Flat Plate Turb STRUCTURE

8/2/2019 Flat Plate Turb STRUCTURE

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J . Fluid M e e h . (1967),vol. 30, part 4,pp. 741-773Printed in Great Britain

741

The structure of turbulent boundary layersBy S. J. KLINE, W . C. REYNOLDS, F. A. SCHRAUBt

AND P. W . RUNSTADLERSDepartment of Mechanical Engineering, Stanford University

(Received 21 February 1967 and in revised form 26 July 1967)Extensive visual and quantitative studies of turbulent boundary layers aredescribed. Visual studies reveal the presence of surprisingly well-organizedspatially and temporally dependent motions within the so-called laminar sub-layer. These motions lead to the formation of low-speed streaks in the regionvery near the wall. The streaksinteract with the outer portions of the flow througha process of gradual lift-up, then sudden oscillation, bursting, and ejection. Itis felt that these processes play a dominant role in the production of new turbu-lence and the transport of turbulence within the boundary layer on smooth walls.

Quantitative data are presented providing an association of the observedstructure features with the accepted regions of the boundary layer in non-dimensional co-ordinates; these data include zero, negative and positive pressuregradients on smooth walls. Instantaneous spanwise velocity profiles for the innerlayers are given, and dimensionless correlations for mean streak-spacing andbreak-up frequency are presented.

Tentative mechanisms for formation and break-up of the low-speed streaksare proposed, and other evidence regarding the implications and importance ofth e streak structure in turbulent boundary layers is rsviewed.1. Introduction

The structure of any turbulent flow reflects the local balance of production,transport, and dissipation of turbulent kinetic energy. In turbulent boundarylayers production plays a primary role, and hence it is important that themechanisms of production be well understood. Since production is concentratedin the regions very near the wall, knowledge of the turbulence structure in thisregion is of special importance. This region is usually rather thin, and even par-tially complete quantitative information has been difficult t o obtain by conven-tional techniques. I n this paper we report the results of an extended study of thestructure of turbulent boundary layers, with particular emphasis on the wallregions. The study is unique to the extent th at the novel techniques employedafforded he opportunity to obtain combined visual and quantitative informationon the motions within the boundary layer including the layers closest to the wall.

The importance of the region near the wall is clearly evidenced by the distribu-tion of the turbulent energy production rate per unit volume across the boundary

t Now a t General Electric Co., San Jose, California.$ Now at the Thayer School of Engineering, Dartmouth College.


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742 X . J . Kl ine , W . C . Reynolds, F . A . Xchraub and P. W . Runstadler

-!? 16 -Wake region -LIII1 I\ g o . o 2 L I I -I II IIII -

II I 0 I0

layer. Figure 1a shows Klebanoffs (1954) production measurements and theassociated regions of the boundary layer. Note tha t a sharp peak of productionoccurs just outside of the so-called laminar sublayer, in the buffer layer,th at is, between the sublayer and the logarithmic portion of the velocity profile.The cumulative turbulence energy production, integrated outward from the wall,

I I I I I I I I I I 11-- Viscous sublayerI,

YlSFIGUREa. Normalized turbulence energy production rate per unit volume in a typicalboundary layer (Klebanoff 1954).

Y PFIGURE. Cumulative turbulence energy production rat e in a typical turbulent boundarylayer (Klebanoff 1954).is shown in figure 1 . Note th at roughly half of the total production occurs withinthe regions very close to the wall, and that the outer 80 % or so of the boundarylayer, the wake, contributes only about 20 yo to the total production. Theseobservations are in qualitative accord with Laufers (1954)measurements in pipeflow, and they support the contention t hat the thin wall region plays a very domi-nant role in determining the structure of the entire boundary layer.

The volumetric rate of turbulent energy production B also provides an im-portant link between the volumetric rate of energy dissipation by the mean


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The structure of turbulent boundary layers

E / V =919.

743velocity field, 9, he scalar kinematic eddy-viscosity, E , and the (kinematic)molecular viscosity, Y,This is a local identity (Kline 1965a). Knowledge of B allows calculation of themean field from the equations of motion, and 9 s expressible in terms of the meanfield. Hence, givenB locally the mean field can be determined. This also suggestsa strong focus on the production mechanisms in turbulent boundary layers.

The combined visual and quantitative techniques employed reveal a number ofsignificant features of turbulent boundary layers; two of these particularly de-serve early mention. First, the laminar sublayer is not two-dimensional andsteady, as simple models have sometimes assumed; rather it contains three-dimensional unsteady motions and these motions remain a large fraction of thelocal mean velocity right down to the wall. While the motions in this region areindeed dominated by viscosity, eddy motions are present throughout the en-tire wall region. Secondly, i t appears that a primary mechanism for productionof turbulent kinetic energy in the inner region of the boundary layer is the ratherviolent ejection of low-speed fluid from the regions very near the wall. Theseburstsare highly suggestive of an instability mechanism, and also appear to playa key role in transporting turbulent kinetic energy to the outer (wake) regions ofthe boundary layer.A positive pressure gradient tends to make the bursting moreviolent and more frequent; on the other hand, negative pressure gradients re-duce the rate of bursting. In a sufficiently accelerated flow, the bursting ceasesentirely, and the boundary layer relaminarizes .

While these studies do provide new understanding of the processes occurringwithin a turbulent boundary layer, they aIso serve to re-emphasize the verycomplex nature of such flows, the nayvet6 of oversimplified flow models, and theneed for additional data on actual flow models of turbulence production for vari-ous types of flows.2. Experimental methods

The experiments were performed in two open-surface recirculating waterchannels, shown schematically in figure 2 . In an early series of experiments afalse floor in th e larger channel was used as a flat plate. Subsequently a false side-wall in the narrower channel was used for studies in a variety of accelerating anddecelerating flows.? Water speeds of the order of 0.2-0.7 ft./sec were employed;these provided quite thick boundary layers over much of the 18ft. length of theactive surfaces. The velocity data reported herein were all obtained in the nar-rower channel, which utilized a curved opposing wall to control the imposedpressure distribution. Water depths of the order of loin. were used, with themaximum channel flow width being of the order of 13in. The channels wereconstructed of lucite to facilitate visualization, and care was taken to eliminateproblems of vibration, unsteadiness, and temperature variation. Artificialtripping was provided upstream of the test section.t The earlier work is described in more detail by Runstadler et al. (1963); he ater workis reported in detail by Schraub& Kline ( 1 9 6 5 ~ ) . hese reports will henceforth be denotedas I and 11, espectively.


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744 8. . Kline, W . C. Reynolds, 3.A . Schraub and P . W . RunstctdlerMean velocity measurements were obtained using a precision constant tem-

perature linearized hot-wire anemometer especially designed for used in low-speed water flows.? Platinum wires of 0.0008 in. diameter and approximatelygin. long welded to platinum leads formed the sensing element. These were

, By-passcontrol

FIGURE. Flow system.operated a t low overheats (30O F ) in de-aerated water. The platinum-platinumsystem avoids stray galvanic currents; the low water conductivity reduces strayconduction;and the de-aeration and low overheat prevent air bubble formationon the wires. Because of the low overheat, low-noise high-gain amplifiers wereused in the control system, and an accurate analogue linearizer was developed.A t the low speeds involved the energetic fluctuation frequencies are in the range5-100 c/s, which made conventional r.m.5. averaging equipment difficult to use.Hence the linearized signal output was integrated for 30 sec using a precisionanalogue integrator, and this integrated voltage was used to determine the meanvelocity. Calibration velocities were determined by measuring the sheddingfrequency of K km&n vortices behind thin circular rods placed in a uniformflow, and using established relationships between this frequency, the flow velo-city, and the fluid properties. This technique was checked by measuring the timerequired for dye markers t o travel down several feet of the channel. As a check onthe anemometer, the velocity profile in a laminar flat-plate boundary layer wasmeasured, and its comparison with the Blasius solution for a comparable dis-placement thickness is shown in figure 3a. On the basis of this check, drift tests,and other analysis, we estimate th at the uncertainty in a single mean-velocitymeasurement is less than 2 yofor the data reported herein (20 :1 odds).

Initial visualization experiments (I)utilized dye injection through thin slotst See Sabin (1965), Uzkan & Reynolds (1967). This device underwent several stages ofimprovement and refinement; most of the da ta reported here were taken with the unit asmodified by Uzkan.


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T h e structure of turbulent b ound ary layers 745in the wall. These studies were instrumental in revealing the essential featuresof the flow structure very near the wall. Subsequently visualization using tinyhydrogen bubbles was adopted since this method provides both qualitative and

0.6

0.4

FIGUREa. Test of the hot wire in a laminar flow. 0 , hot-wire data; x,,,effective originfound by fit.

A@-4% uncertainty- A-%------5o.8 t AA

FIGUREb . Comparison of mean velocity data from hot-wire and bubble techniques.Station 10, dPldx & 0.A, ot wire; 0, ydrogen bubble.


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746 S. J . Kline, W . C . Reynolds, B. A . Schraub and P. W . Runstadlerquantitative information. I n this technique,? a single platinum wire about 6 in.long and 0.001 in. in diameter is used as an electrode to generate small ( w 0.0005in. diameter) hydrogen bubbles. By pulsing the voltage applied to the wire, time-lines can be generated, and, by insulating spanwise portions of the wire, streaksare formed. These combined-time-streak markers can be seen in figure 10,plates 1 to 4; in each figure the wire is at the top of the picture, the flow is from thetop, and the view is towards the wall.

12

8 --.AvN 4 -

0

-0

I I I I I-t

00 -00 -00 -

-0- -

I I I I I

.-v-.tva 2 - momBdp)mD omBdp)- mD0 0.4 0. 8 1.2

U lurnFIGURE. Representative checks on the two-dimensionality of the flow. Station 13,

dP/dx 0 (worst case), y = 4.50 n. 0, z = 10 n.; A, = 7.7 in.; 0, z = 5 .5 in.These markers not only allow a large portion of the flow to be visualized, but

can also be used to determine the instantaneous velocity distribution along thewire. A comprehensive treatment of the uncertainty in these measurements isgiven by Schraub et al. (1965b) . For the present measurements, the estimateduncertainty in a single realization of the streamwise velocity is of the order of3-4 yo (20 :1 odds); the highest value occurs in the region very near the wall. Acomparison of the mean velocity (spanwise average) obtained using the bubblemethods with the velocity (time average) measured with the hot wire is shown infigure 3 b . These data correspond to a severe adverse pressure gradient, where thefluctuations are large, and hence the inaccuracies are greatest. The excellentagreement of these two independent techniques provides considerable basis forconfidence in the instantaneous velocity measurements as deduced from motionpictures of the time-streak markers.

The two-dimensionality of the flow in the test region was checked by appro-priate velocity surveys. Typical results for a strong adverse pressure gradient, theworst case, are shown in figure 4.Here y is th e distance normal to the wall, andx is the spanwise direction. These surveys indicate th at in the worst case the floorboundary layer extends upward only t o about x = 4.5in. and hence the flow in

t See Schraub et al. (1965b), for a detailed description of the measurement o f velocityby hydrogen bubble generation technique, and the film by Kline (1964) for a basic treat-ment of flow visualization with illustrations using th e hydrogen bubble methods.


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0.10

0.08

0.06-d.AI

,

0.04

The structure of turbulen t boundary layersI I I I I I I I0 A U 0

[Relative size 0 AilIf ho t wire

/ / / / , + = l o l o c u s

0 0.1I I I I I

0.2 0.3 0.4

74 7

U (ft /sec)FIGVREa. Determination of the wall shear stress by the wall-slope method.v, station 6; 0,tation 8; A , station 1 1 ; 0, tation 15; d P / d x < 0.0.056

0.0528

B",I0.048

0.044

I I I I I I I I I I I

0 0 2 0.4 0.6 0.8 1oY (in.)

FIGUREb. Determination of the wall shear stress by the cross-plot method. Station 6,dP/dx < 0. */U, = 0.0508, Urn= 0.462 t./sec; v* = 0-023 t./sec.


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T h e structure of turbulent boundary layers( c ) d P / d x = 0 flat plate pressure gradient,( d ) dP/dx < 0 mildly favourable pressure gradient,( e ) dPldx < 0 strongly favourable pressure gradient.Figure 6 b shows the variation in

A=--=---v dU, 1 dPlJ; ax pu:dx

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a non-dimensional pressure gradient parameter, for the flows. While there aremany dimensionless parameters which can be used to characterize the pressure

I I I I I I 1

3X

IIIc(0E;X

II(D

30

X%

1 1 I I I I I I6 8 10 12 14 16 18

x (ft.)FIGUREa. Free-stream velocity distributions. 0, d P / d x < 0 ;A, P / d x < 0 ;v, d P / d x > 0 ;0, P l d x % 0.4

3

210

- I

- 3- 4 6 8 10 12 14 16

x ft.)FIGUREb . Pressure gradient parameter distributions. 0, P / d x < 0 ;8, P / d x < 0; B, d P / d x > 0 ; El, d P / d x $ 0.

106


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7 5 0 X. . K l i n e , W . C . Reynolds, P. . Schruub and P. W . Runstudlergradient, K is simple to measure, and appears to be physically relevant, as willbe discussed later. For comparison, values of K for a few typical flows of practicalinterest are shown. It should be noted th at the pressure gradients imposed on theboundary layers ( a )and ( e )are considerably stronger than in most external flowapplications, but are quite typical of many internal flow situations.

dPldx >>O

StationA 70 10

0 12

0.2 0.477 (ft./sec)

FIGUREa. Mean profiles for the strong positive pressure gradient flow.Mean velocity measurements a t several stations in each of the five flows are

shown in figure 7 . t Shear stress data (u,nd w * ) are included in table 1. The pro-file data are plotted in the usual velocity defect manner in figure 8. The stronglyfavourable flow has been omitted because it seemed to undergo relaminarization,and hence should not really be considered or plotted as a turbulent boundarylayer. Note that the flat plate is in excellent agreement with the correspondingprofile of Clauser (1956). The other three flows shown in figure 8 do not exhibitsufficient similarity that they could be considered as equilbrium layers in thesense of Clauser, although the mild pressure gradient flows are noticeably nearerto equilibrium conditions than are the strong pressure gradient flows.$

t Note the displacement of th e origins for figures 7 b and 7 c .$ Non-equilibrium flows were purposely chosen for th e dP/dx + 0 tests so th at corre-lation parameters obtained, if any, would not be of a restricted nature.


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The structure of turbulent boundary layers 75 1i II i i iStation

0 6A 8

1v 11[ 0 1 5dP/dx> 0

0 6 0.817 0,2tU (ft./sec)

FIGUREb . Mean profiles for the mild positive pressure gradient flow.r-tation0 60 8 nr:r lx = 0A 11v 14

0 0 0 24 40 04- 6 0.8 1o*Y

U (ft./sec)FIGUREc. Mean profiles for the zero pressure gradient flow.


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752 S. J . Kl ine , W. C . Reynolds, F . A . Schraub and P. W . Runstadler

3.0

2.0h.$va

1o

0

4

0.2 0 4U (ft./sec)

0.6

FIGUREd . Mean profiles for th e mild negative presssure gradient flow.

4

0 0.2 0.4U ft /see) 0.6FIGUREe. Mean profiles for the strong negative pressure gradient flow.


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FIGCREob. y+ = 4.-.FICURE0.Photographs of th e striicturc of a flat plate turbulent boimdary layer.

KLINE, RETSOLUS, SCHRAUB AN D RVXSTADLER ( I u c i ~ g . 7 2 2 )


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Journa l of PIirid Mechanics , lrol. 30, par t 4 Plate 2


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Plate 3


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The structure of turbulent boundary layers 753The mean velocity data are shown in the conventional wall-region form in

figure 9. Note that figure 9 a employs v*, the shear velocity determined by thecross-plot method,? and hence each profile fits (2.1) over a portion of its extent.Noticeable spread of the data in the region y+ < 30 occurs in these co-ordinates.i n figure 9b we show the same data normalized with u,, the shear velocity ob-tained by the wall-slope method. This collapses the data in the region y+ < 30,

dP/dx =0 lP/ilX 0;v, d P / d x < 0 .

UL d x


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T h e structure of turbulent boundar y layers 761The average spanwise spacing of the sublayer streaks has been determined

visually for the five flows. In (I) he technique involved counting the number ofdye streaks for a large number of pictures (50). These counts showed th at a re-producible mean spacing exists, though there is considerable variation in thespacing between individual streaks (standard deviation of spacing 30-40 yo ofmean). In (11) he bubble streaks were counted. While there is certainly somesubjectiveness in this procedure, visual counts by different observers were insufficient agreement as t o be clearly meaningful. The data of (11) nvolved count-ing very close to the wire; in (I) he counts were made at a fixed distancedownstream of the dye slot. This difference probably accounts for some of thediscrepancy between the two schemes. Averages over space and time were im-plicit in both counting schemes.

n 1 0 2.0 3.0z (in.)

4.0

FIGURE3. Typical instantaneous spanwise variation in TAand u, determined by the bubblemarker method (y+z 5).

The visual counting indicates tha t the visual mean spacing, A,, correlates onthe wall-layer parameters. Figures 12a and 12b show the value of A: = h,u,/u asa function of velocity and the pressure gradient parameter K respectively for th efour turbulent flows. These data cover a 3 : 1 range in velocities, and a wide rangeof local pressure gradients. The data indicate that the average (spanwise)streak-spacing corresponds approximately to A,+ = 100, which is roughly 15 times thethickness of the laminar sublayer. Hence there appears to be a characteristicscale of motion within the wall regions, determined primarily by the wall-regionparameters 1 and u,.

The hydrogen bubble pictures provide a second more objective method forquantitative determination of the mean streak-spacing. By following the motionof the corners of the time-streak squares, the instantaneous u and w velocity com-ponents along the bubble-generating wire can be deduced. Figure 13 is a sampleof such data; note that a substantial spanwise region can be surveyed at anyinstant. The spanwise correlation of the streamwise velocity fluctuation u,

f (z)u( + zo)dz[u(z)2dzR,,(O,0, zo ; 0) = _______- ,


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762 S. J . Kline, W . C . Reynolds)P. . Xchraub and P. W . Runstadleris then computed numerically for each survey. The Fourier transform of thiscorrelation,

o(1) 410mR,,cos (2m?)dzo,is then formed using appropriate numerical techniques.? o(1)epresents thecontribution of harmonics of wavelength 1 to the instantaneous spanwise velocity

0 2 4 0 2 41 inches1.2 1

Typic al instantaneo us spanwise spectra

70 1 .. 0 2 41 (in.) 1 (in.)

FIUURE 4. Typical instantaneous and average spanwise spectra. dP/tEx + 0, y+ z 2 .variation, and hence a peak in the 0 spectrum is expected. Typical samples ofsuch spectra are shown in figure 14. Note t hat there is considerable variabilitybetween individual surveys, but tha t all display a characteristic peak a t roughlythe same wavelength. The ensemble average of a arge number of surveys be-comes stable with a sufficiently large sample, and the location of the peak in thisaverage spectrum can be used to define the average spacing; this spectral defini-tion we denote by A,. The values determined in this more objective manner areshown in figure 12. Note th at they are in general greater than those determined

t R,, s an even function of z,,, hence the cosine transform. An appropriate spectralwindow was employed (Blackman & Tukey 1959).


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T h e s truc ture of turbulen t boundar y layers 7 6 3by the quicker visual counting scheme (11), but clearly show the same trends asthe visual counts. Some of the upward shift appears to be due to the appearanceof a harmonic at &A not counted in the visual procedure.The variation in streak-spacing is indicated in the peak distribution histogram(figure13). This, together with the variability in the individual spectra, indicatesthat there is no preferred position for the streaks ; .e. they do not arise as a resultof some irregularities in the apparatus. This question was also specifically ex-amined, and plots of streak locations for long enough times do show a uniformdistribution per unit surface area (11).The same average streak-spacing (deter-mined visually) has been found in three water channels with a number of differentactive surfaces, providing further evidence that the streaky structure is a resultof natural phenomena within the flow.

The peak in the ensemble average spectrum is considerably less pronouncedthan in the instantaneous spectra. Time-averaged correlations obtained by hot-wire measurements would appear more like the ensemble average, and hence thestreakiness probably would not be revealed as clearly as by the (instantaneous)visual studies.f-

The second important feature observed in the visual studies is the streak break-up and ejection from the wall. Repeated and careful study of the motion picturesusing dye injection shows that these processes occur intermittently and randomlyover the surface. Most of the time the streak pattern appears to migrate slowlydownstream as a whole, with each streak drifting very slowly outward. Withinthe innermost layer this motion is smooth and straight, with the streak appearingto become thinner as it moves outward. When the streak has reached a pointcorresponding to y+ FZ 8-12, it begins to oscillate. This oscillation amplifies as itgoes outwards and terminates in a very abrupt breakup; most of the breakupsappear to occur in the region 10 < y+ < 30. After breakup the streak becomescontorted and stretched, and a portion of it migrates outward through the boun-dary layer along an identifiable trajectory. A sequence of sketches depictingthese processesis shown in figure 15. These sketches represent typical side views,as seen in the motion pictures. The arrow follows a prominent portion of the ejec-ted streak. The oscillation is clearly evident in the third sketch, and the contor-tion in the fourth and fifth.The motion pictures, particularly more recent side and end views, suggestthat the slow streak lift-up is a result of the streamwise vorticity. These secondarymotions collect low-speed fluid into streaks, and then lift the streaks graduallyaway from the wall until a point isreached where some sort of sudden instabilityappears to occur. The amplifying rapid oscillation we have called breakup henfollows. This process seems almost to fling low-speed fluid away from the walland out into the faster flow. It is the striking violence of this bursting processwhich suggests th at the streak breakup plays a dominant role in the transfer ofmomentum between the inner and outer regions of the boundary layer.It is difficult to quantify the breakup process, but some information has beent Indeed, the ensemble here is still for a limited number of frames (30); there is aquestion if the st reaks will show at all for very long time averages unless filtering is used.See discussion by Kronauer to article by Kline (19653).


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764 8. J . Kline, W. C . Reynolds, P. C . Schraub and P. W .Runstudlerobtained by extensive study of the motion pictures. By examining the plan viewpictures in which wall slot dye injection was employed, the number of breakupsof streaks fed by a certain span of dye slot can be counted for a given time inter-val. Interpretation of these numbers is not entirely clear. While the counting isconfined to a particular field of view, it does not really allow determination of the

0

I = 2 6r

0

FIGURE5. Dye streak breakup; illustration as seen in side view.breakup rate per unit of surface area, since the dye slot only feeds those low-speedregions passing over it. It seems that the best interpretations of the breakup fre-quency P determined in this manner is as the frequency of streak breakup perunit of span. The number l / (Ph)might then be interpreted as the average life-time of a streak.

One might expect to find some correlation of spectral data at a circular fre-quency w = %FA. Black (1966) has indeed found that wall-pressure gradientscorrelate on the wall-layer parameters a t a dimensionless frequencyw f = wv/u: =0.056. This value is also given by his simplified analysis. Our measurements yielduf = 27rP+A+ M 0-06 for the flat plate flow;? this remarkable agreement lendst Note tha t this value does not hold for K + 0 (table 1).


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T he structure of turbulent boundary layers 7 6 5

0 00 1 0 01 (1 I?n, (ft./sec)

FIGURE6a. Burst rate as a function of shear velocity. d P / d x = 0; , Runstadler et al.(1963), 3 velocities; 0 , present data, 3 2 stations.

Relaminarization limit

I I Ia

0 .- 2 -1 0 i 2 3 7 4K x o6

FIGURE 6b . Normalized burst rate as a function of K . A , d P / d x > 0; 7,d P / d x > 0 ;0 , d P / d z = 0 ; , d P / d x < 0 ;4,P / d x < 0.


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766 S. J.Kline, W . C . Reynolds, P. A . Xchraub and P. W . Runstadlercredence to the notion th at there is an inherent breakup frequency for the wall-layer flow.

Assuming that F should be normalized using u and u, (withK as a parameter),dimensional analysis suggests th at the dimensionless group P+= Pv2/u$ houldbe some function of K . The data for the flat plate flow are shown in figure 16a,

I I I I I I I I I

0 0.5 1 o 1.5 2.0t (sec)(4

0 0.5 1 o 1.5 2.0 7.jt (sec)( 6 )

FIGURE7. Trajectories of ejected eddies-flat plate flow. Station 10, d P / d x = 0 ;v, averages; 0 ,maxima.where F is seen to vary as u$ or the range of data available. I n figure 16b , F+is plotted us. K using the data from ithe five flows. The important feature isthe apparent cessation of bursting when K exceeds about 3.7 x 10-6. This isessentially the value of K at which Kays &Moretti (1965)observed relaminariza-tion of a turbulent boundary layer in heat transfer experiments with air andLaunder (1964) found similar results with a hot wire in air. The good agreementof these data further support the view that the bursting process plays a crucialrole in turbulence production and in the interaction between the inner and outerlayers.

The trajectories of the ejected eddies can be evaluated quantitatively, andthis has been done using side view motion pictures (with dye) from the five flows.


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The structure of turbulent boundary layers 76 7In each case there is quite a variation among individual trajectories, but by con-sidering a large enough sample a stable average can be obtained at any point.Figure 17 shows the distribution and average trajectories for the zero-pressure-gradient case. Note that the average trajectory and the most probable tra-jectory are essentially the same, though the variance in trajectories is quitesubstantial. The streamwise velocity component of the dye particle leading theejected streak outwards has alsobeen determined; figure 18shows the ratio of thedye filament velocity to the local average velocity as the filament passes out-wards through the boundary layer. Note that the flat plate data correlate re-markably well. Further examination of this correlation (11)suggests th at beyond

I .1 I I I I I I I I

O t 1orrelation for d P l d i = 0

FIGURE8 . Average velocities of ejected eddies.d P l d x < 0 d P l d x 0 d P l d z = 0Station Station Station@ 8 A 1 @ 6m 15 0 12 1611 0 10 A 10

y+ = 40 the ejected fluid continues to move through the boundary layer at avelocity corresponding to U&, M 13.8, which is essentially the mean velocityat yf = 40 . Hence in a sense the ejected eddies can be viewed as being born inthe wall region, and cast out into the log region fram a position at the edge of thebuffer layer. It is also interesting to note that the ejected fluid moves at some-thing less than the mean velocity, and a t roughly 80 % of the mean velocity inthe outer part of the boundary layer. This is reminiscent of the observation byKlebanoff ( 1954) that the turbulent regions in the intermittent portion of theboundary layer move at about 80 yoof the free-stream speed; however, no clearevidence is yet available concerning either a relation or a Iack of relation betweenthese two observations.

This completes the quantitative information on the flow structure availableat this writing. In the following section we give our present best interpretation


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768 S. J . K l i n e , W . C. Reynolds , F . A . Schraub and P. W . Runstadlerof the complicated processes of the turbulent boundary layer, drawing additionalinsight from further experiments, of a somewhat different nature, now partiallycompleted.4. Discussion

These observations have led us t o the conjecture that the wall-layer streakbreakup plays an important role in determining the structure of the entireturbulent boundary layer ; n particular, we believe it dominates the transferprocesses between the inner and outer (wake)regions. In this section we shall fbstdiscuss the mechanics of streak formation and breakup, and then discuss relatedevidence supporting this conjecture.A plausible physical explanation for the formation of wall-layer streaks wasessentially proposed by Lighthill (1963), though not quite in this connexion.Lighthill observed that a natural effect of flow towards and away from a wall isthe turning of the flow, as shown in figure 19a. This turning action would act toconvect and alter the spanwise vorticity component, as shown in the sketch.Vortex lines would be stretched in regions where the flow is towards the wall, andcompressed in regions of outflow. Since the spanwise component of vorticity isprimarily due to aulay , this stretching and compression would lead to spanwisevariation in u ear the wall. Where the flow is towards the wall, the spanwisecomponent of vorticity would act t o increase the local zc in the sublayer. Wherethe flow is outwards, uwould be reduced by vortex line compression. Hence aspanwise variation in u an develop naturally as a result of the inherent three-dimensionality of the coexisting turbulence. The streamwise vorticity so gener-ated would collect low-speed fluid near the wall, and when markers are put intothe wall layers th e streaks would become visible. The same secondary vorticitywould account for the lifting of the low-speed wall-layer streaks observed experi-mentally prior to the breakup process.

A similar and possibly related streaky structure is observed in the middlestages of natural laminar-turbulent transition (Elder 1960).In a series of experi-ments, Klebanoff et al. (1962) examined the formation and properties of thesetransition streaks.? In some of the experiments, the transition streaks werepurposely fixed in location by their apparatus, and were very regular andperiodic so that detailed studies were possible. It was found that the u componentof velocity was low in the region where the flow was moving away from the wall(Klebanoffs peaks ), in accord with the arguments above.

While considerable similarity exists between the transition streaks and thewall-layer streaks, there are important differences in their respective scales,steadiness, and apparently in their requirements for pre-existing fluctuations.The relatively widely spaced transition streaks break down to form propagatingturbulent spots, with smaller, more closely spaced wall-layer streaks appearingat the wall under the spots. The transition streaks can be fixed in location by rela-tively minor effects such as the screeen weaving far upstream (early experimentsof Klebanoff et u Z . ) . On the other hand, the wall-layer streaks are less sensitive to

In this section we use wall-layer streaks and transition streaks t o distinguish thetwo types clearly.


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The structure of turbulent boundary layers 769minor upstream changes, and they move in position in such a way that their dis-tribution over the area is random for long times. The transition streaks growgradually in a relatively quiescent laminar flow, while the wall-layer streaks havebeen observed only in response to relatively large amplitude fluctuations.tNevertheless, the mechanismsfor formation of the two types of streaks are prob-ably closely related, and hence the transition studies shed considerable light onthe turbulent wall-layer problem.

In examining the mechanisms of wall-layer streak breakup, we again turn tothe analogy with the transition streaks. I n the controlled transition experimentsof Klebanoff et al. (1962) and Kovasnay, Komoda & Vasuedva (1962), intenselocal shear layers (vorticity concentrations) were periodically$ formed in theouter portion of the transition boundary layer in spanwise positions correspond-ing to the streaks (the peaks).This appears to be due to vortex stretching a t theouter edge of the boundary layer. These local shear layers periodically becomelocally unstable and break down in violent oscillation,$ eminiscent of the localbreakdown processes of the wall-layer streaks in the turbulent boundary layer.Stuart (1965) has made a very simple model of the vortex-stretching processesfor the transition problem, and his model displays the important features ob-served experimentally. The vortex-stretching mechanism is found to be essentialto the development of the intense shear layers in these controlled transition ex-periments; the evidence a t hand suggests it is of similar importance in the break-up of wall-layer streaks in a turbulent boundary layer. A picture of this mechan-ism of breakup is given in figure 19b.The suggestion th at vortex stretching leads to the intermittent formation ofintense local shear layers, and hence perhaps to a locally unstable breakup, hasled us to initiate a study of the instantaneous u elocity profiles normal t o thewall. The prime tool in these experiments is a hydrogen bubble generating wiremounted normal to the plate. Preliminary visual studies indeed indicate that therandom eddy motions in the outer portions of the flow interact with the low-speedstreaks to form momentary regions of concentrated vorticity just outside of thesublayer. Those which persist sufficiently long appear to undergo a rapid break-down, possibly because of their dynamic instability. While these early results arenot yet conclusive, they do already provide further evidence for the notion tha trandomly formed local shear layers provide a source of dynamic instability, par-ticularly in the region very near the wall.11 The idea of intermittent breakdown isalso consistent with th e observation that the higher-frequency components of ahot-wire signal are intermittent (Sandborn 1953).

I n any turbulent shear flow turbulence production occurs through t he averaget See, for example, the motion pictures of natural transition by Meyer & Kline (1962).These films show that the process of cross-contamination, i.e. spo t growth, occurs at th espot edges due to a strong wave-like disturbance. This disturbance creates new wall-layerstreaks in fluid that was previously laminar, and the effect is observed only locally wherethe disturbances are large.$ The method of artificial disturbance introduced regular periodicity.5 The movies of Meyer & Kline (1962) vividly show this effect in natural transition./ / A similar idea ha s been suggested by Betchov & Criminale (1964)as a possible mechan-ism of importance a t the outer edge of the boundary layer.49 Fluid Mech. 30


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7 7 0 S. J . Kline, W . C . Reynolds , F . A . Xchraub and P. W . Runsladleraction of the turbulence Reynolds stress against th e mean velocity gradients. Infree shear layers, and in the outer regions of turbulent boundary layers, the tur-bulence consists of weakly correlated (i.e. small u'vl) motions. The strong

Compresscd vortex element

FIGURE90,. The mechanics of streak formation.

iainically unsta ble

Lifted and stretchedvortex elem ent

FIGURE9b . The mechanics of streak breakup.

correlation and high Reynolds stress which characterize the wall region of boundshear flows must arise because of some well-correlated motion; we believe thestreak breakup provides this organized motion. The Reynolds stress associatedwith the break up motions is probably greater than that of the backgroundturbulence, and hence breakup may make a substantial contribution to the


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The structure of turbulent boundary layers 771turbulence energy production per unit volume particularly in the wall region.tMoreover, the ejection extends this highly correlated motion into the outer flowalong the streak trajectory, i.e. over a substantial portion of the entire boundarylayer (figure 17). Hence the dominance of the streaks is not confined to the regionof their origin or breakup; directly or indirectly they affect most of the flow. Atest of these ideas could be obtained by measuring the instantaneous turbulenceproduction rate and correlating this with streak breakup events. Such a study isnow in progress.

There is a considerable body of indirect support for the idea tha t the wall-layer streak formation and breakup play a central role in turbulent boundary-layer processes. The most striking evidence deals with several methods for re-laminarization of turbulent flows by suppression of the streak breakup process.The effect of acceleration has already been discussed. Additionally, Cannon(1965) visualized turbulent flow in a rotating tube fed by fully established tur-bulent pipe flow from a stationary inlet section. He found tha t turbulent flowcan be completely suppressed by rotation a t Reynolds numbers as high as 20000and partially suppressed to 40000 by relatively small amounts of rotation(small Rossby number). An explanation of this phenomenon offered (by S.J.K.)in advance of the experiments was that the centrifugal field induced by rotationwould act preferentially to hold the low-speed streaks on the wall; this in turnreduced bursting action. Similarly, relaminarization has been observed on onewall of a two-dimensional channel rotating about an axis located parallel to thewall,$ while the bursting on the other wall is increased in frequency and intensity.In this case Coriolis forces provide the streak stabilization. Turbulent boundarylayers can also be relaminarized by extremely small amounts of distributed wallsuction (W . Pfenninger, private communication). If one argues that turbulentfluctuations act on passive inner layers, suction should in fact increase the tur-bulence by bringing more fluctuations closer to the wall. If, on the other hand, theturbulence is fed primarily as a result of local intermittent instabilities in theinnermost region, then removal of this region by slight suction should reducethe turbulence throughout the layer. Such is indeed the case. An explanation forthe suppression of turbulent flow by long-chain molecules (polymer additives)has even been offeredin terms of the streaks; Gadd (1965)suggested that the long-chain molecules act to inhibit the bursting of the low-speed streaks away from thewall. Other evidence supporting the importance of the streak breakup processesis cited in (I).

If the wall-layer streaks are important to turbulence production, they shouldnot appear in a wall-bound turbulent flow in which there is no production of newturbulence. Such a flow was recently studied by Uzkan & Reynolds (1967). Theypassed a uniform stream through a grid, and then passed the resulting uniformturbulent flow over a wall moving a t the flow speed. This allowed turbulence tobe impressed upon a solid wall in the absence of a mean velocity gradient. Hot-

t Note added in proof. Our recent measurements of the instantaneous values of -u'dcon6rm that the bursting process indeed contributes th e large values; details to be re-ported separately.$ Halleen & Johnston, ( 1 9 6 7 ) .49-3


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772 8. J . Kline, W . C . Reynolds, F . A . Schraub and P . W . Runstcullerwire studies showed a simple attenuation of the turbulence by the viscous actionnear the wall, and visual studies showed no evidence of wall-layer streaks. Then,the wall speed and mean speed were mismatched slightly; wall-layer streaksappeared, and the turbulence intensity near the wall actually became greaterthan that of the impressed turbulence; these observations provide further evi-dence for the association between streak behaviour and turbulence production.

Some remarks on the relationship of the observed streak phenomena withquantitative studies by other investigators is in order. Previous experimentalstudies of the energy balance in turbulent boundary layers (see Townsend 1956)have indicated that dissipation of turbulence energy exceeds production in thewake region, and that the necessary supply of turbulent energy is supplied byexport from the inner region. It is this supply which keeps the boundary layer ina turbulent state; it is less than either the production or dissipation in the wakeregion, but is clearly crucial to the maintenance of the turbulent layer. We be-lieve that the streak-ejection process is a, dominant contributor to this energyexport process. Measurements (though perhaps less accurate) also indicate th atthere is very little energy transfer from the region y+ < 20 to the region beyond.Hence the source of turbulent energy lies outside of this region. This is consistentwith our observation that the streak breakup begins around y+ = 30, and ex-tends outwards along the ejection trajectory. The general nature of these tra-jectories seems consistent with the space-time correlation measurements ofFavre and his co-workers (Favre, Gaviglio & Dumas 1957, 1958). The generalstructure observed in the viscous sublayer is also consistent with the recent hot-wire explorations of Bakewell & Lumley (1967); hey suggest th at the motionsyielding strong longitudinal vorticity (i.e. the wall-layer streaks) are the domi-nant (big ) eddies in the wall-layer region. In summary, we know of no reliableexperimental data which are inconsistent with our stated conjecture on the im-portance of the wall-layer streaks.

In summary, we view the formation of wall-layer streaks as the result ofvortex stretching due to large fluctuations acting on th e flow near a smooth wall?in the presence of strong mean strain. We believe th at the production of turbu-lence near the wall in such a flow arises primarily from a local, short-duration,intermittent dynamic instability of the instantaneous1 velocity profile near thewall. This instability acts not to alter the mean field flow but rather to maintainit. The ejection of fluid away from the wall in the subsequent process is felt to bethe central mechanism for energy, momentum, and vorticity transfer betweenthe inner and outer layers.

This study was financed jointly by the National Science Foundation and theMechanics Division of the Air Force Office of Scientific Research; their supportis gratefully acknowledged. Professor J.P. Johnston provided many helpfulsuggestions and criticisms throughout the work.should be considered dist inct from th e remarks here on smooth walls.Tiederman 1967).

t Observations on rough walls and in free shear flows show different structures and$ The mean velocity profile is believed to be stable to small disturbances (Reynolds &


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T he structure of turbulent bound ary layers 7 7 3R E F E R E N C E S

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