Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-19T05:11:31.789Z Has data issue: false hasContentIssue false
  • English
  • Français

Theoretical calculations of turbulent bispectra

Published online by Cambridge University Press:  19 April 2006

Jackson R. Herring
Jackson R. Herring
Affiliation:
National Center for Atmospheric Research
The National Center for Atmospheric Research is sponsored by the National Science Foundation.
Boulder, Colorado 80307
Get access Rights & Permissions [Opens in a new window]

Abstract

One-dimensional bispectra are computed from the statistical theory of turbulence (using the Test Field Model) and are compared with experiments. For an inertial range, we obtain B(k1, p1) = εk−3F(θ), where B is the two-dimensional Fourier transform of $\langle u({\bf x})u({\bf x}+\hat{\imath}\xi_1)u({\bf x}+\hat{\imath}\xi_2)\rangle $ with respect to (ξ1, ξ2), ε is the energy dissipation and F(θ) (θ = tan−1(k1/p1) is an angular distribution of order unity, which is compared to measurements of planetary boundary-layer turbulence. We also compare theory to wind tunnel data, as reported by Helland et al. (1978). Finally, we discuss to what extent the bispectra give insight into the dynamics of the flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 97 , Issue 1 , 11 March 1980 , pp. 193 - 204
Copyright
© 1980 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

Craya, A. 1958 Contribution a l'analyse de la turbulence associée a des vitesses moyennes. Publ. Sci. Tech. Minist. Air (France).
Hasselmann, K., Munk, W. & MacDonald, G. 1963 Bispectra of ocean waves. In Time Series Analyses (ed. M. Rosenblatt), pp. 125–139. Wiley.
Helland, K. N., Lii, K. S. & Rosenblatt, M. 1978 Bispectra of atmospheric and wind tunnel turbulence. In Applications of Statistics (ed. P. R. Krishniah), pp. 223–248. North Holland.
Herring, J. R. & Khaichnan, R. H. 1972 Comparison of some approximations for isotropic turbulence. In Statistical Models and Turbulence, Lecture notes in physics, Vol. 12, pp. 148–194.
Herring, J. R., Orszag, S. A., Kraichnan, R. H. & Fox, D. G. 1974 Decay of two-dimensional homogeneous turbulence. J. Fluid Mech. 66, 417–444.Google Scholar
Kraichnan, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497–543.Google Scholar
Kraichnan, R. H. 1971 An almost-Markovian Galilean-invariant turbulence model. J. Fluid Mech. 47, 513–524.Google Scholar
Lesieur, M. & Schertzer, D. 1978 Dynamic des gros Tourbillons et Décroissance de L’énergie Cinétique en Turbulence Tridimensionelle Isotype à Grand Nombre de Reynolds. J. Méc. 17, 609–646.Google Scholar
Lii, T. T., Rosenblatt, M. & Van Atta, C. W. 1976 Bispectral measurements in turbulence. J. Fluid Mech. 77, 45–62.Google Scholar
McComas, C. H. & Briscoe, M. G. 1980 A note on the bispectra of internal waves. J. Fluid Mech. 97, 205–213.Google Scholar
Newman, G. R. & Herring, J. R. 1979 A test field model study of a passive scalar in isotropic turbulence. J. Fluid Mech. 94, 163–194.Google Scholar
Orszag, S. A. 1974 Statistical Theory of Turbulence: Les Houches Summer School on Physics. Gordon & Breach.
Orszag, S. A. & Patterson, G. S. 1972 Numerical simulation of three-dimensional homogeneous isotropic turbulence. Phys. Rev. Lett. 28, 76–79.Google Scholar
Stroud, A. H. & Secrist, D. 1966 Gaussian Quadrature Formulas. Englewood Cliffs, N.J.: Prentice-Hall.
Van Atta, C. W. & Chen, W. Y. 1969 Measurements of spectral energy transfer in grid turbulence. J. Fluid Mech. 38, 743–763.Google Scholar
Van Atta, C. W. 1979 Inertial range bispectra in turbulence. Phys. Fluids. 22, 1440–1442.Google Scholar
Yeh, T. T. & Van Atta, C. W. 1973 Spectral transfer of scalar and velocity fields in heated-grid turbulence. J. Fluid Mech. 58, 233–261.Google Scholar