Onset of three-dimensionality in electromagnetically driven thin-layer flows

Physics of Fluids

Volumn 23, Issue 4, 2011, Pages

  Kelley, Douglas H ^a   Ouellette, Nicholas T ^a  

^a Yale University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

REYNOLDS NUMBER;

ANALYSIS TECHNIQUES; CRITICAL REYNOLDS NUMBER; EXPERIMENTAL MODELING; LOW REYNOLDS NUMBER; OCEANOGRAPHIC DATA; SHEAR INSTABILITY; THIN-LAYER FLOW; TWO-DIMENSIONAL FLUID FLOW;

FLOW OF FLUIDS;

EID: 79955378321     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3570685     Document Type: Article

References (32)

1. Kraichnan R.H. Inertial ranges in two-dimensional turbulence. Phys. Fluids 1967, 10:1417. PHFLE6, 1070-6631, 10.1063/1.1762301.
2. Leith C.E. Diffusion approximation for two-dimensional turbulence. Phys. Fluids 1968, 11:671. PHFLE6, 1070-6631, 10.1063/1.1691968.
3. Batchelor G.K. Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids 1969, 12:II-233. PHFLE6, 1070-6631, 10.1063/1.1692443.
4. Perry A.E. Chong M.S. A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 1987, 19:125. ARVFA3, 0066-4189, 10.1146/annurev.fl.19.010187.001013.
5. Voth G.A. Haller G. Gollub J.P. Experimental measurements of stretching fields in fluid mixing. Phys. Rev. Lett. 2002, 88:254501. PRLTAO, 0031-9007, 10.1103/PhysRevLett.88.254501.
6. Rhines P.B. Geostrophic turbulence. Annu. Rev. Fluid Mech. 1979, 11:401. ARVFA3, 0066-4189, 10.1146/annurev.fl.11.010179.002153.
7. Smith L.M. Chasnov J.R. Waleffe F. Crossover from two- to three-dimensional turbulence. Phys. Rev. Lett. 1996, 77:2467. PRLTAO, 0031-9007, 10.1103/PhysRevLett.77.2467.
8. Tabeling P. Burkhart S. Cardoso O. Willaime H. Experimental study of freely decaying two-dimensional turbulence. Phys. Rev. Lett. 1991, 67:3772. PRLTAO, 0031-9007, 10.1103/PhysRevLett.67.3772.
9. Paret J. Marteau D. Paireau O. Tabeling P. Are flows electromagnetically forced in thin stratified layers two dimensional?. Phys. Fluids 1997, 9:3102. PHFLE6, 1070-6631, 10.1063/1.869419.
10. Jüttner B. Marteau D. Tabeling P. Thess A. Numerical simulations of experiments on quasi-two-dimensional turbulence. Phys. Rev. E 1997, 55:5479. PLEEE8, 1063-651X, 10.1103/PhysRevE.55.5479.
11. Rothstein D. Henry E. Gollub J.P. Persistent patterns in transient chaotic fluid mixing. Nature (London) 1999, 401:770. NATUAS, 0028-0836, 10.1038/44529.
12. Satijn M.P. Cense A.W. Verzicco R. Clercx H.J. H. van Heijst G.J. F. Three-dimensional structure and decay properties of vortices in shallow fluid layers. Phys. Fluids 2001, 13:1932. PHFLE6, 1070-6631, 10.1063/1.1374936.
13. Solomon T.H. Mezić I. Uniform resonant chaotic mixing in fluid flows. Nature (London) 2003, 425:376. NATUAS, 0028-0836, 10.1038/nature01993.
14. Clercx H.J. H. van Heijst G.J. F. Zoeteweij M.L. Quasi-two-dimensional turbulence in shallow fluid layers: The role of bottom friction and fluid layer depth. Phys. Rev. E 2003, 67:066303. PLEEE8, 1063-651X, 10.1103/PhysRevE.67.066303.
15. Rivera M.K. Ecke R.E. Pair dispersion and doubling time statistics in two-dimensional turbulence. Phys. Rev. Lett. 2005, 95:194503. PRLTAO, 0031-9007, 10.1103/PhysRevLett.95.194503.
16. Rossi L. Vassilicos J.C. Hardalupas Y. Electromagnetically controlled multi-scale flows. J. Fluid Mech. 2006, 558:207. JFLSA7, 0022-1120, 10.1017/S0022112006009980.
17. Akkermans R.A. D. Cieslik A.R. Kamp L.P. J. Trieling R.R. Clercx H.J. H. van Heijst G.J. F. The three-dimensional structure of an electromagnetically generated dipolar vortex in a shallow fluid layer. Phys. Fluids 2008, 20:116601. PHFLE6, 1070-6631, 10.1063/1.3005452.
18. Akkermans R.A. D. Kamp L.P. J. Clercx H.J. H. van Heijst G.J. F. Intrinsic three-dimensionality in electromagnetically driven shallow flows. EPL 2008, 83:24001. EULEEJ, 0295-5075, 10.1209/0295-5075/83/24001.
19. Akkermans R.A. D. Kamp L.P. J. Clercx H.J. H. van Heijst G.J. F. Three-dimensional flow in electromagnetically driven shallow two-layer fluids. Phys. Rev. E 2010, 82:026314. PLEEE8, 1063-651X, 10.1103/PhysRevE.82.026314.
20. Clercx H.J. H. van Heijst G.J. F. Two-dimensional Navier-Stokes turbulence in bounded domains. Appl. Mech. Rev. 2009, 62:020802. AMREAD, 0003-6900, 10.1115/1.3077489.
21. Lekien F. Coulliette C. Bank R. Marsden J. Open-boundary modal analysis: Interpolation, extrapolation, and filtering. J. Geophys. Res. 2004, 109:C12004. JGREA2, 0148-0227, 10.1029/2004JC002323.
22. Kelley D.H. Ouellette N.T. Using particle tracking to measure flow instabilities in an undergraduate laboratory experiment. Am. J. Phys. 2011, 79:267. AJPIAS, 0002-9505, 10.1119/1.3536647.
23. Vella D. Mahadevan L. The 'Cheerios effect'. Am. J. Phys. 2005, 73:817. AJPIAS, 0002-9505, 10.1119/1.1898523.
24. Ouellette N.T. O'Malley P.J. J. Gollub J.P. Transport of finite-sized particles in chaotic flow. Phys. Rev. Lett. 2008, 101:174504. PRLTAO, 0031-9007, 10.1103/PhysRevLett.101.174504.
25. Ouellette N.T. Xu H. Bodenschatz E. A quantitative study of three-dimensional Lagrangian particle tracking algorithms. Exp. Fluids 2006, 40:301. EXFLDU, 0723-4864, 10.1007/s00348-005-0068-7.
26. Toschi F. Bodenschatz E. Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 2009, 41:375. ARVFA3, 0066-4189, 10.1146/annurev.fluid.010908.165210.
27. Mordant N. Crawford A.M. Bodenschatz E. Experimental Lagrangian acceleration probability density function measurement. Physica D 2004, 193:245. PDNPDT, 0167-2789, 10.1016/j.physd.2004.01.041.
28. Ouellette N.T. Xu H. Bodenschatz E. Springer Handbook of Experimental Fluid Mechanics 2007, C. Tropea, A. L. Yarin, J. F. Foss, and in edited by and (Springer-Verlag, Berlin, ).
29. Arfken G.B. Weber H.J. Mathematical Methods for Physicists 2001, and 5th ed. (Harcourt Academic, San Diego, ).
30. Lynch P. Partitioning the wind in a limited domain. Mon. Weather Rev. 1989, 117:1492. MWREAB, 0027-0644, 10.1175/1520-0493(1989)117<1492:PTWIAL>2.0.CO;2.
31. Press W.H. Teukolsky S.A. Vetterling W.T. Flannery B.P. Numerical Recipes: The Art of Scientific Computing 2007, and 3rd ed. (Cambridge University Press, London, ).
32. Garrett C. Munk W. Internal waves in the ocean. Annu. Rev. Fluid Mech. 1979, 11:339. ARVFA3, 0066-4189, 10.1146/annurev.fl.11.010179.002011.