260
z. ZARIC
5. CONCLUSIONS
Probability density distribution analysis is found to be a very useful tool
in statistical analysis of the wall turbulence. The overall shapc of the probability distribution is found to represent a characteristic feature of the turbulence at a given nomlimensional distance lrom the wall as wtll as to
indicate the presence of intermittent processes going on inside the wall
layers. However, conventional averaging analysis over a long period could
only indicate a certain process but is unabk to describe it in detail.
Conditional averaging analysis, proven to be an efficient technique in
investigations of outer-layer intermittency, is found to be very useful in
turbulence analysis of the inner layers also. While the criteria by which the
presented results are obtained are not optimized, the results clearly indicate
the relative importance of different intermittent phases as a function of
nondimensional distance from the wall. Through the analysis presented, the
shape of the probability distributions at different Y+ could be explained. It
is believed that further development of the analysis could eventually lead to
a quantitative description of turbulent transport processes in wall layers.
REFERENCES
Armistead, R. A.. Jr., and Key-. J. J., Jr. (1968). J . Hear Trantfer 90. 13.
Blackwelder. R. F., and Kaplan. R. E. (1972). l U T A M Meet., 13th. Moscowi.
Blackwelder. R. F., and Kovaeznay. L. S. G. (1972). Phys. Fluids 15, 1545- 1357.
Comte-Bellot, G. (1963). T h k . Univ. dc Grenobk. Grenoble.
Corino. E. R.. and Brodkey. R. S. (1969). J . Fluid Me& 37, 1-30,
Corrsin, S.. and Kistler. A. L. (1955). Rep. 1244 NACA (Not. Adv. Comm. Aeronaut.)
Duhamel. P., and Py. B. (1972). Colloq. Aerodin. Appl. AAAF, 9th. Pmb.
Eckclman, H. (1970). Mitt. Max-Ploeck-lnsr., Goertingen No. 48.
Frcnkiel, F., and Klebanofl, P. S. (1967). Phys. Fluids 10, 507-520.
Grass, A. J. (1971). J. FluId Mech. SO, 233-255.
Gupta, A. K., Laufer, J., and Kaplan, R. E. (1971). J . Fhld Mech. Se. 493-512.
Kim, H. T.. Klinc. S. J., and Reynolds, W. C. (1968). Rep. MD-20. BPI. Mcch. Eng.,
Klebanoff. P. C. (1955). Rep. No. 1247 NACA (Nat. Mv. Comm. Aeronaut.)
Kline, S. J., Reynolds. W. C., Schraub, F. A.. and Runstrdkr, P. W. (1967). J . Fluid Mech. 30,
Kovasznay, L. S. G., Kibens, V., and Blackwelder, R. F. (1970). J . Fluid Mech. 41,283-325.
Marcillat, J. (1964). T h k , Univ. de Aix-Marseille, Maneilb.
.Meek, R. L., and Baw. A. D. (1970). AIChB J . 16,841-848.
Popovich, A. T. (1969). fn(l. Eng. Chem., Fundam. 609-614.
Shlanchiauekas, A. A. (1972). In "Teplo- i Massoperenos" Vol. 1, Part 1. pp. 8-17. Inst.
Townmd, A. A. (1949). Proc. Roy. Soc., Ser. A 191, 124-140.
Wallace, J. W.. Eckelrnan, H.. and Brodkey, R. S. (1972). 1. Fluid Merh. 54, 3 9 . 4 .
Willmarth. W. W.. and Lu, S. S. (1972). J. Fluicl Mrrh. 55. 65-92.
Stanford Univ., Stanford, Calif.
741.
Tcplo-rnmoobmena Minsk.
z. ZARIC
5. CONCLUSIONS
Probability density distribution analysis is found to be a very useful tool
in statistical analysis of the wall turbulence. The overall shapc of the probability distribution is found to represent a characteristic feature of the turbulence at a given nomlimensional distance lrom the wall as wtll as to
indicate the presence of intermittent processes going on inside the wall
layers. However, conventional averaging analysis over a long period could
only indicate a certain process but is unabk to describe it in detail.
Conditional averaging analysis, proven to be an efficient technique in
investigations of outer-layer intermittency, is found to be very useful in
turbulence analysis of the inner layers also. While the criteria by which the
presented results are obtained are not optimized, the results clearly indicate
the relative importance of different intermittent phases as a function of
nondimensional distance from the wall. Through the analysis presented, the
shape of the probability distributions at different Y+ could be explained. It
is believed that further development of the analysis could eventually lead to
a quantitative description of turbulent transport processes in wall layers.
REFERENCES
Armistead, R. A.. Jr., and Key-. J. J., Jr. (1968). J . Hear Trantfer 90. 13.
Blackwelder. R. F., and Kaplan. R. E. (1972). l U T A M Meet., 13th. Moscowi.
Blackwelder. R. F., and Kovaeznay. L. S. G. (1972). Phys. Fluids 15, 1545- 1357.
Comte-Bellot, G. (1963). T h k . Univ. dc Grenobk. Grenoble.
Corino. E. R.. and Brodkey. R. S. (1969). J . Fluid Me& 37, 1-30,
Corrsin, S.. and Kistler. A. L. (1955). Rep. 1244 NACA (Not. Adv. Comm. Aeronaut.)
Duhamel. P., and Py. B. (1972). Colloq. Aerodin. Appl. AAAF, 9th. Pmb.
Eckclman, H. (1970). Mitt. Max-Ploeck-lnsr., Goertingen No. 48.
Frcnkiel, F., and Klebanofl, P. S. (1967). Phys. Fluids 10, 507-520.
Grass, A. J. (1971). J. FluId Mech. SO, 233-255.
Gupta, A. K., Laufer, J., and Kaplan, R. E. (1971). J . Fhld Mech. Se. 493-512.
Kim, H. T.. Klinc. S. J., and Reynolds, W. C. (1968). Rep. MD-20. BPI. Mcch. Eng.,
Klebanoff. P. C. (1955). Rep. No. 1247 NACA (Nat. Mv. Comm. Aeronaut.)
Kline, S. J., Reynolds. W. C., Schraub, F. A.. and Runstrdkr, P. W. (1967). J . Fluid Mech. 30,
Kovasznay, L. S. G., Kibens, V., and Blackwelder, R. F. (1970). J . Fluid Mech. 41,283-325.
Marcillat, J. (1964). T h k , Univ. de Aix-Marseille, Maneilb.
.Meek, R. L., and Baw. A. D. (1970). AIChB J . 16,841-848.
Popovich, A. T. (1969). fn(l. Eng. Chem., Fundam. 609-614.
Shlanchiauekas, A. A. (1972). In "Teplo- i Massoperenos" Vol. 1, Part 1. pp. 8-17. Inst.
Townmd, A. A. (1949). Proc. Roy. Soc., Ser. A 191, 124-140.
Wallace, J. W.. Eckelrnan, H.. and Brodkey, R. S. (1972). 1. Fluid Merh. 54, 3 9 . 4 .
Willmarth. W. W.. and Lu, S. S. (1972). J. Fluicl Mrrh. 55. 65-92.
Stanford Univ., Stanford, Calif.
741.
Tcplo-rnmoobmena Minsk.