Skip to main content Accessibility help
×
Home
Hostname: page-component-59b7f5684b-qn7h5 Total loading time: 0.29 Render date: 2022-09-28T23:24:50.093Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

Zero-crossings in turbulent signals

Published online by Cambridge University Press:  20 April 2006

K. R. Sreenivasan
Affiliation:
Applied Mechanics, Yale University
A. Prabhu
Affiliation:
Indian Institute of Science, Bangalore
R. Narasimha
Affiliation:
Indian Institute of Science, Bangalore

Abstract

A primary motivation for this work arises from the contradictory results obtained in some recent measurements of the zero-crossing frequency of turbulent fluctuations in shear flows. A systematic study of the various factors involved in zero-crossing measurements shows that the dynamic range of the signal, the discriminator characteristics, filter frequency and noise contamination have a strong bearing on the results obtained. These effects are analysed, and explicit corrections for noise contamination have been worked out. New measurements of the zero-crossing frequency N0 have been made for the longitudinal velocity fluctuation in boundary layers and a wake, for wall shear stress in a channel, and for temperature derivatives in a heated boundary layer. All these measurements show that a zero-crossing microscale, defined as Λ = (2πN0)−1, is always nearly equal to the well-known Taylor microscale λ (in time). These measurements, as well as a brief analysis, show that even strong departures from Gaussianity do not necessarily yield values appreciably different from unity for the ratio Λ/λ. Further, the variation of N0/N0 max across the boundary layer is found to correlate with the familiar wall and outer coordinates; the outer scaling for N0 max is totally inappropriate, and the inner scaling shows only a weak Reynolds-number dependence. It is also found that the distribution of the interval between successive zero-crossings can be approximated by a combination of a lognormal and an exponential, or (if the shortest intervals are ignored) even of two exponentials, one of which characterizes crossings whose duration is of the order of the wall-variable timescale ν/U2*, while the other characterizes crossings whose duration is of the order of the large-eddy timescale δ/U. The significance of these results is discussed, and it is particularly argued that the pulse frequency of Rao, Narasimha & Badri Narayanan (1971) is appreciably less than the zero-crossing rate.

Type
Research Article
Copyright
© 1983 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Antonia, R. A. 1973 Phys. Fluids 16, 1198.
Antonia, R. A., Danh, H. Q. & Prabhu, A. 1976 Phys. Fluids 19, 1680.
Antonia, R. A., Danh, H. Q. & Prabhu, A. 1977 J. Fluid Mech. 80, 153.
Antonia, R. A., Prabhu, A. & Stephenson, A. 1975 J. Fluid Mech. 72, 455.
Bakewell, H. P. & Lumley, J. L. 1976 Phys. Fluids 10, 1880.
Batchelor, G. K. 1956 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. & Townsend, A. A. 1949 Proc. R. Soc. Lond. A, 199, 238.
Badri Narayanan, M. A., Rajagopalan, S. & Narasimha, R. 1974 Some experimental investigations of the fine structure of turbulence. Rep. 74 FM 15, Dept Aero. Engng, Indian Inst. of Science.Google Scholar
Badri Narayanan, M. A., Rajagopalan, S. & Narasimha, R. 1977 J. Fluid Mech. 80, 237.
Blackwelder, R. F. & Kovasznay, L. S. G. 1970 Large scale motion of a turbulent boundary layer with a zero and a favourable pressure gradient. Interim Tech. Rep., Dept Mech., The Johns Hopkins University.Google Scholar
Bowen, R. 1970 Proc. Symp. Pure Math. 14, 23.
Brown, G. L. & Thomas, A. S. W. 1977 Phys. Fluids Suppl. 20, S243.
Clauser, F. 1955 Adv. Appl. Mech. 4, 1.
Comte-Bellot, G. 1963 Ph.D. thesis, Univ. of Grenoble [English transl. by p. Bradshaw, ARC FM 4102 (1969)].
Feller, W. 1957 An Introduction to Probability Theory and its Applications. Wiley.
Gupta, A. K. & Kaplan, R. E. 1972 Phys. Fluids 15, 981.
Klebanoff, P. S. 1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA TR 1247.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 J. Fluid Mech. 30, 741.
Kuo, A. S. & Corrsin, S. 1971 J. Fluid Mech. 50, 285.
Kuznetsov, P. L., Stratonovich, R. L. & Tiknonov, V. I. 1954 J. Tech. Phys., Moscow 24, 103.
Laufer, J. 1950 J. Aero. Sci. 17, 277.
Liepmann, H. W. 1949 Helv. Phys. Acta 22, 119.
Liepmann, H. W., Laufer, J. C. & Liepmann, K. 1951 On the spectrum of isotropic turbulence. NACA TN 2473.Google Scholar
Longuet-Higgins, M. S. 1958 Proc. R. Soc. Lond. A, 246, 99.
Rao, K. N., Narasimha, R. & Badri Narayanan, M. A. 1971 J. Fluid Mech. 48, 339.
Repik, Ye. U. & Sosedko, YU. P. 1976 Fluid Mech.-Sov. Res. 5, 39.
Rice, S. O. 1945 Bell Syst. Tech. J. 24, 46.
Sreenivasan, K. R. 1983 Submitted for publication.
Sreenivasan, K. R., Antonia, R. A. & Danh, H. Q. 1977 Phys. Fluids 20, 1800.
Townsend, A. A. 1951 Proc. Camb. Phil. Soc. 47, 375.
Ueda, H. & Hinze, J. O. 1975 J. Fluid Mech. 67, 125.
Wetzel, J. M. & Killen, J. M. 1972 A preliminary report on the zero-crossing rate technique for average shear measurement in flowing fluid. Rep. 134, Univ. Minnesota, St Anthony Falls Hydraulics Lab.Google Scholar
Wygnanski, I. & Fiedler, H. 1969 J. Fluid Mech. 38, 577.
Ylvisaker, N. D. 1965 Ann. Math. Stat. 36, 1043.
98
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Zero-crossings in turbulent signals
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Zero-crossings in turbulent signals
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Zero-crossings in turbulent signals
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *