Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-26T13:10:19.968Z Has data issue: false hasContentIssue false
  • English
  • Français

An investigation of high-wavenumber temperature and velocity spectra in air

Published online by Cambridge University Press:  29 March 2006

Noel E. J. Boston  and
R. W. Burling
Noel E. J. Boston
Affiliation:
Institute of Oceanography, University of British Columbia, Vancouver, Canada Present address: Department of Oceanography, Naval Postgraduate School, Monterey, California 93940.
R. W. Burling
Affiliation:
Institute of Oceanography, University of British Columbia, Vancouver, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

Turbulent temperature and velocity fluctuations in air were measured at a height of 4 m over a tidal mud flat. Particular attention was focused on the high-wavenumber, small-scale region of the spectra of these fluctuations. The measurements of the velocity fluctuations were made with a constant-temperature hot-wire anemometer; the hot wire consisted of a platinum wire 5 μm in diameter and approximately 1 mm in length. Temperature fluctuations were measured with a platinum resistance thermometer which consisted of a platinum wire 0·25 μm in diameter and about 0·30 mm in length.

The velocity spectra results agree well with the classical results of Grant, Stewart & Moilliet (1962) and Pond, Stewart & Burling (1963). In addition, they extend the velocity spectrum in air to slightly higher wavenumbers. The one-dimensional Kolmogorov constant K’ estimated from these data was 0·51.

The temperature spectra clearly show the shape of the one-dimensional temperature spectrum in air beyond the $-\frac{5}{3}$ region. In air temperature and velocity spectra are very similar. The value of the scalar constant K’0, which appears in the scalar $-\frac{5}{3}$ law, computed from these data was 0·81. Direct measurement was made of all parameters that enter into the calculation of it.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 55 , Issue 3 , 10 October 1972 , pp. 473 - 492
Copyright
© 1972 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

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in a turbulent fluid. Part 1. J. Fluid Mech. 5, 113.Google Scholar
Batchelor, G. K., Howells, J. D. & Townsend, A. A. 1959 Small-scale variation of convected quantities like temperature in a turbulent fluid. Part 2. J. Fluid Mech. 5, 134.Google Scholar
Boston, N. E. J. 1970 An investigation of high-wavenumber temperature and velocity spectra in air. Ph.D. thesis, University of British Columbia.
Corrsin, S. 1951 On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys. 22, 469.Google Scholar
Gibson, C. H. 1962 Scalar mixing in turbulent flow. Ph.D. thesis, Stanford University
Gibson, C. H. 1968a Fine structure of scalar fields mixed by turbulence. 1. Zero-gradient points and minimal gradient surfaces. Phys. Fluids, 11, 2305.Google Scholar
Gibson, C. H. 1968b Fine structure of scalar fields mixed by turbulence. 2. Spectral theory. Phys. Fluids, 11, 2316.Google Scholar
Gibson, C. H. & Schwarz, W. H. 1963 The universal equilibrium spectra of turbulent velocity and scalar fields. J. Fluid Mech. 16, 365.Google Scholar
Gibson, C. H., Stegen, G. R. & Williams, R. B. 1970 Statistics of the fine structure of turbulent and temperature fields measured at high Reynolds number. J. Fluid Mech. 41, 153.Google Scholar
Gibson, M. M. 1963 Spectra of turbulence in a round jet. J. Fluid Mech. 15, 161.Google Scholar
Granatstein, V. L., Buchsbaum, S. J. & Bugnolo, D. S. 1966 Fluctuation spectrum of a plasma additive in a turbulent gas. Phys. Rev. Lett. 16, 504.Google Scholar
Grant, H. L., Hughes, B. A., Vogel, W. M. & Moilliet, A. 1968 The spectrum of temperature fluctuations in turbulent flow. J. Fluid Mech. 34, 423.Google Scholar
Grant, H. L., Stewart, R. W. & Moilliet, A. 1962 Turbulence spectra from a tidal channel. J. Fluid Mech. 12, 241.Google Scholar
Gurvich, A. S. & Kravchenko, T. L. 1962 On the frequency spectrum of temperature fluctuations in the small-scale region. Trudy Inst. Atmospheric Phys. ANSSSR, 4, 144.Google Scholar
Gurvich, A. S. & Zubkovski, S. L. 1966 Evaluation of structural characteristics of temperature pulses in the atmosphere. Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. 2 (2), 118–120.Google Scholar
Hinze, J. O. 1959 Turbulence. McGraw-Hill.
Howells, I. D. 1960 An approximate equation for the spectrum of a conserved scalar quantity in a turbulent fluid. J. Fluid Mech. 9, 104.Google Scholar
Kistler, A. L. & Vrebalovich, T. 1966 Grid turbulence at large Reynolds numbers. J. Fluid Mech. 26, 37.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C.R. Acad. Sci. U.R.S.S. 30, 301.Google Scholar
Kolmogorov, A. N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 82.Google Scholar
Kraichnan, R. H. 1968 Small-scale structure of a scalar field convected by turbulence. Phys. Fluids, 11, 945.Google Scholar
Lanza, J. & Schwarz, W. H. 1966 The scalar spectrum for the equilibrium range of wavenumbers. Department of Chemical Engineering, Stanford University.
Lumley, J. L. & Panofsky, H. A. 1964 The Structure of Atmospheric Turbulence. Wiley.
Nasmyth, P. W. 1970 Oceanic turbulence. Ph.D. thesis, University of British Columbia.
Obukhov, A. M. 1949 Structure of the temperature field in turbulent streams. Izvestia ANSSSR, Geogr. Geophys. no. 13, p. 58.Google Scholar
Pao, Y. 1965 Structure of turbulent velocity and scalar fields at large wavenumbers. Phys. Fluids, 8, 1063.Google Scholar
Paquin, J. E. & Pond, S. 1971 The determination of the Kolmogoroff constants for velocity, temperature and humidity fluctuations from second- and third-order structure functions. J. Fluid Mech. 50, 257.Google Scholar
Pond, S. 1965 Turbulence spectra in the atmospheric boundary layer over the sea. Ph.D. thesis, University of British Columbia.
Pond, S., Smith, S. D., Hamblin, P. F. & Burling, R. W. 1966 Spectra of velocity and temperature fluctuations in the atmospheric boundary layer over the sea. J. Atmos. Sci. 23, 376.Google Scholar
Pond, S., Stewart, R. W. & Burling, R. W. 1963 Turbulence spectra in the wind over waves. J. Atmos. Sci. 20, 319.Google Scholar
Rust, H. H. & Sesonke, A. 1966 Turbulent temperature fluctuations in mercury and ethylene glycol in pipe flow. Int. J. Heat Mass Transfer, 9, 215.Google Scholar
Sheih, C. M., Tennekes, H. & Lumley, J. L. 1971 Airborne hot-wire measurements of the small-scale structure of atmospheric turbulence. Phys. Fluids, 14, 201.Google Scholar
Stewart, R. W. & Townsend, A. A. 1951 Similarity and self-preservation in isotropic turbulence. Phil. Trans. A 243, 359.Google Scholar
Stewart, R. W., Wilson, J. R. & Burling, R. W. 1970 Some statistical properties of small-scale turbulence in an atmospheric boundary layer. J. Fluid Mech. 41, 141.Google Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. Roy. Soc. A 164, 476.Google Scholar
Van Atta, C. W. 1971 Influence of fluctuations in local dissipation rates on turbulent scalar characteristics in the inertial subrange. Phys. Fluids, 14, 1803.Google Scholar
Weiler, H. S. & Burling, R. W. 1967 Direct measurements of stress and spectra of turbulence in the boundary layer over the sea. J. Atmos. Sci. 24, 653.Google Scholar
Wyngaard, J. C. & Tennekes, H. 1970 Measurements of the small-scale structure of turbulence at moderate Reynolds numbers. Phys. Fluids, 13, 1962.Google Scholar
Yaglom, A. M. 1966 Sov. Phys. Dokl. 11, 26.