Abstract.
We present the results of an experimental study of the spatial Fourier modes of the vorticity in a turbulent jet flow. By means of an acoustic scattering setup we have recorded the evolution in time of Fourier modes of the vorticity field, characterized by well defined wavevectors k. By computing the auto-correlation of the amplitude of the Fourier modes we evidence that, whatever the length scale (or equivalently k), the dynamic evolution of the vorticity field involves two well separated time scales. We have also performed the simultaneous acquisitions of pairs of Fourier modes with two wavevectors k and k'. Whatever the spectral gap k- k', any pair of Fourier modes exhibits a significant cross-correlation over long time delays, indicating a strong statistical dependence between scales.
Similar content being viewed by others
References
U. Frisch, Turbulence, The Legacy of A.N. Kolmogorov (Cambridge University Press, Cambridge, 1995)
A.N. Kolmogorov, Dokl. Akad. Nauk. SSSR 30, 299 (1941), reprinted in Proc. R. Soc. Lond. A 434, 9 (1991)
R.H. Kraichnan, J. Acoust, Soc. Am. 25, 1096 (1953)
C. Baudet, S. Ciliberto, J.F. Pinton, Phys. Rev. Lett. 67, 193 (1991)
A.N. Kolmogorov, J. Fluid Mech. 13, 82 (1962)
A.K. Kuczaj, B.J. Geurts, D. Lohse, Europhys. Lett. 73, 851 (2006)
S. Dhar, A. Sain, R. Pandit, Phys. Rev. Lett. 78, (1997) 2964; D. Mitra, R. Pandit, Physica A: Statistical Mechanics and its Applications 318, Issues 1-2 (2003) 179; D. Mitra, R. Pandit, Phys. Rev. Lett. 93, 024501 (2004)
S. Chen, R.H. Kraichnan, Phys. Fluids A 1, 2019 (1989)
Y. Kaneda, T. Ishihara, K. Gotoh, Phys. Fluids 11, 2154 (1999)
M. Nelkin, M. Tabor, Phys. Fluids A, 2, 81 (1990)
B. Castaing, Eur. Phys. J. B 29, 357 (2002)
R.H. Kraichnan, J. Fluid Mech. 83, 349 (1977)
F. Lund, C. Rojas, Physica D 37, 508 (1989)
M.A. Kallistratova, Dokl. Akad. Nauk. SSSR 125, 69 (1959)
C.M. Ho, L.S.G. Kovàsznay, J. Acoust. Soc. Am. 60, 40 (1976)
B. Dernoncourt, J.-F. Pinton, S. Fauve, Physica D 117, 181 (1998)
C. Baudet, O. Michel, W.J. Williams, Physica D 128, 1 (1999)
C. Poulain, N. Mazellier, P. Gervais, Y. Gagne, C. Baudet, Flow, Turb. Comb. 72, 245 (2004)
As a consequence of the Born approximation, equation ([SEE TEXT]) is valid in the far field limit, at low Mach numbers u/c and low acoustic intensity such that v ≪u ≪c, where v is the typical amplitude of the acoustic velocity fluctuations
W. Heisenberg, Z. Phys. 124, 628 (1948)
R.H. Kraichnan, J. Fluid Mech. 5, 497 (1959)
A.A. Praskovsky et al., J. Fluid Mech. 248, 493 (1993)
H. Tennekes J. Fluid Mech. 67, 561 (1975)
V. Yakhot et al., Phys. Fluids A 1, 2, 184 (1989)
P.A. O'Gorman, D.I. Pullin, J. of Turb. 5, 035 (2004)
A. Alexakis, P.D. Mininni, A. Pouquet, Phys. Rev. Lett. 95, 264503 (2005)
L. Chevillard, N. Mazellier, C. Poulain, Y. Gagne, C. Baudet, Phys. Rev. Lett. 95–20, 200203 (2005)
S. Piétropinto, C. Poulain, C. Baudet, B. Castaing, B. Chabaud, Y. Gagne, P. Gervais, B. Hébral, Y. Ladam, P. Lebrun, O. Pirotte, Very high Reynolds turbulence with low-temperature gaseous helium, Proceedings of the 9th European Turbulence Conference, Southampton UK 279 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Poulain, C., Mazellier, N., Chevillard, L. et al. Dynamics of spatial Fourier modes in turbulence. Eur. Phys. J. B 53, 219–224 (2006). https://doi.org/10.1140/epjb/e2006-00354-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2006-00354-y