Skip to main content Accessibility help

Visualization of the Ludford column

  • Oleg Andreev (a1), Yurii Kolesnikov (a1) and André Thess (a1)


When a liquid metal flows around a truncated cylinder in the presence of a magnetic field which is parallel to the axis of the cylinder, a stagnant region develops above the cylinder. We call this region a Ludford column. The Ludford column represents the magnetohydrodynamics (MHD) analogue of the well-known Taylor columns in rotating flows. Whereas Taylor columns can be easily visualized using dye, the visualization of Ludford columns has remained elusive up to now because liquid metals are opaque. We demonstrate that this fundamental limitation of experimental MHD can be overcome by using a superconducting 5 T magnet. This facility permits us to perform MHD experiments in which the opaque liquid metals are replaced with a transparent electrolyte while maintaining the key MHD effects. We report results of a series of flow experiments in which an aqueous solution of sulphuric acid flows around a bar with square cross-section (which for simplicity shall be referred to as a cylinder). We vary the Reynolds number in the range $5\lt Re\lt 100$ and the Hartmann number in the range $0\lt Ha\lt 14$ . The experimental procedure involves flow visualizations using tracer particles as well as velocity measurements using particle image velocimetry (PIV). Our experiments provide direct access to the Ludford column for the first time and reveal the spatial structure of this basic feature of MHD flows.


Corresponding author

Email address for correspondence:


Hide All

Present address: Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany.



Hide All
Andreev, O. & Kolesnikov, Yu 1997 MHD instabilities at transverse flow around a circular cylinder in an axial magnetic field. In Third International Conference on Transfer Phenomena in Magnetohydrodynamic and Electroconducting Flows, pp. 205210. Aussois.
Branover, G. G., Gel’fgat, Yu. M., Turuntaev, S. V. & Tsinober, A. B. 1969 Effect of a transverse magnetic field on velocity perturbations behind a circular cylinder swept by an electrolyte. Magnetohydrodynamics 5 (3), 4146.
Davidson, P. A 1997 The role of angular momentum in the magnetic damping of turbulence. J. Fluid Mech. 336, 123150.
Davidson, P. 1999 Magnetohydrodynamics in materials processing. Annu. Rev. Fluid Mech. 31, 273300.
Dousset, V. & Pothérat, A. 2008 Numerical simulations of a cylinder wake under a strong axial magnetic field. Phys. Fluids 20, 017104.
Dousset, V. & Pothérat, A. 2010 Formation mechanism of hairpin vortices in the wake of truncated square cylinder in a duct. J. Fluid Mech. 653, 519536.
Dousset, V. & Pothérat, A. 2012 Characterisation of the flow around a truncated cylinder in a duct in a spanwise magnetic field. J. Fluid Mech. 691, 341367.
Frank, M., Barleon, L. & Müller, U. 2001 Visual analysis of two-dimensional magnetohydro- dynamics. Phys. Fluids 13 (8), 22872295.
Greenspan, H. P. 1969 The Theory of Rotating Fluids. Cambridge University Press.
Hunt, J. C. R., Abell, C. J., Peterka, J. A. & Woo, H. 1978 Kinematical studies of the flows around free or surface-mounted mounted obstacles; applying topology to flow visualization. J. Fluid Mech. 86, 179200.
Hunt, J. C. R. & Leibovich, S. 1967 Magnetohydrodynamic flow in channels of variable cross-section with strong transverse magnetic fields. J. Fluid Mech. 28, 241260.
Hunt, J. C. R. & Ludford, G. S. S. 1968 Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 1. Obstacles in a constant area channel. J. Fluid Mech. 33, 693714.
Josserand, J., Marty, P. & Alémany, A. 1993 Pressure and drag measurements on a cylinder in a liquid metal flow with an aligned magnetic field. Fluid Dyn. Res. 11, 107117.
Kolesnikov, Yu. & Andreev, O. 1997 Heat transfer intensification promoted by vortical structures in a closed channel under magnetic field. J. Expl Therm. Fluid Sci. 15 (2), 8290.
Kolesnikov, Yu. & Andreev, O. 2000 Two scaling flow around a cylinder in axial magnetic field. In The 4th International Conference: MHD at Dawn of 3rd Millennium, pp. 3338. Giens.
Kolesnikov, Yu. B. & Tsinober, A. B. 1972 Two-dimensional turbulent flow behind a circular cylinder (experiment). Magnetohydrodynamics 8 (3), 300307.
Lahjomri, J., Capéran, P. & Alémany, A. 1993 The cylinder wake in a magnetic field aligned with the velocity. J. Fluid Mech. 253, 421448.
Ludford, G. S. S. 1961 The effect of a very strong magnetic cross-field on steady motion through a slightly conducting fluid. J. Fluid Mech. 10, 141155.
Moreau, R. 1990 Magnetohydrodynamics. Kluwer.
Müller, U. & Bühler, L. 2010 Magnetofluiddynamics in Channels and Containers. Springer.
Mutschke, G., Gerbeth, G., Shatrov, V. & Tomboulides, A. 1997 Two- and three dimensional instabilities of the cylinder wake in an aligned magnetic field. Phys. Fluids 9 (11), 31143116.
Pothérat, A., Sommeria, J. & Moreau, R. 2000 An effective two-dimensional model for MHD flows with transverse magnetic field. J. Fluid Mech. 424, 75100.
Raffel, M., Willert, C. E. & Kompenhans, J. 1998 Particle Image Velocimetry. Springer.
Shercliff, J. A. 1953 Steady motion of conducting fluids in pipes under transverse magnetic fields. Proc. Camb. Phil. Soc. 49, 136144.
Shercliff, J. A. 1962 The Theory of Electromagnetic Flow-measurement. Cambridge University Press.
Shercliff, J. A. 1975 Some duct flow problems at high Hartmann number. Z. Angew. Math. Phys. 26, 537548.
Sommeria, J. & Moreau, R. 1982 Why, how, and when, MHD turbulence becomes two-dimensional. J. Fluid Mech. 118, 507518.
Takizawa, Y, Matsuda, A., Sato, S., Abe, T. & Konigorski, D. 2006 Experimental investigation of the electromagnetic effect on a shock layer around a blunt body in a weakly ionized flow. Phys. Fluids 18, 117105.
Zaytsev, I. D. & Aseyev, G. G. 1992 Properties of Aqueous Solutions of Electrolytes. CRC.
Zdravkovich, M. M. 1997 Flow Around Circular Cylinders. Fundamentals, vol. 1, Oxford University Press.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

Visualization of the Ludford column

  • Oleg Andreev (a1), Yurii Kolesnikov (a1) and André Thess (a1)


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.