高精度、高分辨率变间距的紧致有限差分方法,直接数值模拟了在自由来流湍流与二维壁面局部粗糙相互作用下边界层内的当地感受性问题.数值计算发现,在自由来流湍流与二维壁面局部粗糙作用下,边界层内诱导形成的当地感受性过程是真实存在的;且被激发的一组三维T-S波波包沿流向发展的过程中流向涡结构将逐渐形成,其强度将越演越烈.数值结果还显示,边界层内被诱导产生当地感受性过程的波长转换机制仅使流向波数发生改变,而展向波数保持不变;以及自由来流湍流运动方向的改变将决定三维T-S波波包的传播方向,但其传播速度的大小都近似为无穷远来流速度的1/3.另外,还建立了自由来流湍流的强度和运动方向以及二维壁面局部粗糙的长度和高度与边界层内的当地感受性问题之间的关系等.这一课题的深入研究,将在进一步理解和认识层流向湍流转捩的理论机制,以及湍流的形成机理等方面均起到十分重要的作用.     

源于膨胀波边界层理论中的一类奇异边值问题

对源于膨胀波边界层理论中的一类奇异边值问题进行了研究,利用单调逼近方法得到了满足物理意义上正解的存在性和唯一性的充分条件,同时给出了用速度比例参数表示的壁摩擦的估计公式, 利用打靶法技巧得到了问题的数值解.数值结果证明了估计公式的可靠性和有效性.     

Remarks on Boundary Layer Expansions

A systematic mathematical methodology for derivation of boundary layer expansions is presented. An explicit calculation of boundary layer sizes is given and proved to be coordinates system independent. It relies on asymptotic properties of symbols of operators. Several examples, including the quasigeostrophic model, are discussed.     

On a Boundary Layer Problem

This is a continuation of our earlier article concerning the boundary-value problem     where A , B are prescribed constants, and 0 < ε ≪ 1 is a small positive parameter. In that article, we assumed the coefficients a ( x ) and b ( x ) are sufficiently smooth functions with the behavior given by a ( x ) ∼ αx and b ( x ) ∼ β as x → 0, where α > 0 and β / α ≠ 1, 2, 3,…. In the present article, we are concerned with the case α < 0 and β / α ≠ 0, −1, −2,…. An asymptotic solution is obtained for the problem, which holds uniformly for all x in [ x ₋, x ₊]. Our result is proved rigorously, and shows that a previous result in the literature is incorrect.     

Active Control of Separating Boundary Layer

Flow control refers to the ability to alter flows with the aim of achieving a desired effect: examples include drag reduction, noise attenuation, improved mixing or increased combustion efficiency among many other industrial applications. The reduction and control of the viscous drag force exerted on bodies moving in a fluid is of great technical interest. Several active and passive methods to achieve a delay of separation in the boundary layer have been developed and are being developed. In this paper we present a new concept for boundary layer separation control that is based on the synthetic jet concept which converts acoustic oscillations into mean fluid motions. We use synthetic jets as methods for Coanda effect's amplification. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Qualitative Properties of Separating Flows in the Prandtl Boundary Layer

We study the behavior of solutions to the system of Prandtl boundary layer equations beyond the separation point of the boundary layer. We obtain conditions on the positive pressure gradient which guarantee the attachment of the boundary layer to the streamlined surface after separation. We prove the possibility of controlling the boundary layer by alternating suction and injection.     

On Boundary Layer Control Using Suction in the Wind Tunnels

In this paper a closed-form analysis of flow in a two-dimensional transonic wind tunnel that uses sidewall distributed suction around the model to reduce sidewall boundary-layer effects is presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)