Skip to main content

Experimental study of the influence of anisotropy on the inertial scales of turbulence

  • Kelken Chang (a1), Gregory P. Bewley (a1) and Eberhard Bodenschatz (a1)

We ask whether the scaling exponents or the Kolmogorov constants depend on the anisotropy of the velocity fluctuations in a turbulent flow with no shear. According to our experiment, the answer is no for the Eulerian second-order transverse velocity structure function. The experiment consisted of 32 loudspeaker-driven jets pointed toward the centre of a spherical chamber. We generated anisotropy by controlling the strengths of the jets. We found that the form of the anisotropy of the velocity fluctuations was the same as that in the strength of the jets. We then varied the anisotropy, as measured by the ratio of axial to radial root-mean-square (r.m.s.) velocity fluctuations, between 0.6 and 2.3. The Reynolds number was approximately constant at around . In a central volume with a radius of 50 mm, the turbulence was approximately homogeneous, axisymmetric, and had no shear and no mean flow. We observed that the scaling exponent of the structure function was , independent of the anisotropy and regardless of the direction in which we measured it. The Kolmogorov constant, , was also independent of direction and anisotropy to within the experimental error of 4 %.

Corresponding author
Email address for correspondence:
Hide All
1.Albrecht, H.-E., Borys, M., Damaschke, N. & Tropea, C. 2003 Laser Doppler and Phase Doppler Measurement Techniques. Springer.
2.Andereck, C. D., Liu, S. S. & Swinney, H. L. 1986 Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155183.
3.Benzi, R., Ciliberto, S., Baudet, C. & Chavarria, G. R. 1995 On the scaling of three-dimensional homogeneous and isotropic turbulence. Physica D 80, 385398.
4.Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F. & Succi, S. 1993 Extended self-similarity in turbulent flows. Phys. Rev. E 48, R29R32.
5.Bewley, G. P., Sreenivasan, K. R. & Lathrop, D. P. 2008 Particles for tracing turbulent liquid helium. Exp. Fluids 44, 887896.
6.Biferale, L. & Procaccia, I. 2005 Anisotropy in turbulent flows and in turbulent transport. Phys. Rep. 414, 43164.
7.Buchhave, P. 1975 Biasing errors in individual particle measurements. In LDA Symposium of Copenhagen, Tonsbakken 16–18, 2740 Skovlunde, Denmark, pp. 258–278.
8.Buchhave, P., George, W. K. Jr & Lumley, J. L. 1979 The measurement of turbulence with the laser-Doppler anemometer. Annu. Rev. Fluid Mech. 11, 443504.
9.Buša, J., Hnatich, M., Honkonen, J. & Horvath, D. 1997 Stability of Kolmogorov scaling in anisotropically forced turbulence. Phys. Rev. E 55, 381394.
10.Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25, 657682.
11.Fox, R. F., Gatland, I. R., Roy, R. & Vemuri, G. 1988 Fast, accurate algorithm for numerical simulation of exponentially correlated coloured noise. Phys. Rev. A 38, 59385940.
12.Glezer, A. & Amitay, M. 2002 Synthetic jets. Annu. Rev. Fluid Mech. 34, 503529.
13.Goepfert, C., Marié, J.-L., Chareyron, D. & Lance, M. 2010 Characterization of a system generating a homogeneous isotropic turbulence field by free synthetic jets. Exp. Fluids 48, 809822.
14.Hussein, H. J., Capp, S. P. & George, W. K. 1994 Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet. J. Fluid Mech. 258, 3175.
15.Hwang, W. & Eaton, J. K. 2004 Creating homogeneous and isotropic turbulence without a mean flow. Exp. Fluids 36, 444454.
16.Kolmogorov, A. N. 1941 Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299303.
17.Kurien, S. & Sreenivasan, K. R. 2001 Measures of anisotropy and the universal properties of turbulence. In New Trends in Turbulence (Turbulence: Nouveaux Aspects), Les Houches Session LXXIV, pp. 53–111. Springer.
18.Lu, J., Fugal, J. P., Nordsiek, H., Saw, E. W., Shaw, R. A. & Yang, W. 2008 Lagrangian particle tracking in three dimensions via single-camera in-line digital holography. New J. Phys. 10, 125013.
19.Ouellette, N. T., Xu, H., Bourgoin, M. & Bodenschatz, E. 2006 Small-scale anisotropy in Lagrangian turbulence. New J. Phys. 8, 102.
20.Saddoughi, S. G. & Veeravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333372.
21.Shen, X. & Warhaft, Z. 2002 Longitudinal and transverse structure functions in sheared and unsheared wind-tunnel turbulence. Phys. Fluids 14, 370381.
22.Sreenivasan, K. R. 1995 On the universality of the Kolmogorov constant. Phys. Fluids 7, 27782784.
23.Staicu, A., Vorselaars, B. & van de Water, W. 2003 Turbulence anisotropy and the SO(3) description. Phys. Rev. E 68, 046303.
24.Tavoularis, S. & Corrsin, S. 1981 Experiments in nearly homogeneous turbulent shear flow with uniform mean temperature gradient. Part 1. J. Fluid Mech. 104, 311347.
25.Voth, G. A., La Porta, A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2002 Measurement of particle accelerations in fully developed turbulence. J. Fluid Mech. 469, 121160.
26.Warnaars, T. A., Hondzo, M. & Carper, M. A. 2006 A desktop apparatus for studying interactions between microorganisms and small-scale fluid motion. Hydrobiologia 563, 431443.
27.Webster, D. R., Brathwaite, A. & Yen, J. 2004 A novel laboratory apparatus for simulating isotropic oceanic turbulence at low Reynolds number. Limnol. Oceanogr. Methods 2, 112.
28.Yeung, P. K. & Brasseur, J. G. 1991 The response of isotropic turbulence to isotropic and anisotropic forcing at the large scales. Phys. Fluids A 3, 884897.
29.Zimmermann, R., Xu, H., Gasteuil, Y., Bourgoin, M., Volk, R., Pinton, J.-F. & Bodenschatz, E. 2010 The Lagrangian exploration module: an apparatus for the study of statistically homogeneous and isotropic turbulence. Rev. Sci. Instrum. 81, 055112.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed