Space-time velocity correlation measurements between fluctuations occurring in the convoluting outer edge of a flat boundary layer with fluctuations occurring near the viscous subregion were made. The correlations indicate that information is propagated from the outer region to the inner region. The migration of turbulence away from the wall was previously studied in the open literature. The results presented here along with the migration results lend support to the limit cycle model for turbulence production

Cliff, W. C.

Sandborn, V. A.

English

NASA Technical Reports Server

N A S A  TECHNICAL 
MEMORANDUM 
NASA TM X-64935 
CORRELATION BEnnlEEN THE OUTER FLOW 
AND THE TURBULENT PRClDUCTION 
IN A BOUNDARY lAYER 
By William C. Cliff and Virgil A. Sandborn 
May 1975 
NASA 
Geqe C. Mar&aZZ Space Flight Center 
Mmhall  Space Flight Center, Alabama 
https://ntrs.nasa.gov/search.jsp?R=19750017015 2020-03-22T22:10:51+00:00Z
TECHNICAL REPORT S T  ANOARO TITLE PAG! 
I .  REPORT NO. 2. G O V L I I N Y  I(T ACCESSIOW IK). 3. RECIPIEYT'S CATALOG YO. 
NA!% El X-64935 
b .  T I T L E  AND S W T I T L E  S. REPORT DATE 
Cor re l a t ion  Between the  Outer Flow and the  Turbulent ?lay 197 5 
Production i n  a  Boundary Layer 6. PERFORMING ORGAMI-A. :ON CCOE 
William C. C l i f f  and V i r g i l  A .  Sandborn I 
9. PERFORWNG OIIGANIZATIOW NAME W D  LDDRESS 10. WORK UNIT NO. 
George C. Marshal l  Space F'ight Center  
Marshal l  S p ~ c e  F l i g h t  Center ,  Alabama 35812 1 1. COYTRACT OR GRANT NO. 
National  Aeronautics  and Space Administrat ion I Technical  Memorandum 
Washington, D. C.  20546 
14.  SPONSORING AGENCY CODE 
I 
PS. SUPPLEMEN7ARY N O l E S  
16. ABSTRACT 
Space-time v e l o c i t y  c o r r e l a t i o n  measurements between f luc tuac ions  occu r r ing  i n  
the  convclu t ing  ou te r  edge of a  f l a t  p l a t e  boundary l a y e r  wi th  f l u c t u a t i o n s  
occurr ing  near  the  v iscous  subregion have been per formed. The c o r r e l a t i o n s  i n d i c a t e  
t h a t  informat ion  i s  propagated from the  o u t e r  reg ion  t o  the  inner  reg ion .  The 
migra t ion  o f  turbulence  away from t h e  wa l l  has been previous ly  s tudied  i n  the  
open l i t e r a t u r e .  Ihe  r e s u l t s  presented i n  t h i s  r e p o r t  along wi th  t h e  migra t ion  
r e s u l t s  lend support  t o  t h e  " l i m i t  cyc le"  model f o r  turbulence  production. 
1 
19. SECURITY CLASSIF. (d thh  n p a W  20. S E C U I T Y  CLASSIC. (d tN .  p ~ )  2 1 .  YO. OF PAGES 2 2 .  PRICE 
17 .  KE' YvRDS 
Unclas s i f i ed  
18. OlSTAl lUTlOU S T  ATEMLNT 
Unclass i f ied  - Unlimited 
TABU OF CCNTENTS 
Page 
m O W C T I O N  .................................................. 1 
BA CKGROUND.................................................... 1 
TEST S E W  ANTI PROCE D U R E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3 
.......................... EXPERIMINTAL RESULTS AND DISCUSS TON. 4 
REFERENCES .................................................... 7 
iii  
CORRELATION BETWEEN rtiE OUTER FLOW AND THE TUFBULENT 
PRODUCTION I N  A BOUNDARY LAYER 
I. INTRODUCTION 
Space-time co r re l a t ion  measurements show a r e l a t i o n  between 
the undulating outer  edge boundary layer  flow and the turbulent  
production region near the surface.  The observation ind ica tes  
t h a t  information i s  prcpagated from the  outer  region t o  the inner 
region. 
11. BACKGROUND 
The processes involved i n  the i n i t i a t i o n  and p ro l i f e r a t ion  of 
turbulence i n  the  f l a t  p l a t e  boundary layer  a r e  a t  present not 
wel l  understood. Laufer and Bandri Narayanan have presented 
evidence t h a t  t he  turbulent  production mechanism near the wal l  of 
a turbulent  boundary layer  s ca l e s  with the outer  flow parameters 
1 They suggest a " l i m i t  cycle" model f o r  the turbulent  pro- 
duct ion which appears cons is ten t  with the physical &e l  proposed 
by C l i f f  and Sandborn [ 2 ] .  
Kline e t  a l .  exadned  the t r a j e c t o r i e s  of turbulent  pockets 
a s  they migrated from the near wal l  region toward the  outer  re8ions 
of the boundary layer  C31. A d e t a i  led mapping of space-time auto- 
correlations of the ve loc i ty  components was taken across 8 f l a t  
p la te  boundary layer  by Blackwelder and Kovasznay [ 4 ] .  The mapping 
gave i soco r re l a t ion  l i nes  of 0 .8 ,  0 . 6 ,  0 . 4 ,  0.3, 0 . 2 ,  and 0.1 f o r  
the u component of ve loc i ty .  Blackwelder and Kovasznay noted 
tha t  the locus of  t he  maximum space-time co r r e l a t i ons  was 
approximately along the t r a j e c t o r y  of  eddy migration a s  reported 
by Kline i 33 .  The work of Kline e t  z l .  [3I and Blackwelder and 
Kovasznay ind ica tes  an outward migration of eddies  which a re  
produced i n  a formation zone near t he  wal l .  lhis migration 
phenomenon supports the  hypothesis t h a t  the  eddies  formed near 
the wal l  a re  u l t imate ly  associated with the convoluting oute r  
edge of  the boundary layer .  A c los ing  bf the " l i m i t  cycle," 
proposed and s tud ied  i n  t h i s  repor t ,  r e l a t e s  t he  convoluting 
outer  edge to  the generat ion of  turbulence near  the wal l .  The 
convoluting oute r  edge of  the  tu rbulen t  boundary layer  has been 
shown t o  produce la rge  per turbat ions i n  the l oca l  v e l o c i t i e s  
and pressures ,  a s  reported by Kovasznay, Kibens, and Blackwelder 
[5]. It i s  postulated t h a t  the ~ e r t u r b a t i o n s  t r a v e l  through the  
boundary layer  and give r i s e  t o  the turbulent  production process 
which occurs near the viscous sublayer.  A p a r t  of the  turbulence 
produced near the wal l ,  i n  t u r n ,  moves outward and eventual ly  
produces the convoluting oute r  edge of  the boundary layer  t o  r e -  
produce and sus t a in  i t s e l f .  (The motion outward has been shown 
e a r l i e r  by Kline e t  a l .  [33 and Blackwelder and Kovasznay 
.) 
Space-time co r r e l a t i on  techniques a r e  .a method of examining, 
a t  l e a s t  i n  p a r t ,  the  inward r e l a t i o n  between the undulating 
outer  edge and the turbulent  production region of a boundary layer .  
The space-time c o r r e l a t i o n  of ve loc i ty  f l uc tua t ions  occurr ing i n  
the undulating outer  region with ve loc i ty  f  luccuations occsr r ing  
near t he  viscous subregion has been performed. The objec t ive  of 
t h i s  repor t  is t o  presept the co r r e l a t i on  d a t a  and i n t e r p r e t  t he  
r e s u l t s .  
111. TJiST SETUP AND PROCEDURE 
The experiment was performed i n  a small ,  open-return-type 
wind tunnel.  A honeycomb, which i s  located i n  a la rge  c i r c u l a r  
i n l e t ,  i s  used t o  s t r a igh t en  the  i n l e t  flow and break up any 
large-scale  dis turbances.  From the i n l e t  the  flow passes through 
a s e t t l i n g  chamber and then acce l e r a t e s  i n t o  a t e s t  s ec t i on ,  
where the  c ross  s ec t i on  narrows t o  0.457 m by 0.457 m. The c e i l i n g  
of the  tunnel  was adjusted so as  t o  develop a near zero pressure 
gradient  f l a t  p l a t e  boundary layer .  The co r r e l a t i on  measurements 
were performed a t  1.22 m from the s t a r t  of the t e s t  sec t ion .  Two 
stendard constent temperature hot  wire anemometers were used with 
0.01 rn diameter platinum ir idium wire. Normal annealing and 
c a l i b r a t i o n  of the  hot wires  were p e r f o r a d  as  described i n  Reference 
2. 
One hot wire was placed i n  the  undulating oute r  edge of the  
boundary layer  and one was placed very near the wal l .  The boundary 
layer  was approximately 7 cm high. 
Signals  from the  hot wir dere fed d i r e c t l y  i n t o  a coamercial 
time delay co r r e l a to r  , RMS meters,  and tape t r a m p o r t .  
IV. EXPERIMENTAL RESULTS AND DISCUSSIONS 
As was pointed out  e a r l i e r ,  Kline e t  a l .  [31 and Blackwelder 
and Kovas may [ 4 ]  have per formed experiments which support the 
hypothesis t h a t  turbulence generated ne. i. the wal l  migrates out-  
ward and i s  u t l imate ly  associated with the convcluting oute r  
edge G F  the boundary layer .  
The following experiment was conceived and performed i n  an 
a t t ~ n p t  t o  determine i f  any c o r r e l a t i o n  e x i s t s  between the convo- 
l u t i ng  outer  edge and the  production region w a r  the  wal l .  That 
i s ,  t o  see i f  there  i s  some c o r r e l a t i o n  which would support a  
hypothesis of an inward flow of information from the outer  edge 
which may be responsible  fo r  the i n i t i a t i o n  of turbulence near 
the wal l .  
Measurements of the c o r r e l a t i o n  between two hot  wire anemom- 
e t e r  s i gna l s  (u components), one from the i n t e rmi t t en t  ou te r  
region (y/6 = 0.8) and the  o ther  from the turbulent  production 
1 
region of a  tu rbulen t  boundary l a y s r ,  have been performed [2] .  
Figure 1 shows a  t yp i ca l  space-tine c o r r e l a t i o n  curve fo r  the two 
anemmeter s igna ls .  The v e l o c i t y  d i s t r i b u t i o n  and v e r t i c a l  lo- 
ca t ion  of the hot wires a r e  noted i n  Figure 1. It was found t h a t  
a measurable c o r r e l a t i o n  ex i s t ed  only fo r  the  case where the hot 
wire i n  t he  ou te r  flow was s l i g h t l y  upstream of the probe near the 
'The wire i n  the outer  region was wei?. beyond the region invest igated 
by Blackwelder and Kovasznay. 
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viscour sublayer.  No c o - r e l a t i o n  cocld be measured when t h e  
other  wire was s l i g h t l y  downstream of the sublayer wire. I f  
the wires were i n  the region inves t iga ted  by Blackwelder and 
Kovasznay, mvement of the  upper wire i n  the downstream d i r e c t i o n  
would have increased the  c o r r e l a t i o n  value [41. 
The exis tence of a  c o r r e l a t i o n  between the  ou t e r  and imsr 
turbulent  s i gna l s  would appear t o  fu r the r  support the  m d e l  
suggested by Laufer and Badri Narayanan [I].  The co r r e l a t i on  
was always found t o  peak a t  a  time de lay  o the r  than zero such 
t h a t  information was always sensed f i r s t  by the other  probe and 
l a t e r  by the inner probe. This s h i f t  i n  t i t r e  delay ind ica tes  
t h a t  information i s  propagated inward from the  ou t e r  region t o  
the wal l  region of the turbulent  boundary layer .  No attempt 
was made t o  i nves t i ga t e  whether o r  not the ' ' l i m i t  cycle" could 
be closed by the  ex is tence  o f  a  c o r r e l a t i o n  when the outer  wire 
i s  f a r  downstream of  the wire near the sur face ,  although the  work 
by Kline e t  a l .  [3I and Blackwelder and hvasznay  lends support 
t o  such a  hypothesis.  
REFERENCES .- 
1. Laufer,  J.  ; and Badri Narayanan, M. A. : Physics o f  F l u i d s ,  
14, 1971. 
2. C l i f f ,  W. C . ,  and Sandborn, V. A.: Measurements and a mdel 
f o r  convective v e l o c i t i e s  i n  t h e  t u r b u l e n t  boundary l a y e r ,  
NASA TI!!-7416, October 1973. 
3. Kl ine ,  S. J.; Reynolds, W. C.;  Schraub, F. A. ;  and Funds tad le r ,  
P. W . :  The s t r u c t u r e  of t u r b u i e n t  boundary l a y e r s ,  JFM, Vol. 30, 
P a r t  4 ,  1967. 
4. Blackwelder, R. F. ; and Kovasznay, L. S. G.: Time s c a l e s  and 
c o r r e l a t i o n s  i n  a t u r b u l e n t  boundary l a y e r ,  Physics of F l u i d s ,  
No. 9 ,  15, 1972. 
5. Kovasznay, L. S. G . ;  Kibe,.a, V . ;  and Blackwelder, R.  F.: 
Large s c a l e  motion i n  the  i n t e r m i t t e n  reg ion  of a t u r b u l e n t  
boundary l ayer .  JPM, Vol. 41,  p a r t  2 ,  1970. 
APPROVA L 
CORRELATION BETWEEN THE OUTER FLOW AND THE TURBULENT 
PRODUCTION I N  A BOUNDARY LAYER 
By William C. C l i f f  and V i r g i l  A. Sandborn 
The informat ion i n  t h i s  r e p o r t  has  been reviewed f o r  s e c u r i t y  
c l a s s i f i c a t i o n .  Review of  any informat ion concerning Department 
of Defense o r  Atomic Energy Commission rrograms has been made 
by the  MSFC S e c u r i t y  C l a s s i f i c a t i o n  O f f i c e r .  This r e p o r t ,  i n  
i ts  e n t i r e t y ,  has  been determined t o  be u n c l a s s i f i e d .  
This document has a l s o  been reviewed and approved f o r  t e c h n i c a l  
accuracy. 
&?J George H. 2& 
c h i e f ,  H r o n m e n t a  1 Dynamics Branch 
' - +y&. 
William W. Vaughan 
Chief ,  ~ e r o s ~ a c e  ~ n v i r o q d n t  Divis ion 
Char les  A .  Lundquist /- 
D i r e c t o r ,  Space Sciences Laboratory 


Correlation between the outer flow and the turbulent production in a boundary layer

CER74-75WCC-VAS19.May 1975.Includes bibliographical references.Space-time velocity correlation measurements between fluctuations occurring in the convoluting outer edge of a flat plate boundary layer with fluctuations occurring near the viscous subregion have been performed. The correlations indicate that information is propagated from the outer region to the inner region. The migration of turbulence away from the wall has been previously studied in the open literature. The results presented in this report along with the migration results lend support to the "limit cycle" model for turbulence production

Cliff, William C.

Sandborn, Virgil A.

Mountain Scholar (Digital Collections of Colorado and Wyoming)

• 訂14- ,s//? CE芪 NASA TECHNICAL II 癰_ _ MEMORANDUM NASA TM X-64935 1 -、' ＇75library CORRELATION BETWEEN THE OUTER FLOW AND THE TURBULENT PRODUCTION IN A BOUNDARY LAYER By William C. Cliff and Virgil A. Sandborn May 1975 NASA ^. Ge,1rge C. Marshall Space Flight Center M,irshall Space Flight Center, Alabama = MSFC • Form 3190 (Rev June 1971) GER 屮{-?`，mce-V目SI('TECHNIC~l.._REPORT STANDARD TITLE PAGE 1. REPORT NO, 2 . GOVERN讜 NT ACCESSION NO. 3 . RECIPIENT•$ CATALOG HO, NASA 1M X-64935 4. TITLE ANO SUBTITLE 5. REPORT DATE Correlation Between the Outer Flow and the Turbulent May 1975 Production in a Boundary Layer 6 . PERFORMING ORGANIZATION C(IQE 7. AUTHOR(S) 8. PERFORMING ORGANIZATION REPOR「#William C. Cliff and Virgil A. Sandborn 9. PERFORMING ORGANIZATION NAME ANO ADDRESS 10. WORK UHl1: HO. George C. Marshall Space Flight Center Marshall Space Flight Center, Alabama 35812 t t . CONTRACT OR GRANT NO. 13. TYPE OF REPORi. 8c PERIOD COVERED 12, SPONSORING AGENCY NAME ANO ADDRESS National Aeronautics and Space Administration Technical Memorandum Washington, D. C. 20546 14. SPONSORING AGENCY CODE 15 . SUPPLEMENTARY NOTES 18, ABSTRACT Space-time velocity correlation measurements between fluctuations occurring in the convoluting outer edge of a flat plate boundary layer with fluctuations occurring near the viscous subregion have been performed. The correlations indicate that information is propagated from the outer region to the inner region. The migration of turbulence away from the wall has been previously studied in the open literature. 咋e results presented in this report along with the migration results lend support to the "limit cycle" model for turbulence production. .· I IIIIIl IIl lllllIlllllllllllllllllll' I U184 □ 1 □□ 74077 17. KE丶 WORDS 18. DISTRIBUTION STATEMENT /J~ Unclassified - Unlimited fa. 乙乙乏19 . SECURITY CLASSIF. (ol thl■ report 、 20 . SECURITY CLASSIF, (of thla s>el•) 21. NO. OF PAGES 22. PRICE Unclassified Unclassified 10 NTIS MSFC • Form 3292 (May 1969) ACKNOWLEDGMENTS The authors wish to extend their appreciation to Mrs. A. Tingle A and Ms. G. Meeks for editing and prepar\:ion of the manuscript. ' TABLE OF CONTENTS Page INTRODUCTION.............................. : ................... 1 BACKGROUND........... .... ..................................... 1 TE ST SETUP AND PROCEDURE................................... . .. 3 EXPERIMENTAL RESULTS AND DISCUSSION........................... 4 REFERENCES.................................................... 7 .l .l .l CORREIATION BETWEEN THE OUTER FI.OW AND THE TURBULENT PRODUCTION IN A BOUNDARY !AYER I. INTRODUCTION Space-time correlation measurements show a relation between the undulating outer edge boundary layer flow and the turbulent production region near the surface. The observation indicates that information is propagated from the outer region to the inner region. I I. BACKGROUND The processes involved in the initiation and proliferation of turbulence in the flat plate boundary layer are at present not well understood. Laufer and Bandri Narayanan have presented evidence that the turbulent production mechanism near the wall of a turbulent boundary layer scales with the outer flow parameters [lJ. They suggest a "limit cycle" model for the turbulent p「o­duction which appears consistent with the physical model proposed by Cliff and Sandborn [ 2]. Kline et al. examined the trajectories of turbulent pockets · as they migrated from the near wall region toward the outer regions of the boundary layer [3]. A detailed mapping of space-time auto-correlations of the velocity components was taken across a flat plate boundary layer by Blackwelder and Kovasznay [4]. The mapping gave isocorrelation lines of 0.8, 0.6, 0.4, 0.3, 0.2, and 0.1 for the u component of velocity. Blackwelder and Kovasznay noted that the locus of the maximum space -time correlations was approximately along the trajectory of eddy migration as reported by Kline [ 3] . The ·work of Kline et al, [ 3 」 and Blackwelder and Kova s znay indicates an outward migration of eddies which are produced in a formation zone near the wall. Th.is migration phenomenon supports the hypothesis that the eddies formed near the wall are ultimately associated with the convoluting outer edge of the boundary layer. A closing of the "limit cycle," proposed and studied in this report, relates the convoluting outer edge to the generation of turbulence near the wall. The convoluting outer edge of the turbulent boundary layer has been shown to produce large perturbations in the local velocities and pressures, as reported by Kovasznay, Kibens, and Blackwelder [ 5]. It is postulated that the perturbations travel through the boundary layer and give rise to the turbulent production process which occurs near the viscous sublayer. A part of the turbulence produced near the wall, in turn, moves outward and eventually produces the convoluting outer edge of the boundary layer to re-produce and sustain itself. (The motion outward has been shown earlier by Kline et al. [3] and Blackwelder and Kovasznay [4].) Space-time correlation techniques are a method of examining, at least in part, the inw~rd relation between the undulating 2 outer edge and the turbulent production region of a boundary layer. The space-time correlation of velocity fluctuations occurring in the undulating outer region with velocity fluctuations occurring near the viscous subregion has been performed. The objective of this report is to present the correlation data and interpret the results. III . TEST SETUP AND PROCEDURE The experiment was performed in a small, open-return-type wind tunnel. A honeycomb, which is located in a large circular inlet, is used to straighten the inlet flow and break up any large-scale disturbances. From the inlet the flow passes through a settling chamber and then accelerates into a test section, where the cross section narrows to 0,457 m by 0.457 m. The ceiling of the tunnel was adjusted so as to develop a near zero pressure gradient flat plate boundary layer. The correlation measurements were performed at 1.22 m from the start of the test section. Two standard constant temperature hot wire anemometers were used with 0.01 nun diameter platinum iridium wire. Normal annealing and calibration of the hot wires were performed as described in Reference 2. One hot wire was placed in the undulating outer edge of the boundary layer and one was placed very near the wall. The boundary layer was approximately 7 cm high, Signals from the hot wires were fed directly into a commercial time ?elay correlator, RMS meters, and tape transport. 3 IV . EXPERIMENTAL RESULTS AND DISCUSS IONS As was pointed out earlier, Kline et al. [3] and Blackwelder and Kova sznay [4] have performed experiments which support the hypothesis that turbulence generated near the wall migrates out-war·d and is utlimate ly associated with the convoluting outer edge of the boundary layer. The following experiment was conceived and performed in an attempt to determine if any correlation exists between the convo-luting outer edge and the production region near the wall. That is, to see if there is some correlation which would support a hypothesis of an inward flow of information from the outer edge which may be responsible for the initiation of turbulence near the wall. Measurements of the correlation between two hot wire anemom-eter signals (u components), one from the intermittent outer region (y/o = 0.8) and the other from the turbulent production 1 region of a turbulent boundary layer, have been performed [2]. Figure 1 shows a typical space-time correlation curve for the two anemometer signals. The velocity distribution and vertical lo-cation of the hot wires are noted in Figure 1. It was found that a measurable correlation existed only for the case where the hot wire in the outer flow was slightly upstream of the probe near the 1 咋e wire in the outer region was well beyond the region investigated by Blackwelder and Kovasznay. . 4 VELOCITY DIS TR/BU「/ONDISTANCE ABOVE SURFACE (cm) 6 4 2 , 。ELEVATION OF OUTER PROBE i ELEVATION OF INNER PROBE i COVARIANCE 0.1 INNER PROBE SIGNAL DELAYED OUTER PROBE SIGNAL DELAYED 5 10 15 VELOCITY (m/sec) NOTE: OUTER PROBE ~5 mm UPSTREAM FROM INNER PROBE 。TIME DELAY 0.1 sec FIG. 1. NORMALIZED CROSS COVARIANCE VS「/MEDELAY FOR VERTICALLY SEPERATEO HOT WIRE PROBES IN A FLAT PLA「E(SLIGHT ADVERSE PRESSURE GRADIENT) BOUNDARY LAYER. viscous sublayer. No correlation could be measured when the ,uhy ~ wire was slightly downstream of the sublayer wire. If the wires were in the region investigated by Blackwelder and Kovasznay, movement of the upper wire in the downstream direction would have increased the correlation value [4]. The existence of a correlation between the outer and inner turbulent signals would appear to further support the model suggested by Laufer and Badri Narayanan [1]. The correlation was always found to peak at a time delay other than zero such oUfer that information was always sensed first by thee`+``r probe and later by the inner probe. This shift in time delay indicates that information is propagated inward from the outer region to the wall region of the turbulent boundary layer. No attempt was made to investigate whether or not the "limit cycle" could be closed by the existence of a correlation when the outer wire is far downstream of the wire near the surface, although the work by Kline et al. [3] and Blackwelder and Kovasznay lends support to such a hypothesis. 6 REFERENCES 1. Laufer, 」． ;and Badri Narayanan, M.A.: Physics of Fluids, 14, 1971. 2. Cliff, W. C.; and Sandborn, V. A.: Measurements and a model for convective velocities in the turbulent boundary layer, NASA TND-7416, October 1973. 3. Kline, S. J.; Reynolds, W. C.; Schraub, F. A.; and Fundstadler, P. W.: The structure of turbulent boundary layers, JFM, Vo 1. 30, Part 4, 1967. 4. Blackwelder, R. F.; and Kovasznay, L. S. G.: Time scales and correlations in a turbulent boundary layer, Physics of Fluids, No. 9, 15, 1972. 5. Kovasznay, L. S. G.; Kibens, V.; and Blackwelder, R. F.: Large scale motion in the intermitten region of a turbulent boundary layer. JFM, Vo 1. 41, part 2, 1970. 7 APPROVAL CORRELATION BETWEEN THE OUTER · FLOW AND TIIE TURBULENT PRODUCTION IN A BOUNDARY LAYER By William C. Cliff and Virgil A. Sandborn The information in this report has been reviewed for security classification. Review of any information concerning Department of Defense or Atomic Energy Commission programs has been made by the 'MSFC Security Classification Officer. This report, in its entirety, has been determined to be unclassified. This document has also been reviewed and approved for technical accuracy. y2必乙～｀（辶羞William W. Vaughan Chief, Aerospace Enviro Division Lundquist Director, Space Sciences 8 

Correlation between the outer flow and the turbulent production in a boundary layer

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Mountain Scholar (Digital Collections of Colorado and Wyoming)