Scaling in convective evaporation and sidewall boundary layer

Turbulent convection at aspect ratios from 0.06 to 2 is investigated in the laboratory with evaporation experiments from vertical cylinders having different diameters and liquid levels. With alcohol, only diffusive evaporation takes place. With water, for small diameters, evaporation proceeds by diffusion whereas convective evaporation develops when the diameter is increased. This onset can be effectively interpreted in terms of a viscous sidewall boundary layer, whose thickness δ varies with respect to the available height h according to δ/h = 3.4 Ra^-0.28±0.01 versus Rayleigh number Ra. The Sherwood number Sh, analog of the Nusselt number, exhibits a power law variation Sh = 0.6 Ra^0.27±0.02 for Ra varying from 10⁴ to 3 ×10⁸. The scaling observed in this case of an open boundary is thus similar to the scaling measured in confined Rayleigh-Bénard convection.     

Dynamic model of coherent structure in the wall region of a turbulent boundary layer

Based on the theoretical model for a single coherent structure in the wall region of a turbulent boundary layer, we studied the interaction of two coherent structures by direct numerical simulation in order to explain the mechanism for the formation of low-speed streaks.     

Analytical model of the time developing turbulent boundary layer

An analytical model for the time-developing turbulent boundary layer (TD TBL) over a flat plate is presented. The model provides explicit formulae for the temporal behavior of the wall-shear stress and both the temporal and spatial distributions of the mean streamwise velocity, the turbulence kinetic energy and Reynolds shear stress. The resulting profiles are in good agreement with the DNS results of spatially-developing turbulent boundary layers at momentum thickness Reynolds numbers equal to 1430 and 2900 [5–7]. Our analytical model is, to the best of our knowledge, the first of its kind for TD TBL. The text was submitted by the authors in English.     

An explicit algebraic model of the planetary boundary layer turbulence: test computation of the neutrally stratified atmospheric boundary layer

An explicit algebraic model of Reynolds stresses and the turbulent heat flux vector for the planetary boundary layer in a neutrally stratified boundary layer of the atmosphere above a homogeneous rough surface is tested. The version of the algebraic model under consideration is constructed on the physical principles of the RANS (Reynolds-averaged Navier?Stokes) approximation for describing stratified turbulence, it employs three forecasting equations, and a correct reproduction of the main characteristics of a neutral atmospheric boundary layer — the components of the mean wind velocity, the wind turn angle, and the turbulent statistics is shown. Test computations show that the proposed model may be used for goal-oriented investigations of the atmospheric boundary layer.     

Influence of short roughness strip on the turbulent boundary layer structure

Hot-wire measurements have been undertaken in a turbulent boundary layer which is subjected to an impulse in form of a short roughness strip with the aim of examining its influence on the structure of the turbulent boundary layer. The results indicate that, while the energy containing motion is shifted from low wave number to high wave number near the wall due to the interfering of the roughness strip with the near-wall structure, the reverse is the case in the outer region. While the anisotropy at small scale changes appreciably, there is no discernable change at the large scale when distance from the wall is increased as reflected in the collapses of spectra shear correlation coefficient at the low wave number. It further shows that the roughness strip alters the flow dynamics of the boundary layer as shown in the changes in the mixing length distribution.     

大气边界层模式中随机参数的反演与不确定性分析

在大气边界层气象中湍流黏性系数是一个很重要的参数,通过直接观测往往无法得到其准确值,仅能通过间接观测获得大致范围.本文选用随机广义Ekman动力近似模式中的湍流黏性系数进行反演研究与不确定性分析.首先利用风速观测数据,并采用基于混沌多项式的集合Kalman滤波方法对系数进行反演,降低其不确定性,缩小可能取值的范围,该方法的核心思想是将集合Kalman滤波方法中求解模式不确定性传播的方法由蒙特卡罗法改为混沌多项式展开,从而避免大规模采样带来的计算资源耗费.然后进行数值实验,结果表明该方法能够有效且快速地求解出湍流黏性的后验概率分布,从而达到降低系数不确定性的目的.根据系数的先验分布计算出风速的先验分布,从而找到风速不确定性大的区域,且揭示了在不确定性大的区域内的观测数据进行系数反演可得到十分明显的效果,这对于观测点位置的选择提供了重要的指导.     

Energy spectra of the stable boundary layer: A theoretical model

Summary A derivation of spectral energy functions for stable atmospheric boundary layers is presented for a local similarity regime. Previous studies of this nocturnal atmospheric conditions were usually carried through purely kinematic modellizations. In this study, the atmospheric turbulence energy content is derived from a dynamical viewpoint. This is achieved through the use of the energy balance relation obtained by Rotta from Navier-Stokes equations. The result is an appropriate physical rooting of the spectral energy curves known as Kaimal’s Isopleths. The authors of this paper have agreed to not receive the proofs for correction.     

Electronic structure of a model grain boundary

We present a calculation of the electronic structure of a model symmetrical tilt (130) grain boundary in a f.c.c. metal. The local density of states for atoms at and near the boundary is evaluated for a tight-binding s-like Hamiltonian by the transfer matric method. Relaxation of the energy levels of the atoms near the boundary is introduced to preserve charge neutrality. A band of localized states is found above the Fermi level.     

A new parameterization of temperature structure parameter in entraining convective boundary layer

Temperature structure parameter () controls the propagation of electromagnetic and acoustic waves in the atmospheric boundary layer (ABL), but it is difficult to be measured, especially in the upper part of the ABL. In this paper, optical turbulence is simulated in a laboratory convective tank, and profiles in the tank are measured by using laser beam patterns. Simulation results show that the Wyngaard’s scaling relationship for in the entrainment layer is only valid for large convective Richardson number (Ri > 40) cases. When Ri < 40, a new scaling relationship is proposed based on the laboratory and field measurements. The application of these relationships in estimating optical turbulence in the entrainment layer is discussed.     

Analytic model of the universal structure of turbulent boundary layers

Turbulent boundary layers exhibit a universal structure that nevertheless is rather complex and is composed of a viscous sublayer, a buffer zone, and a turbulent log-law region. In this letter, we present a simple analytic model of turbulent boundary layers that culminates in explicit formulas for the profiles of the mean velocity, the kinetic energy, and the Reynolds stress as a function of the distance from the wall. The resulting profiles are in close quantitative agreement with measurements over the entire structure of the boundary layer without any need of refitting in the different zones. The text was submitted by the authors in English.     

Eddy diffusivities derived from a numerical model of the convective planetary boundary layer

Summary Functional forms for the vertical eddy diffusivityK _z (z) are sought that optimize the performance of theK-theory diffusion equation. The method developed to determine the optimal diffusivity is first tested by applying it to analytic solution of the diffusion equation in which the functional form of the diffusivity is known precisely. In all test cases performed, the technique yields the correctK _z profile regardless of the initial estimate ofK _z from which the technique’s search procedure begins. When applied to “observed” mean, cross-wind-integrated point source concentration fields derived from Lagrangian diffusion theory and data from a numerical turbulence model jointly, the technique yields optimal diffusivities that make the solution of the diffusion equation agree within ±20% of the “observed” values within the core of point source plumes. Expressed in terms of the convective-velocity scalew _* and the mixed-layer depthz _i , the optimal diffusivity has a quasiuniversal form for atmospheric stabilities in the rangez _i /L⪯-10 whereL is the Monin-Obukhov length. The optimal diffusivity is found to be strongly dependent on the source hight. TheK _z profiles derived for the two source heightsz _s∼-0.025z _i andz _s ∼-0.25z _i are of opposite shape, but they have comparable maximum values ofK _z ∼-0.25w _* z _i .

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Riassunto Si cercano forme funzionali per la diffusibilità turbolenta verticaleK _z (z) che rendano ottimale l’efficacia dell’equazione di diffusione della teoriaK. II metodo sviluppato per determinare la diffusibilità ottimale è dapprima controllato applicandolo a soluzioni analitiche dell’equazione di diffusione in cui la forma funzionale della diffusibilità è nota esattamente. In tutti i casi di prova la tecnica dà il profilo corretto diK _z qualunque sia la stima iniziale diK _z da cui prende inizio il procedimento di ricerca della tecnica. Quando è applicata contemporaneamente ai campi di concentrazione medi “osservati”, a sorgente puntiforme integrati sui venti trasversali, derivati dalla teoria di diffusione lagrangiana ed ai dati presi dal modello di turbolenza numerico, la tecnica dà diffusibilità ottimali per le quali la soluzione dell’equazione di diffusione è in buon accordo entro il ±20% dei valori “osservati” nel nocciolo di pennacchi della sorgente puntiforme. Espressa in termini della scala di velocità di convezionew _* e della profondità dello strato mistoz _i , la diffusibilità ottimale dipende fortemente dall’altezza della sorgente. I profili diK _z derivati per due altezze di sorgentez _s ∼-0.025z _s ez _s ∼-0.25z _i sono di forma opposta ma hanno valori massimi diK _z paragonabili,K _z ∼-0.25w _* z _i .

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Резюме Определяются функциональные выражения для вертикального вихревого козффициента диффузииK _z (Z), которые оптимизируют получение уравнения диффузии вK-теории. Развитый метод для определения оптимального коэффициента диффузии сначала проверяется на аналитических решениях уравнения диффузии, в которых функциональное выражение козффициента диффузии известно точно. Во всех исследованных случаях предложенный метод дает правильный профильK _z . Предложенный метод дает оптимальные козффициенты диффузии, при которых решение уравнения дуффузии согласуется, в пределах ±20%, с ≪наблюдаемыми≫ величинами. Выраженный через масштаб конвекционной скоростиw _* и глубину смешанного слояz _i оптимальный коэффициент диффузии имеет квази-универсальную форму для атмосферных устойчивостей в областиz _i /L≤10, гдеL есть длина Монина-Обухова. Обнаружено, что оптимальный козффнциент диффузии сильно зависит от высоты источника. ПрофилиK _z , выведенные для двух высот источниковz _i ≅0.025z _i иz _i ≅0.25z _i , имеют противоположную форму, но они имеют сравнимые максимальные значенияK _z ≅0.25w _* z _i .

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To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Convection and correlation of coherent structure in turbulent boundary layer using tomographic particle image velocimetry

The present experimental work focuses on a new model for space–time correlation and the scale-dependencies of convection velocity and sweep velocity in turbulent boundary layer over a flat wall. A turbulent boundary layer flow at Reθ= 2460 is measured by tomographic particle image velocimetry(tomographic PIV). It is demonstrated that arch, cane,and hairpin vortices are dominant in the logarithmic layer. Hairpins and hairpin packets are responsible for the elongated low-momentum zones observed in the instantaneous flow field. The conditionally-averaged coherent structures systemically illustrate the key roles of hairpin vortice in the turbulence dynamic events, such as ejection and sweep events and energy transport. The space–time correlations of instantaneous streamwise fluctuation velocity are calculated and confirm the new elliptic model for the space–time correlation instead of Taylor hypothesis. The convection velocities derived from the space–time correlation and conditionally-averaged method both suggest the scaling with the local mean velocity in the logarithmic layer. Convection velocity result based on Fourier decomposition(FD) shows stronger scale- dependency in the spanwise direction than in streamwise direction. Compared with FD, the proper orthogonal decomposition(POD) has a distinct distribution of convection velocity for the large- and small-scales which are separated in light of their contributions of turbulent kinetic energy.     

Development of a boundary layer model for evaluation of dispersion in complex terrain

Summary Trajectories in the turbulent boundary layer have been computed using a dynamic model, for a separating and a nonseparating case. The turbulent kinetic energy, the eddy diffusion coefficient and the hill factor have been evaluated along the trajectories, to get some insight into the different dispersion properties of such flows. Paper presented at the IV Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 22–24, 1987, Rome.     

Near-surface turbulence in the atmospheric boundary layer

Measurements of the near-surface turbulence in the atmospheric boundary layer have been made using hot-wire probes above the salt flats of northwestern Utah, where the momentum thickness Reynolds number, R_θ, is O(10⁶), and the surface is smooth and nearly devoid of flow obstructions. The measurements were made with arrays of up to 24 parallel straight sensors and with a modular 12-sensor probe capable of measuring all of the components of the instantaneous velocity vector and velocity gradient tensor. Measurements were also made in a laboratory wind tunnel at R_θ=1730 using 22 straight sensors. The data analysis focuses on the effects of the Reynolds number on turbulence properties and on the physics of the dissipation rate of turbulent kinetic energy.Some properties are found to be dependent on the Reynolds number when normalized with inner variables, while others are not. Among those that show the significant Reynolds number dependence are the rms and the skewness factor of the streamwise velocity fluctuations.Significant differences in flow structure, particularly those related to high rates of dissipation, are implied by the data. The joint PDF and covariance integrand of streamwise and wall normal vorticity fluctuations show less preferred orientation of the vorticity vector in the buffer layer at R_θ of O(10⁶) than at R_θ=1070. The largest contribution to the dissipation rate, at O(10⁶) is by the ∂w/∂z velocity gradient, while this term makes a quite small contribution to the dissipation rate at low R_θ. Here w and z are the spanwise velocity fluctuations and direction, respectively. Conditional analysis in the streamwise-wall normal (x−y) plane based on high instantaneous dissipation rate shows that the typical high dissipation rate events are generally similar at high and low Reynolds numbers, but display some significant differences.     

Properties of the boundary layer in selective transport

A study is reported for the boundary layer of lubricant arising under conditions of selective transport; it is considered that electrochemical processes dominate this transport, and a study has been made of the emf generated, the rectified voltage, and the resistance of the boundary layer as functions of the nominal load. The frictional force was also measured. It is found that the selective transfer occurs in the steady state through a boundary layer of lubricant that interacts chemically with the surfaces. The resulting boundary layers have rectified properties, while the system St. 40Kh-glycerol-Br. OTsS generates an emf as a galvanic cell. The effects have been examined as functions of the friction conditions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 41–45, May, 1973.