The intermittently turbulent region of the boundary layer

CHIEF

Lab. y. Scheepsbouwknde

US CAE 110

Technische Hogeschool

November 1968

De

UNIVERSITY OF SOUThERN CALIFORNIA

SCHOOL OF ENGINEERING

THE INTERMITTENTLY TURBULENT REGION OF THE BOUNDARY LAYER

R. E. Kaplan and John Laufer

Office of Naval Research Contract Nonr 228(33)

National Science Foundation Grant GK-1256

DEPARTMENT OF AEROSPACE ENGINEERING

The Intermittently Turbulent Region of the Bpundary.Laye.r

There.is increasing evidence that fully developed turbulent shear

flows exhibit a velocity structure that ¡s more coherent than generally expected. It is possible to detect añ ordered, reltively coherent structure that moves randomly in space and time ànd has charácteristic

lifetiriies and length scales which arei in general, much larger than the dissipation scale of the flow.

Péi'haps the mo dramatic evdeice of the existéncè òf this type.of

quàsi-ordered motion ¡n the boundary layer is found in the worlç of Kim, Kline, and Reynolds (Ref. 1), in which such a structuré isdetected near

the sublayer by measurement of instantaneOus velocity distributions using the hydrogen búbble technique. ihese measurements shòwed the repeated appearance

of

this characteristic structure at random intervals of time.

It is clear that without a set of "instantafleous velocity profiles, conventiònal time averaging of the velocities wOuld have overlooked such a phenomena. The interest, of course, is not in the phenomena itself, but on any light that it may cast on the production of turbulent energy by the shear flow, in this case through a possible instability of the basic flow.

The phenomenon to which we address ourselves is the structure

associated with the motion of the interface between the turbulént añd non-turbulent fluid at the outer edge of the turbulént boundary layer, although sirnilär phenomena occur in turbulent jets, wakes, and shear

techniques yield litti _{evidence.öf such struture, since they weigh} equally contributioñs frOm the turbulent and non-turbulent regi:oñs of

the flOw. _{However, investigators sUch as Kovasnay and Kibens (Ref.- 2),}

and the authors, have demonstrated the existence of _{such a structuré and}

made detailed quantittive méasurements of it properties. The question

that is-relevant in this region of the flow ¡s.the relationship betwéen

this detetablê structure and the entrainment _{process of nöñturbu.lent}

fluid.

For the purpose of analyzing such phenomena, a facility for the digital processing of turbuleht bOundary layer data was established at the University of Southern California _{The following is a description} of the initial measurement.s processed by this facility some interpre-tation of the results, and à brief account of the techniques used.

:conitional Sampling and Detector Functions

ihere are two basic requirements that must be rhet before the probing randomly occurring coherent structures can proceed.

i) The first of these is the ability tö measure velocities at

several points ¡n the flow field simultaneously. This necessitátes the use öf an array of velocity sensors (hot

wire anemometers) with the size-of the array of the order

of the characteristic scàlé of the. structure. _This

tech-nique was ¡n fact sucessfully used by Kovasznay alid

Komodà (Ref. 3) _{in their study of the formation of} turbu-lent spots during transition.

3

The second requirement ¡s the capability

of

performing a con-ditionàl sampling of these signals,. that is the ability to sample only during the period when the structure passes the array of sensors. We can compare this process to conventional time averages by performing the appropriate statistics not on U(x,t), but on the product of U with a detector function D(t) which has the value 1 during the time passage of the structure,

and O at all other times.

It is our contention that these two requirements are cômmön to all problems of the type under discussion, with the major difference from problem tò problem iñ the generation of the detector function. In the

intermittent zone, the question of what to detect is quite straightfor-ward.; namely, the presence or abseñce of turbuleñce., While it is clear what is to be detected, there are many possible techniques fOr mechanizing the detection. These are (in a rough chronological order), the sensing of the streamwise component of vorticity (Ref. 14), the sensing of the spanwise component of vorticity (Ref. 2), sensing transport' of a marked species (such as smoke') (Ref. .5), and sensing the amplitude in a frequency band

of theu' fluctuations (Ref. 6).

In brief, the detector evaluation is as follows. The désired

criter-ion functcriter-ion (enumerated above) is significantly larger in the turbulent regiOn than in the non-turbulent region of the flow.- The criterion is

conditioned, amplified, and rectified, and a threshold level is set. When the criterion function exceeds this.threshold, the detectò functiOn

is

set to 1, otherwise it is O. The major problem ¡n the detection is that

the criterion function ¡s not explicitly zero in the non-turbulent portion, and quite often crosses zero in the turbulent portion Hence some sort of logic must be used to ascertain whether the indication given by the detector function is a. true indication of the state, or a trañsient.

This problem has been solved to one degree or another by the investigators

Ïisted àböve,, but only in the case öf the last two has the question really been crucial. When the detector function is used for conditional

sam-ling, it is "differentiated" to' compute certaiñ types of conditional

averages. Any spurious indications of interface, position can bias certai.n types of averages with an excess of signal not belonging to that sample

set. Hence it is 'important that great care be given in the generation of

the detectOr function.; In this regard it 'is most fortunate that the work. of Kovasznay and Kibers, cited earlier,' used an entirely separate tech-nique for the gène.rátion Of thé detéctor function, for it demonstratéd that the conditional average's described herein are independent of the form of the criterion function The details of our criterion functton

generation aré described later. . '

Part of the studies in the intermittent zone havebeen based solely

on the detector function The intermittency factor y is an appropriate

time average of the detector function, .

y()

co-ordinate normal to thé wall. Iñ the same sense, wé may define averages of some property Q,.under some function f of D as

= Tf

(D(y,t))Q(t)dt

For example, turbulent zone averages use f(D) D, while non-turbu-lent zone averages use f(D) = l-D The function Vf is generalized to be

an integral over f(D), and hence when f(D) ¡s a positive dérivàtive(a

Dirac delta), y measure the number of discrete non-zero values of f(D) with a similar result for the negative derivatives. The latter two averages are associated with the passage of the ¡nterface at a detectör

lôcation and are formally equivalent to summations over appropriate

interface crossings. It is clear that by proper adjustment of the

thresh-old levels at the disposal of the experimentalist, that the intermittency

factors can be brought into reasonable experimental agreement, because the resultant function D is integrated. In the iñtèrfácé averages, how-ever, when the integral is ¡n fact replaced by a summation, differences in the detector function cause significant differéncés in the averages.

It is for this reason that we shall discuss formation of the detector function ¡n some detail.

Generation of the Detector Function

The technique described in thé following paragrphs are well suited

to digital processing but is significantly more difficult to perform in the laboratory. We have mentioned a criterion function, which is the

detec-tor function is derived, In general, the criterion friction shOuld be

small in the non-turbulent regions, ànd ofappreciable magnitude in the turbulent, regions. The most physical quantity availablefor this use

is the velocity fl'uctuàt ion ¡tsèlf, but a judgment based on this, or even its time derivative is quite difficult becaùse there are stiil appreci-able velocity.fluctuation.s in the non-turbulent portions of the flow.

The "best" criterion is based on the local vorticity which i.s zéro ¡n.

the non-turbulent regions and quite large in thé turbulent regiOns. The

vorticitywas used by Corrsin and Kistler (Ref. k), and a component of

vorticity by Kovasznay and Kibens (Ref. 2). The problem withusing

vorticity as a criterion, in our view, is (i) that artiulti-wlre probe

must be Used merely to detect the iñterface position, and (ii) that the

outputs of the wires in 'general must be linearized and carefully bálanced to. prevent the dorñinance of the 'u' fluctuation prom one of the sensors.

A more serious drawback of an instantaneous measurement is the fact that

it ¡s desired o base the detection on the emergence of the criteri:on

function from à window ¡n some phase plane (Kovasznay and Kibens used as

their criterion that both

2u/yt

and

3u/yt2

must be larger than a sèt valué). But the cHterion function öften crosses zero, and while

filtering cn help remove sorne of these spuriou.s zero crossings, and not seriously affect the transit ion ¡n which the criterioh function goes from a small to a large value, the other interface crossing (when the.

crite.rion function goes from a large to à small valué) is made mOre ambig-. uous by the discharge of the. filter capacitor, and the detailed setting

7

of the threshold can have a profound ¡nfluence on the results. It became apparent to the authors that an important reqUirement for good detection was some knowledge of the future. the same conclusion was reached inde-pendently by Kovasznay ànd Kibens, who take some time to generate the detector function, and consequently must delay the signal from other wires to account for this delay. In the present study, signals were stored ¡n the computer for a small time interval so that various amounts of time delay (and lead) were attainable.

The détection technique used universally in this study was based on a detectOr consisting of a single hot wire.. The variance of the time derivative of the hot wire voltage about the mean was computed over a

relatively short time interval (the time interval varied from 2.5 to 8

msec). It can be observed from Fig. that this variance was small when

the wire was ¡h a noturbu1eht región df thé flOw and large When the

wire was in a turbulent region In the figure, trace (a)

is

the hot

wire voltage, (b) its derivative, (c) the short time variance, and

(4)

the detector function The threshold for the detector function was de-rived by taking a fraction of the local máxima Of the criterion function over a reasonable tithe interval. Since the short time variance exhibited

no "zero-crossings", the filtration effect of the trailing edge of the

criterion function was avoided, although a type of filtration was inher-ent in the length of time interval över which the variance was evaluated.

The variance was ascribed to sOme

point'

in the time interval, and the

8

statistics. Hence the filtering process was roughly centered about the

time ¡h questibn, With information from the ner past and future equally

weighed. It can be shown that this is a low pass filter that is lacking in phase shift., but with terminal siópe asyÌhptÖte the same as an analog

'exponential'' filter. While this is ¡n no sense an optimal filter, it appears to be much more suited tö the problem at hand than the type of linear filters with continuous analytic describing functions

9

The Structure of the Iñteimittent Region

The first computations performed in the. intermittently turbulent

region of the boundary layer involved processing signals coming frpm the ten wire vertical rake ¡llustrated ¡n Fig. 6.. (A brief descriptiòn of the rake, data gathering systérn and the digital analysis system ¡s given

in the Appendix.) The Ó.000l inch diameter platinum wires were arranged

parallel to the plate and normal to the flow, with a noriìinal 0.1 inch

spacing, and functioned ás U wires. The rake was mounted to traverse the intermittent zone. The results reported in the following paragraphs were made t a nominal 20 ft/sec free stream velocity, zero p:ressure

gradient boundary layer 3.05 in. thick, artificially tripped 15 ft.

ahead of the test station with Reynolds number based on the momentum

thickness of 3600. _{Previous experiments performed in the tunnel}

estab-lished that the boundary layer was a repeseñttive one, and that ts

intermittency distribution followed the familiar scalihy laws.

The recorded data for this configuration was initially programmed to reproduce the results of Kovasznay and Kibens for a similar flow

situation. The recorded sigrìalsdid not provide vertical velocity in-formation (V'), and hence those measurements could hot be checked.

The analysis of the signals pOceeded as follows. Each wire in turn

was used to generate a detector function. This detector function was then. used to compute intermittency., turbulent and nôn-turbulent zone averages and variances, and conditional point avei-ages associated with the passage

of the interface.. The. familiar curve of iñtermittency distribution y(y)

10

scatter band. _{The conditional averages measured in the present study} are in agreement with those of Ref. 2, as illustrated ¡n Fig. 2. _(The notation, is that of Ref. 2.) _{The conditional point average associàted}

with the leading interface encounter (leading edge averages)

correspond-¡ng to.the transition from non-turbulent _{to turbulent fluid, were alsò} substantially the same as those found in Ref. 2. The geometry of the

point averages are illustrated ¡n Fig. _5.

The only areaof disagreement with Réf. 3 came ¡n the evaluationof

the trailing edge averages. In Réf. 2, these were essentially the same

as the leading edge averages, and ¡h fact, this similarity was used as

a means of evaluating the time delay inherent ¡n their detector function

generation Use of the present detector function indicáted a consistent

difference in the trailing edge averages, incapable of being resolved by

varying the appropriate time delay. _{The present results indicate a smáll}

but definite velocity defect fòr trailing edge point _{averages as córlipared}

to the leading edge averages. _{Figure 3 illustrates thee pöint averaged} velocities at the interface location. This sugests that thé particle. velocity is measurably smaller in the vicinity of the trailing edge of

the turbulent bump, and in particular at the interface. _{While no}

conclu-sion can be made abòut the velocity of the interface at the present time,

one can anticipate a corresponding difference in interface velocity. If the latter conjecture is true, there should be an observable difference in the interface geometry. With this goal, an attempt was

made to provide a visual display of the ¡ntermittéñt zone. The result of just such an experiment ¡s presented ¡n Fig. Li. At each time increment, a decision was made as to whether a given hot wire was in a turbulent or non-turbulent region of the flow. These decisions were presented on the

line printer as asteiisks (*) if the detector function was 1, and a blank otherwise. Each horizontal line of asterisks correspond to à given wire output. To conserve space, ten sucçessive timê ¡ntervals were presented

on the sñe figuie. The t:ime sequence ¡n the figure proceeds from the

lower left hand corner, left to right, continuing in the left side of the next higher row. The time between successive presentations is

approx-¡mately 1 msec, and the wire locations varied from y/ô of .7 to 1, cor-responding to inteíthittehcy factor yof .6 to 1. Thé apparent $lopes on the figure are approximately 1.5 times the physical slopes to be expected

if the pattern weré frozen in space.

Several results aré apparent from figures such as this.. The first is that thére is a regular difference between the leading and trailing edges of the interface, with the former being uniformly steeper correspon-ding to its higher velocity. The second is the apparent absence of regions of non-turbulent imbedded in a mass of turbulént fluid, and thé converse, even though ¡t is now known that the bumps are highly three dimensional, and the two dimensiohal rake could easily "graze the side'.' of protruding turbulent lump. Thirdly, it is noted that the indication öf turbulence

12

and vice versa. lhis quality is not progrßmmed into the logic of formin.y the détector function, but ¡s ¿ consequence of the criterion function

used. Finally, the extent of the large scale motions are apparent, and

complement the conditionally sampled .struçtures piesented here and in

Ref. 2..

While the indication of the interface, strfttlyspéakFng, yields its

elevation at a given streamwise location as a function of time, its spatial

structure is believed not to be significantly different t:han the situation as pictured. Referrin.g to Êig. 5, the tentative interpretation is that

the entrainment of non-turbulent fluid Occurs predominantly along the

relatively diffúsè trailing edge of thé protruding turbulent zpne. Further measurements of the propagatioñ velocity of the turbulent front are' needed

to verifythis interpretation.

Conclusion

In summary, ¡t is noted that these initial results from the present

facility shed further light on the procésses associ:te with the

entrain-ment of non-turbulent fluid. The presence of the large scale motions Of the interface and the lOcal proagatioñ of the fronts through small scale

turbulent diffusion are in fact consistent with Townsehd's ¡dèas. Whèthèr

the large scale motion is in fact due to a Kelvn-Helrnholtz type of insta-bility as suggested by him, cannot be ascertained at this stage

References

i. Kim, IL, Kliñê, S., añd Reynolds, W. An Experimental Study of Turbulence Production Near a Smooth Wall ¡n a Turbulent Boundary Layer with ZerQ Pressure Gradient. AFOSR Sci. Rept. AFOSR-68-0383

Jan. 1968.

2 Kovasznay, L S G , and Kibens, V -- To be published

Refer tb Kibens, V., The Intermittentj Region of a Turbulént. Boundary

Layer. Dissertation, Johns Hopkins Univ., Feb. 1968.

3. Kovasznay, L.S.G. and Komoda, "Detailed Flow Field ¡n Transition." Proc. 1962 Heat Transfer and Fluid Mech. Inst:. Stanfórd Univ. Press, 1962.

L1 CorrsFn,S., and Kistler, A.L. Free St:ream Boundaries of Turbulent

Flows. ÑACA Report 121+4, 1955.

5. Fiedler, H. and :Heàd M.R. Intermi.ttency Measurements ¡n the Turbu-lent Boundary Layer. J.F.M. 2k, k, Aug. _1966.

6 Laufer, J and Kaplan, R E Concerning the Large Scale Motion in the

Turbulent Boundary Layei Fourth Euromech. Cbllqyium "The Structure

óf Turbulence." Southampton, March 1967.

7. Townsend, A.A. The Mechanism of Entrainment ¡n Free Turbulent Flows. J. Fl. Mech. 26, k,

pp. 689-715

(1966).

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Flow dagram of. the Analysis Facility

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COMPUTER.

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Apperidi X

Turbulence Data Processing System

The data reported ¡n this paper was processed ¡n a unique digital

facility. The system has two parts, which aré separated both physically

and logically. The dataj gathering portion of the facility resided in

the Low Turbulence wind tunnel and consisted first of a probe with ten hot wire anemometers arranged in a vertical two-dimensional rake with

0.1 inch spacing. All wires we.re inserted in a bank of constant resis-tance bridges so they operated as constant temperature hot wire

anemom-eters. At the typical velocities of the test (20 ft/sec.) aI wires had frequency response abcve 3,0 kHz as determined from à pulse test. The output from these bridges was recorded as channels l-10 on a 14 channel

FM tape recorder at 60 ips (in/sec). At this speed, the signal to noise

ratio (re 40% modulation) was 48 db. To counteract loosing the small velocity fluctuatiön,s in the tape noise, signal conditioners consisting

of a bucking DC amplifier, which subtracted most of the DC component of the wire output, and a 20 db amplification of the difference voltage

were recorded. The frequency response of these components were in excess of 25 kHz for the signal levels typical of those from the hot wires. The. frequency response of the tape recorder was DC-20 kHz. From the system gain, it is estimated that the signal to noise ratio of the fluctuations alone was in excess of 36 db, while for the reconstructed

hot wire voltages it exceeded 70db.

22

Simultaneously, the' voltage output from a pressure transducer

moni-toring tunnel dynamic pressure was recorded FM and a 20 kHz square wave

was recOrded direct.

The recording procedure was as follows.

First,

five short runs were made to calibrate the hot wire anemometers.

The

first two of these consisted of dialing indicated pressures into the

pressure transducer system to calibrate that portion of the electronics,,

placing the hot wire. array in the free strearfi of the tunnél, and recording

the dynamic pressure and hot wire voltages at three separate tunnel

veloc-ities providing data for a linearizatiOn program which fitted King's Law

to the wire Outputs ove.r the small velocity range of interest.

The

cal-ibration was completed in less than 5 minutés, and was foliöwed

imme-diately by from two to four data runs of one minute duration with the

rake at various elevations from the surface.

Generally calibration and

data gathering occupied, fr-orn 10-12 ríiiñutes elapsed tirnè ¡n the tunnel,

although setup of the ten probes, determination of the rake position

relative to the wall, balancing and optimizing the frequenc.y response

of thé ten bridges, and adjustment of record levels could consume an

hour's time.

The ne.t result of this phase was the production of än

analog, tape. with severa] experimental arrangement's recorded on ¡t.

This tape was then carried, to the analysis facility, physically

located in the USC'School of Engineering Systems Simulation Laboratory.

In this laboratory wäs located the playback recorder (Identical to the

recording unit at the 'wind tunnel), an IBM 360/L14 digital computer with

unit.. _{The latter device communi'cáted with the analog portion of the} laboratory through digital _{in (Di) and digital out (Do) lines to sense}

and transmit voltage levels and operate relays. The portion of thé

interface of particular interest was the Adagè analog to digital

Con-verter (ADC), the Voltage Multiplexor (vMx)., and the digital to analog converters (DAC). _{These devices were capable of being operated by the}

IBM 1827 and transmitting (or receiving.) control _{signals and data.}

our case, the ADC conversion provided a 1k bit conversion (including sign) in 2's complement notation. _{Additionally the cbmputér has as a} standard feature, 6 uncommitted external ¡nterrrupt _{lines, the use of} which will be described later.

A unique feature of the facility, was the absense of an intermediate storage medium for the conversions, due ¡ntiall.y to the lack of digital

tape units ¡n the laboratory and the small capacity of the, system's random access discs. _{As development of the. system progressed, the lack}

of this intermediate storage was not missed, and actually simplified

the tape accounting.

The programming system consists of a series of' FORTRAN and assembly

language subröutines compatable with the 76ó/kk Programming _System

provided by IBM. _{The major feature of these routines was that they}

usurped many of the functions generally reserved to the Supervisor

pro-gram, enabling the support of hybrid cómputation and the external inter-rupt feature.. _{Only these system's programs were assembly language}

programs, the computatión was performed by FORTRAN programs, with a

2+

sequent loss of computing speed. Without going into the details of the programming, several general points of interest will be noted.

The first phase of the computation was the calibration of the hot wire channels and the pressure transducer. The assumptions made in this calibrátion were (i) that the recorders, playback amplifiers, and con-vertèrs were linear (experimentally verified), (ii) that both the gains and offsets of the recorded signais werê unknown, and (iii) that King's Law held for the constant temperature hot wire outputs. The calibration proceeded as follows: Froñi the two pressure transducer calibration signais, the dynamic pressure calibration factors were recòrded. This

information wàs then used in the fitting of King's law to the converted numbers from the Hot wire channels, with the velocity determined from the measured dynamic pressure. Several thousand conversions were made during these calibration runs to minimize the effects of tape noise ôn the calibration (three velocities provide the minimum ¡nformation to f-it King's Law when the offset for hot wire voltage is not known).

Since the problem of intèrest involved only a narrow range of velocities, the details of how the cali:bration were performed are Of small

impor-tance. While there is still some small discrepancies in the stadc (Dc) calibrations of the wires for the last runs in the grOups, the slope of

the calibration is still sufficiently accurate to provide velocity dif-ferences for..á given wire of 0.1% (the limits of the system). This was felt essential ¡h view of the small differences between the conditional averages and- the time averages.

The second phase of the computation was the actual eváluation of

desired experimental results. A detector function was generated from

the converted hot wire voltáges for all ten channels, añd the hot wire voltages were linearized to give a velocity array, and stored ¡n a small

ring buffèr The computation of conditional averages proceeded as follows.

First, a decision as to whether the detector function for a given wire was

either O or i was made., and the appropriate suIrmiation of velocity ánd squares of velocity for that wire was updated. Then a decision was made

as to whether the detector function had changed. If it had, the appro-priate conditional average for ali wires (and thé squares) was updated. Since each wire of the ten could generate a detector function for its position, this process was cohtinued for all wires.

it is obvious from even the brief desci9ptioh given aboyé, that the time to update all of the appropriate summations would vary appreciably, from a minimum when no detector fuñction changed, tö a maximum when all detector functions changed. Since large amounts of bulk storage were not available at the cömputer, the conversions were occurring at the

saje time as the cornputatiön. If the conversion and calculation

pro-ceeded serially, the interval between conversion would have to be long

enough to insure that the longest calculation coùld be cOmpleted. This

would have resulted in an unduly longtime interval between conversions. However, if ¡t ¡s recognized that the maximum calculation time occurs

only rarely,. the conversions and calculation can be overlapped. This

overlapping requires a small buffer to keep active informàtion from the 25

26

recent. past, and ¡n practice, conversions from only 16 time slices in the past were retained.

The programming feature that enabled the overlapping of conversion

and calculation was essentially a small timé sharing _{system, Operating}

internally under control of än external clock. _{Upon receipt of pulse} from the _{xternal clock (at 16 msec intervals) on one of the six} avail-able external interrupt lines uïiêntiöned previously, the _computer

inter-rupts its current task, stores the results of a previous cOnversion in locations açcess:ible to the calculating _{program, updates the current} conversion count, initiates a new conversion and returns, the

calcu-lating program is entire1 _{unaware of the interruption, and resumes} òperation with the next instruction, and for all practical púrposes, is unaware of the source of data it is reducing. Two checks are built in;

namely that the calculating program does not Overtake and pass the

con-version routine, and because of the relatively small buffer size, fall too far behind.

It should be stressed that the calòulation prpgrams were written ¡n

IBM supplied FORtRAN IV, and computation times could have been reduced

by at least a factor of ¿ _{if assembly language programs hád been used.} It was felt that the added programming huisance Of assembly programming

was unwarranted at this stage of the system development, but will

cer-tainly become necessary for future timing sensitive calculations. As a final note on the versatility of the programming scheme, ¡t

was qenerally true that the calculations program had at its disposal velocities at Il past time segments, and 5 future time segments of the

time assigned to the detector function. This allowed the investigation of the importance of detector time delay on the evaluated conditional averages. The buffer would have to be enlarged only slightly to enable

space time corr-elation to bemade over reâsonable time intervals, although the generation of conventional correlations were not a goal

in this experiment.

UNCLASSIFIED

Security Classification

'i'('tItit\ Cnii1t'..ti.,

DOCUMEÑT CONTROL DATA - R & D

(Security classification et title, body of abstract end indexing annotation must be entered when the_overall report is classified)

,

1. ORIGINATING ACTIVITY (Côlporate author) '

University of Southern California

Department of Aerospace Engineering

Los Angeles, California 90007

2a.REF'òRT SEC'üRITv CLASSIFICATION

UNCLASSIFJED 2b. GROLiP'

3. REPORT TITLE

THE INTERMITTENTLY TURBULENT REGION OF THE BOUNDARY LAYER

4. DESCRIPTIVE NOTES (Type of report and inclusive dates) Scientific Interim .

5. ALI THORISI (First name, middle initial. lasth'"

Richard E.. Kaplan and John Laufer

6 REPORT DATE

November 1.968

7e. TOTAL NO. OF PAGES

27

lb. NO. ÒF REFS

7

Sa. CON TRAC T OP GRANT NO. '

Nonr 228(33) and GK-'1256

b. PROJECT NO.

C.

d.

96. ORIGINATÖRS 'REPORT NUMBERIS)

USCAE 110

Sb. OTHER REPÒHT NO)SI (Any other numbers that may be assigned

this report)

IO. DISTRIBUTION STATEMENT

1. Distribution of this document is uni imitêd.

TI. SUPPLEMENTARY NOTES _{IS. SPONSORING MILITARY ACTIVITY}

Office of Naval Research National Science Foundátion

3. ABSTRACT

Measurements were made ¡n the region of the turbulent boundary layer

where the flow state alternates between turbulent and non-turbulent. _The emphasis of the experimen.t was to explore the technique of using arrays of hot wire anemometers and analyzing the signals of _{these wires with a} digital computer. _{A technique similar to the one used is necessary to}

determine statistics of the intermittent flow _{more sophisticated than the}

conventional and familiar ¡ntermittency distribution.

Techniques and criteria for forming a broader class of "ensemble"

averages for intermittent flows are d'iscussed. _{In particular, emphasis} ¡s placed on the concept of "conditional" 'averages of pertinent physical variables ¡n this type of flow. _{Useful examples of this type of average}

arethe average _{velocity distribûtiön in the turbulent region, and}

velocity distributions related to 'a specified position of _{the' interface} between the tur'bulent and non-túrbulent fluid.

'e

FORM

I NOV 65

tJNCLASSIF!ED

UNCL-ASS IF lED

Se c urityC la s sil icat ion

ürity CIaSsLflCatLOfl

LINK A L IN K B LINK C

KEY WORDS

ROLE wr ROLE wr R O L E WT

Turbulent Interface