Advertisement

Experiments in Fluids

, Volume 43, Issue 1, pp 125–133 | Cite as

Decaying turbulence in soap films: energy and enstrophy evolution

  • Tanveer Shakeel
  • Peter Vorobieff
Research Article

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.

Keywords

Vorticity Digital Particle Image Velocimetry Downstream Distance Soap Film Grid Turbulence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Adrian RJ (1995) Limiting resolution of particle image velocimetry for turbulent flow. Adv Turbul Res 2:1Google Scholar
  2. Batchelor GK (1969) Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys Fluids Suppl II:II-233CrossRefGoogle Scholar
  3. 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 11:1196CrossRefMATHGoogle Scholar
  4. Borue V (1994) Inverse energy cascade in stationary two-dimensional homogeneous turbulence. Phys Rev Lett 72:1475CrossRefGoogle Scholar
  5. Cardoso O, Marteau D, Tabeling P (1994) Quantitative experimental study of the free decay of quasi-two-dimensional turbulence. Phys Rev E 49:454CrossRefGoogle Scholar
  6. Chasnov JR (1997) On the decay of two-dimensional homogeneous turbulence. Phys Fluids 9:171CrossRefGoogle Scholar
  7. Chen SY, Ecke RE, Eyink GL, Wang X, Xiao Z (2003) Physical mechanism of the two-dimensional enstrophy cascade. Phys Rev Lett 91:214501CrossRefGoogle Scholar
  8. Chomáz JM (2001) The dynamics of a viscous soap film with soluble surfactant. J Fluid Mech 442:387MATHCrossRefMathSciNetGoogle Scholar
  9. Chong MS, Perry AE, Cantwell BJ (1990) A general classification of three-dimensional flow fields. Phys Fluids A Fluid Dyn 2:765CrossRefMathSciNetGoogle Scholar
  10. Clercx HJH, van Hejist GJF (2000) Energy spectra for decaying 2D turbulence in a bounded domain. Phys Rev Lett 85:306CrossRefGoogle Scholar
  11. 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 80:5129CrossRefGoogle Scholar
  12. Clercx HJH, Maassen SR, van Hejist GJF (1999) Decaying two-dimensional turbulence in square containers with no-slip or stress-free boundaries. Phys Fluids 11:611CrossRefMATHGoogle Scholar
  13. 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 67:066303CrossRefGoogle Scholar
  14. Collected Papers of Sir James Dewar, vol 2. Cambridge University Press, London, 1334 (1927)Google Scholar
  15. Couder Y (1984) Two-dimensional grid turbulence in a thin liquid film. J Phys (France) Lett 45:353Google Scholar
  16. Couder Y, Basdevant C (1986) Experimental and numerical study of vortex couples in two-dimensional flows. J Fluid Mech 173:225CrossRefGoogle Scholar
  17. Frisch U, Sulem PL (1984) Numerical Simulation of the inverse cascade in two-dimensional turbulence. Phys Fluids 27:1921MATHCrossRefGoogle Scholar
  18. Georgiev D, Vorobieff P (2002) The slowest soap-film tunnel in the Southwest. Rev Sci Instrum 73:1177CrossRefGoogle Scholar
  19. Goldburg WI, Rutgers MA, Wu X-l (1997) Experiments on turbulence in soap films. Phys A 239:340CrossRefGoogle Scholar
  20. Kraichnan RH (1967) Inertial ranges in two-dimensional turbulence. Phys Fluids 10:1417CrossRefGoogle Scholar
  21. 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 17:324CrossRefGoogle Scholar
  22. Martin BK, Wu XL, Goldburg WI (1998) Spectra of decaying turbulence in a soap film. Phys Rev Lett 80:3964CrossRefGoogle Scholar
  23. Paret J, Tabeling P (1997) Experimental observation of the two-dimensional inverse energy cascade. Phys Rev Lett 79:4162CrossRefGoogle Scholar
  24. Prasad AK, Adrian RJ, Landreth CC, Offutt PW (1992) Effect of resolution on the speed and accuracy of particle image velocimetry interrogations. Exp Fluids 13:105CrossRefGoogle Scholar
  25. Rivera MK, Ecke RE (2005) Pair dispersion and doubling time statistics in two-dimensional turbulence. Phys Rev Lett 95:194503CrossRefGoogle Scholar
  26. Rivera MK, Vorobieff P, Ecke RE (1998) Turbulence in flowing soap films: velocity, vorticity, and thickness fields. Phys Rev Lett 81:1417CrossRefGoogle Scholar
  27. Rivera MK, Daniel WB, Chen SY, Ecke RE (2003) Energy and enstrophy transfer in decaying two-dimensional turbulence. Phys Rev Lett 90:104502CrossRefGoogle Scholar
  28. Rutgers MA (1998) Forced 2D turbulence: experimental evidence of simultaneous inverse energy and forward enstrophy cascades. Phys Rev Lett 81:2244CrossRefGoogle Scholar
  29. 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 8:2847CrossRefGoogle Scholar
  30. Rutgers MA, Wu XL, Daniel WB (2001) Conducting fluid dynamics experiments with vertically falling soap films. Rev Sci Instrum 72:3025CrossRefGoogle Scholar
  31. Saffman PG (1971) On the spectrum and decay of random two-dimensional vorticity distributions at large Reynolds number. Stud Appl Math 50(4):377MATHGoogle Scholar
  32. Smith LM, Yakhot V (1993) Bose condensation and small-scale structure generation in a random force driven 2D turbulence. Phys Rev Lett 71:352CrossRefGoogle Scholar
  33. Sommeria J, Moreau R (1982) Why, how and when MHD turbulence becomes two-dimensional. J Fluid Mech 118:507MATHCrossRefGoogle Scholar
  34. VidPIV Rowan Version 4.0g, Intelligent Laser Applications GmbH, Karl-Heinz Beckurts-Strasse 13, 52428, Jülich, Germany, ©  2002Google Scholar
  35. Vorobieff P, Korlimarla A (2004) Evolution of a quasi-2D shear layer in a soap film flow. Bull Am Phys Soc 49(10):116Google Scholar
  36. Vorobieff P, Rivera M, Ecke RE (1999) Soap film flows: statistics of two-dimensional turbulence. Phys Fluids 11:2167CrossRefMATHMathSciNetGoogle Scholar
  37. Vorobieff P, Rivera MK, Ecke RE (2001) Imaging 2D turbulence. J Vis 3:323CrossRefGoogle Scholar
  38. Westerweel J (1997) Fundamentals of digital particle image velocimetry. Meas Sci Technol 8:1379CrossRefGoogle Scholar
  39. Williams BS, Marteau D, Gollub JP (1997) Mixing of a passive scalar in magnetically forced two-dimensional turbulence. Phys Fluids 9:2061CrossRefMATHMathSciNetGoogle Scholar
  40. Wu XL, Rivera MK (2000) External dissipation in driven two-dimensional turbulence. Phys Rev Lett 85:976CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringThe University of New MexicoAlbuquerqueUSA
  2. 2.Department of Mechanical EngineeringThe University of New MexicoAlbuquerqueUSA

Personalised recommendations