Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T01:09:35.924Z Has data issue: false hasContentIssue false
  • English
  • Français

Electrically driven vortices in a weak dipolar magnetic field in a shallow electrolytic layer

Published online by Cambridge University Press:  25 November 2009

ALDO FIGUEROA ,
FRANÇOIS DEMIAUX ,
SERGIO CUEVAS  and
EDUARDO RAMOS
ALDO FIGUEROA
Affiliation:
Centro de Investigación en Energía, Universidad Nacional Autónoma de México, A. P. 34, Temixco, Mor. 62580, México
FRANÇOIS DEMIAUX
Affiliation:
Mechanical Engineering Development Department, INSA-Lyon, 20 Av. Albert Einstein, 69621 Villeurbanne Cedex, France
SERGIO CUEVAS*
Affiliation:
Centro de Investigación en Energía, Universidad Nacional Autónoma de México, A. P. 34, Temixco, Mor. 62580, México
EDUARDO RAMOS
Affiliation:
Centro de Investigación en Energía, Universidad Nacional Autónoma de México, A. P. 34, Temixco, Mor. 62580, México
*
†Email address for correspondence: scg@cie.unam.mx
Get access Rights & Permissions [Opens in a new window]

Abstract

Steady dipolar vortices continuously driven by electromagnetic forcing in a shallow layer of an electrolytic fluid are studied experimentally and theoretically. The driving Lorentz force is generated by the interaction of a dc uniform electric current injected in the thin layer and the non-uniform magnetic field produced by a small dipolar permanent magnet (0.33 T). Laminar velocity profiles in the neighbourhood of the zone affected by the magnetic field were obtained with particle image velocimetry in planes parallel and normal to the bottom wall. Flow planes at different depths of the layer were explored for injected currents ranging from 10 to 100 mA. Measurements of the boundary layer attached to the bottom wall reveal that owing to the variation of the field in the normal direction, a slightly flattened developing profile with no shear stresses at the free surface is formed. A quasi-two-dimensional magnetohydrodynamic numerical model that introduces the non-uniformity of the magnetic field, particularly its decay in the normal direction, was developed. Vertical diffusion produced by the bottom friction was modelled through a linear friction term. The model reproduces the main characteristic behaviour of the electromagnetically forced flow.

JFM classification

MHD and Electrohydrodynamics: MHD and Electrohydrodynamics Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 245 - 261
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Alboussière, T. 2004 A geostrophic-like model for large Hartmann number flows. J. Fluid Mech. 521, 125–154.Google Scholar
Andreev, O., Heberstroh, Ch. & Thess, A. 2001 MHD flow in electrolytes at high Hartmann numbers. Magnetohydrodynamics, 37 (1–2), 151–160.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 (1), 454–461.CrossRefGoogle ScholarPubMed
Clercx, H. J. H. & van Heijst, G. J. F. 2002 Dissipation of kinetic energy in two-dimensional bounded flows. Phys. Rev. E 65, 066305.Google Scholar
Clercx, H. J. H., van Heijst, G. J. F. & Zoeteweij, 2003 Quasi-two-dimensional turbulence in shallow fluid layers: the role of bottom friction and fluid layer depth. Phys. Rev. E 67, 066303.Google Scholar
Cuevas, S., Smolentsev, S. & Abdou, M. 2006 On the flow past a magnetic obstacle. J. Fluid Mech. 553, 227–252.CrossRefGoogle Scholar
Griebel, M., Dornseifer, T. & Neunhoeffer, T. 1998 Numerical Simulation in Fluid Dynamics. SIAM.CrossRefGoogle Scholar
Hansen, A. E., Marteau, D. & Tabeling, P. 1998 Two-dimensional turbulence and dispersion in a freely decaying system. Phys. Rev. E 58, 7261–7271.CrossRefGoogle Scholar
Lavrent'ev, I. V., Molokov, S. Yu., Sidorenkov, S. I. & Shishko, A. R. 1990 Stokes flow in a rectangular magnetohydrodynamic channel with nonconducting walls within a non-uniform magnetic field at large Hartmann numbers. Magnetohydrodynamics 26 (3), 328–338.Google Scholar
Marteau, D., Cardoso, O. & Tabeling, P. 1995 Equilibrium states of two-dimensional turbulence: an experimental study. Phys. Rev. E 51, 5124–5127.Google Scholar
McCaig, M. 1977 Permanent Magnets in Theory and Practice. Wiley.Google Scholar
Messadek, K. & Moreau, R. 2002 An experimental investigation of MHD quasi-two-dimensional turbulent shear flows. J. Fluid Mech. 456, 137–159.CrossRefGoogle Scholar
Moreau, R. 1990 Magnetohydrodynamics. Kluwer.Google Scholar
Paret, J., Marteau, D., Paireau, O. & Tabeling, P. 1997 Are flows electromagnetically forced in stratified layers two-dimensional? Phys. Fluids 7 (10), 3102–3104.Google Scholar
Paret, J. & Tabeling, P. 1997 Experimental observation of the two-dimensional inverse energy cascade. Phys. Rev. Lett. 79 (21), 4162–4165.Google Scholar
Potherát, A., Sommeria, J. & Moreau, R. 2000 An effective two-dimensional model for MHD flows with transverse magnetic fields. J. Fluid Mech. 424, 75–100.CrossRefGoogle Scholar
Rothstein, D., Henry, E. & Gollub, J. P. 1999 Persistent patterns in transient chaotic fluid mixing. Nature, 401 770–772.Google Scholar
Rossi, L., Vassilicos, J. C. & Hardalupas, Y. 2006 a Electromagnetically controlled multi-scale flows. J. Fluid Mech. 558, 207–242.Google Scholar
Rossi, L., Vassilicos, J. C. & Hardalupas, Y. 2006 b Multiscale laminar flows with turbulentlike properties. Phys. Rev. Lett. 97, 144501.CrossRefGoogle ScholarPubMed
Satijn, M. P., Cense, A. W., Verzicco, R., Clercx, H. J. H. & van Heijst, G. J. F. 2001 Three-dimensional structure and decay properties of vortices in shallow fluid layers. Phys. Fluids 13, 1932–1945.Google Scholar
Smolentsev, S. 1997 Averaged model in MHD duct flow calculations. Magnetohydrodynamics 33 (1), 42–47.Google Scholar
Sommeria, J. 1986 Experimental study of the two-dimensional inverse energy cascade in a square box. J. Fluid Mech. 170, 139–168.Google Scholar
Sommeria, J. 1988 a Electrically driven vortices in a strong magnetic field. J. Fluid Mech. 189, 553–569.CrossRefGoogle Scholar
Sommeria, J. 1988 b Experimental characterization of steady two-dimensional vortex couples. J. Fluid Mech. 192, 175–192.Google Scholar
Sommeria, J. & Moreau, R. 1982 Why, how, and when, MHD turbulence becomes two-dimensional. J. Fluid Mech. 118, 507–518.Google Scholar
Tabeling, P. 2002 Two-dimensional turbulence: a physicist approach. Phys. Rep. 362, 1–62.CrossRefGoogle Scholar
Voth, G. A., Haller, G. & Gollub, J. P. 2002 Experimental measurements of stretching fields in fluid mixing. Phys. Rev. Lett. 88 (15) 254501.CrossRefGoogle ScholarPubMed
Voth, G. A., Saint, T. C., Dobler, G. & Gollub, J. P. 2003 Mixing rates and symmetry breaking in two-dimensional chaotic flow. Phys. Fluids 15 2560–2566.CrossRefGoogle Scholar
Williams, B. S., Marteau, D. & Gollub, J. P. 1997 Mixing of a passive scalar in magnetically forced two-dimensional turbulence. Phys. Fluids 9 2061–2079.Google Scholar
Zavala Sansón, L., van Heijst, G. J. F. & Backx, N. A. 2001 Ekman decay of a dipolar vortex in a rotating fluid. Phys. Fluids 13, 440–451.Google Scholar