Skip to main content
SpringerLink
Log in

Decaying turbulence in soap films: energy and enstrophy evolution

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

This experimental study of quasi-two-dimensional grid turbulence in gravity-driven soap-film flow focuses on the differences between the behavior of the flow and the theoretical picture of two-dimensional turbulence. A previously unattainable quality of velocity field acquisition facilitates simultaneous measurement of velocity field features in the scale range spanning over two orders of magnitude. The highly-resolved flow field data are analyzed statistically in terms of velocity structure functions, as well as energy and enstrophy averages at different downstream positions. We find the rate of decay of these averages to be quantifiably greater than the predictions of the two-dimensional turbulence theory. This increased decay is likely to be the manifestation of the extra dissipation mechanism present in soap-film flows and prominent on the larger scales—air drag. The structure function analysis confirms the notion.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Adrian RJ (1995) Limiting resolution of particle image velocimetry for turbulent flow. Adv Turbul Res 2:1

    Google Scholar 

  • Batchelor GK (1969) Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys Fluids Suppl II:II-233

    Article  Google Scholar 

  • Belmonte A, Goldburg WI, Kellay H, Rutgers MA, Martin B, Wu XL (1999) Velocity fluctuations in a turbulent soap film: the third moment in two dimensions. Phys Fluids 11:1196

    Article  MATH  Google Scholar 

  • Borue V (1994) Inverse energy cascade in stationary two-dimensional homogeneous turbulence. Phys Rev Lett 72:1475

    Article  Google Scholar 

  • Cardoso O, Marteau D, Tabeling P (1994) Quantitative experimental study of the free decay of quasi-two-dimensional turbulence. Phys Rev E 49:454

    Article  Google Scholar 

  • Chasnov JR (1997) On the decay of two-dimensional homogeneous turbulence. Phys Fluids 9:171

    Article  Google Scholar 

  • Chen SY, Ecke RE, Eyink GL, Wang X, Xiao Z (2003) Physical mechanism of the two-dimensional enstrophy cascade. Phys Rev Lett 91:214501

    Article  Google Scholar 

  • Chomáz JM (2001) The dynamics of a viscous soap film with soluble surfactant. J Fluid Mech 442:387

    Article  MATH  MathSciNet  Google Scholar 

  • Chong MS, Perry AE, Cantwell BJ (1990) A general classification of three-dimensional flow fields. Phys Fluids A Fluid Dyn 2:765

    Article  MathSciNet  Google Scholar 

  • Clercx HJH, van Hejist GJF (2000) Energy spectra for decaying 2D turbulence in a bounded domain. Phys Rev Lett 85:306

    Article  Google Scholar 

  • Clercx HJH, Maassen SR, van Hejist GJF (1998) Spontaneous spin-up during the decay of 2D turbulence in a square container with rigid boundaries. Phys Rev Lett 80:5129

    Article  Google Scholar 

  • Clercx HJH, Maassen SR, van Hejist GJF (1999) Decaying two-dimensional turbulence in square containers with no-slip or stress-free boundaries. Phys Fluids 11:611

    Article  MATH  Google Scholar 

  • Clercx HJH, van Hejist GJF, Zoeteweij MJ (2003) Quasi-two-dimensional turbulence in shallow fluid layers: the role of bottom friction and fluid layer depth. Phys Rev E 67:066303

    Article  Google Scholar 

  • Collected Papers of Sir James Dewar, vol 2. Cambridge University Press, London, 1334 (1927)

  • Couder Y (1984) Two-dimensional grid turbulence in a thin liquid film. J Phys (France) Lett 45:353

    Google Scholar 

  • Couder Y, Basdevant C (1986) Experimental and numerical study of vortex couples in two-dimensional flows. J Fluid Mech 173:225

    Article  Google Scholar 

  • Frisch U, Sulem PL (1984) Numerical Simulation of the inverse cascade in two-dimensional turbulence. Phys Fluids 27:1921

    Article  MATH  Google Scholar 

  • Georgiev D, Vorobieff P (2002) The slowest soap-film tunnel in the Southwest. Rev Sci Instrum 73:1177

    Article  Google Scholar 

  • Goldburg WI, Rutgers MA, Wu X-l (1997) Experiments on turbulence in soap films. Phys A 239:340

    Article  Google Scholar 

  • Kraichnan RH (1967) Inertial ranges in two-dimensional turbulence. Phys Fluids 10:1417

    Article  Google Scholar 

  • Lamballais E, Lesieur M, Métais O (1996) Effects of spanwise rotation on the vorticity stretching in transitional and turbulent channel flow. Int J Heat Fluid Flow 17:324

    Article  Google Scholar 

  • Martin BK, Wu XL, Goldburg WI (1998) Spectra of decaying turbulence in a soap film. Phys Rev Lett 80:3964

    Article  Google Scholar 

  • Paret J, Tabeling P (1997) Experimental observation of the two-dimensional inverse energy cascade. Phys Rev Lett 79:4162

    Article  Google Scholar 

  • Prasad AK, Adrian RJ, Landreth CC, Offutt PW (1992) Effect of resolution on the speed and accuracy of particle image velocimetry interrogations. Exp Fluids 13:105

    Article  Google Scholar 

  • Rivera MK, Ecke RE (2005) Pair dispersion and doubling time statistics in two-dimensional turbulence. Phys Rev Lett 95:194503

    Article  Google Scholar 

  • Rivera MK, Vorobieff P, Ecke RE (1998) Turbulence in flowing soap films: velocity, vorticity, and thickness fields. Phys Rev Lett 81:1417

    Article  Google Scholar 

  • Rivera MK, Daniel WB, Chen SY, Ecke RE (2003) Energy and enstrophy transfer in decaying two-dimensional turbulence. Phys Rev Lett 90:104502

    Article  Google Scholar 

  • Rutgers MA (1998) Forced 2D turbulence: experimental evidence of simultaneous inverse energy and forward enstrophy cascades. Phys Rev Lett 81:2244

    Article  Google Scholar 

  • Rutgers MA, Wu X-l, Petersen AA, Baghavatula R, Goldburg WI (1996) Two dimensional velocity profiles and laminar boundary layers in flowing soap films. Phys Fluids 8:2847

    Article  Google Scholar 

  • Rutgers MA, Wu XL, Daniel WB (2001) Conducting fluid dynamics experiments with vertically falling soap films. Rev Sci Instrum 72:3025

    Article  Google Scholar 

  • Saffman PG (1971) On the spectrum and decay of random two-dimensional vorticity distributions at large Reynolds number. Stud Appl Math 50(4):377

    MATH  Google Scholar 

  • Smith LM, Yakhot V (1993) Bose condensation and small-scale structure generation in a random force driven 2D turbulence. Phys Rev Lett 71:352

    Article  Google Scholar 

  • Sommeria J, Moreau R (1982) Why, how and when MHD turbulence becomes two-dimensional. J Fluid Mech 118:507

    Article  MATH  Google Scholar 

  • VidPIV Rowan Version 4.0g, Intelligent Laser Applications GmbH, Karl-Heinz Beckurts-Strasse 13, 52428, Jülich, Germany, ©  2002

  • Vorobieff P, Korlimarla A (2004) Evolution of a quasi-2D shear layer in a soap film flow. Bull Am Phys Soc 49(10):116

    Google Scholar 

  • Vorobieff P, Rivera M, Ecke RE (1999) Soap film flows: statistics of two-dimensional turbulence. Phys Fluids 11:2167

    Article  MATH  MathSciNet  Google Scholar 

  • Vorobieff P, Rivera MK, Ecke RE (2001) Imaging 2D turbulence. J Vis 3:323

    Article  Google Scholar 

  • Westerweel J (1997) Fundamentals of digital particle image velocimetry. Meas Sci Technol 8:1379

    Article  Google Scholar 

  • Williams BS, Marteau D, Gollub JP (1997) Mixing of a passive scalar in magnetically forced two-dimensional turbulence. Phys Fluids 9:2061

    Article  MATH  MathSciNet  Google Scholar 

  • Wu XL, Rivera MK (2000) External dissipation in driven two-dimensional turbulence. Phys Rev Lett 85:976

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, The University of New Mexico, 122 Redondo Dr. NE, Albuquerque, NM, 87109, USA

    Tanveer Shakeel

  2. Department of Mechanical Engineering, The University of New Mexico, Albuquerque, NM, 87131, USA

    Peter Vorobieff

Authors
  1. Tanveer Shakeel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Vorobieff
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter Vorobieff.

Additional information

This research was supported by Los Alamos National Laboratory, task order BG109.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shakeel, T., Vorobieff, P. Decaying turbulence in soap films: energy and enstrophy evolution. Exp Fluids 43, 125–133 (2007). https://doi.org/10.1007/s00348-007-0334-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-007-0334-y

Keywords

Search

Navigation