Statistical Study of Turbulence: Spectral Functions and Correlation Coefficients

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In reading the publications on turbulence of different authors, one often runs the risk of confusing the various correlation coefficients and turbulence spectra. We have made a point of defining, by appropriate concepts, the differences which exist between these functions. Besides, we introduce in the symbols a few new characteristics of turbulence. In the first chapter, we study some relations between the correlation coefficients and the different turbulence spectra. Certain relations are given by means of demonstrations which could be called intuitive rather than mathematical. In this way we demonstrate that the correlation coefficients between the simultaneous turbulent velocities at ... continued below

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Frenkiel, Francois N. July 1, 1958.

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This report is part of the collection entitled: National Advisory Committee for Aeronautics Collection and one other and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 124 times . More information about this report can be viewed below.

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  • Main Title: Statistical Study of Turbulence: Spectral Functions and Correlation Coefficients
  • Series Title: NACA Technical Memorandums

Description

In reading the publications on turbulence of different authors, one often runs the risk of confusing the various correlation coefficients and turbulence spectra. We have made a point of defining, by appropriate concepts, the differences which exist between these functions. Besides, we introduce in the symbols a few new characteristics of turbulence. In the first chapter, we study some relations between the correlation coefficients and the different turbulence spectra. Certain relations are given by means of demonstrations which could be called intuitive rather than mathematical. In this way we demonstrate that the correlation coefficients between the simultaneous turbulent velocities at two points are identical, whether studied in Lagrange's or in Euler's systems. We then consider new spectra of turbulence, obtained by study of the simultaneous velocities along a straight line of given direction. We determine some relations between these spectra and the correlation coefficients. Examining the relation between the spectrum of the turbulence measured at a fixed point and the longitudinal-correlation curve given by G. I. Taylor, we find that this equation is exact only when the coefficient is very small.

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  • ONERA; No. 34

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  • URL: http://hdl.handle.net/2060/20030067904 External Link
  • Report No.: NACA-TM-1436
  • Center for AeroSpace Information Number: 20030067904
  • Archival Resource Key: ark:/67531/metadc63983

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National Advisory Committee for Aeronautics Collection

The National Advisory Committee for Aeronautics (NACA) was a U.S. federal agency founded on March 3, 1915 to undertake, promote, and institutionalize aeronautical research. On October 1, 1958 the agency was dissolved, and its assets and personnel transferred to the newly created National Aeronautics and Space Administration (NASA).

Technical Report Archive and Image Library

This selection of materials from the Technical Report Archive and Image Library (TRAIL) includes hard-to-find reports published by various government agencies. The technical publications contain reports, images, and technical descriptions of research performed for U.S. government agencies. Topics range from mining, desalination, and radiation to broader physics, biology, and chemistry studies. Some reports include maps, foldouts, blueprints, and other oversize materials.

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Creation Date

  • July 1, 1958

Added to The UNT Digital Library

  • Nov. 17, 2011, 5:13 p.m.

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  • Feb. 6, 2017, 5:47 p.m.

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Frenkiel, Francois N. Statistical Study of Turbulence: Spectral Functions and Correlation Coefficients, report, July 1, 1958; (digital.library.unt.edu/ark:/67531/metadc63983/: accessed December 14, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.