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Spin-up of a magnetically driven tornado-like vortex

Published online by Cambridge University Press:  14 November 2013

Tobias Vogt ,
Ilmārs Grants ,
Sven Eckert  and
Gunter Gerbeth
Tobias Vogt*
Affiliation:
Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, PO Box 510119, 01314 Dresden, Germany
Ilmārs Grants
Affiliation:
Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, PO Box 510119, 01314 Dresden, Germany
Sven Eckert
Affiliation:
Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, PO Box 510119, 01314 Dresden, Germany
Gunter Gerbeth
Affiliation:
Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, PO Box 510119, 01314 Dresden, Germany
*
†Email address for correspondence: t.vogt@hzdr.de
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Abstract

The spin-up of a concentrated vortex in a liquid metal cylinder with a free surface is considered experimentally and numerically. The vortex is driven by two flow-independent magnetic body forces. A continuously applied rotating magnetic field provides the source of the angular momentum. A pulse of about one order of magnitude stronger travelling magnetic field drives a converging flow that temporarily focuses this angular momentum towards the axis of the container. A highly concentrated vortex forms that produces a funnel-shaped surface depression. We explore experimentally the duration, the depth and the conditions of formation of this funnel. Additionally, we measure the axial velocity and calculate the axisymmetric flow field of this transient vortex at a lower force magnitude. The spin-up vortex is similar to the corresponding developed time-averaged turbulent vortex driven by the same magnetic forces (Grants et al., J. Fluid Mech., vol. 616, 2008, pp. 135–152). There are two main differences. First, the maximum swirl concentration condition cannot be expressed as a constant ratio of the two driving forces. Second, a much higher degree of swirl concentration is feasible. We explain these differences as due to a much lower turbulence during the spin-up.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Rotating flows Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 736 , 10 December 2013 , pp. 641 - 662
Copyright
©2013 Cambridge University Press 

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References

Andersen, A., Bohr, T., Stenum, B., Juul Rasmussen, J. & Lautrup, B. 2006 The bathtub vortex in a rotating container. J. Fluid Mech. 556, 121–146.CrossRefGoogle Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zhang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.Google Scholar
Church, C. R., Snow, J. T. & Agee, E. M. 1977 Tornado vortex simulation at Purdue University. Bull. Am. Meteorol. Soc. 58, 900–909.2.0.CO;2>CrossRefGoogle Scholar
Church, C. R., Snow, J. T., Baker, G. L. & Agee, E. M. 1979 Characteristics of tornado-like vortices as a function of swirl ratio: a laboratory investigation. J. Atmos. Sci. 36, 1755–1776.2.0.CO;2>CrossRefGoogle Scholar
Cramer, A., Pal, J. & & Gerbeth, G. 2007 Experimental investigation of a flow driven by a combination of a rotating and a travelling magnetic field. Phys. Fluids 19 (11), 118109.Google Scholar
Davidson, P. A. 1992 Swirling flow in an axisymmetric cavity of arbitrary profile, driven by a rotating magnetic field. J. Fluid Mech. 254, 669–699.Google Scholar
Emanuel, K. A. 1991 The theory of hurricanes. Annu. Rev. Fluid Mech. 23 (1), 179–196.CrossRefGoogle Scholar
Emanuel, K. 2003 Tropical cyclones. Annu. Rev. Earth Planet. Sci. 31 (1), 75–104.Google Scholar
Fiedler, B. H. 1995 On modelling tornadoes in isolation from the parent storm. Atmos.-Ocean 33 (3), 501–512.Google Scholar
Fiedler, B. H. 1998 Wind-speed limits in numerically simulated tornadoes with suction vortices. Q. J. R. Meteorol. Soc. 124, 2377–2392.Google Scholar
Fiedler, B. 2009 Suction vortices and spiral breakdown in numerical simulations of tornado-like vortices. Atmos. Sci. Lett. 10 (2), 109–114.Google Scholar
Grants, I. & Gerbeth, G. 2001 Stability of axially symmetric flow driven by a rotating magnetic field in a cylindrical cavity. J. Fluid Mech. 431, 407–426.Google Scholar
Grants, I. & Gerbeth, G. 2004 Stability of melt flow due to a travelling magnetic field in a closed ampoule. J. Cryst. Growth 269 (2), 630–638.Google Scholar
Grants, I., Zhang, C., Eckert, S. & Gerbeth, G. 2008 Experimental observation of swirl accumulation in a magnetically driven flow. J. Fluid Mech. 616, 135–152.Google Scholar
Grants, I., Zhang, C., Eckert, S. & Gerbeth, G. 2009 Liquid metal tornado. In Proceedings of 6th International Conference on Electromagnetic Processing of Materials (ed. Gerbeth, G. & Fautrelle, Y.), pp. 102–105. Helmholtz-Zentrum Dresden-Rossendorf.Google Scholar
Halász, G., Gyüre, B., Jánosi, I. M., Szabó, K. G. & Tél, T. 2007 Vortex flow generated by a magnetic stirrer. Am. J. Phys. 75, 1092–1098.Google Scholar
Klemp, J. B. 1987 Dynamics of tornadic thunderstorms. Annu. Rev. Fluid Mech. 19 (1), 369–402.CrossRefGoogle Scholar
Lantzsch, R., Galindo, V., Grants, I., Zhang, C., Pätzold, O., Gerbeth, G. & Stelter, M. 2007 Experimental and numerical results on the fluid flow driven by a travelling magnetic field. J. Cryst. Growth 305, 249–256.CrossRefGoogle Scholar
Lewellen, D. C., Lewellen, W. S. & Xia, J. 2000 The influence of a local swirl ratio on tornado intensification near the surface. J. Atmos. Sci. 57 (4), 527–544.Google Scholar
Lewellen, W. S., Lewellen, D. C. & Sykes, R. I. 1997 Large-eddy simulation of a tornado’s interaction with the surface. J. Atmos. Sci. 54 (5), 581–605.Google Scholar
Markowski, P., Richardson, Y., Rasmussen, E., Straka, J., Davies-Jones, R. & Trapp, R. J. 2008 Vortex lines within low-level mesocyclones obtained from pseudo-dual-Doppler radar observations. Mon. Weath. Rev. 136 (9), 3513–3535.CrossRefGoogle Scholar
Nikrityuk, P. A., Ungarish, M., Eckert, K. & Grundmann, R. 2005 Spin-up of a liquid metal flow driven by a rotating magnetic field in a finite cylinder: a numerical and an analytical study. Phys. Fluids 17, 067101.Google Scholar
Nolan, D. S. 2005 A new scaling for tornado-like vortices. J. Atmos. Sci. 62 (7), 2639–2645.Google Scholar
Prochazka, A. & Pullin, D. I. 1995 On the two-dimensional stability of the axisymmetric Burgers vortex. Phys. Fluids 7, 1788–1790.Google Scholar
Räbiger, D., Eckert, S. & Gerbeth, G. 2010 Measurements of an unsteady liquid metal flow during spin-up driven by a rotating magnetic field. Exp. Fluids 48 (2), 233–244.Google Scholar
Robinson, T. & Larsson, K. 1973 An experimental investigation of a magnetically driven rotating liquid-metal flow. J. Fluid Mech. 60, 641–664.Google Scholar
Rotunno, R. 2013 The fluid dynamics of tornadoes. Annu. Rev. Fluid Mech. 45 (1), 59–84.Google Scholar
Tacke, K. H. & Schwerdtfeger, K. 1979 Rührgeschwindigkeit in Rundstrangguss bei Rührung mit elektromagnetischen Drehfeldern. Stahl Eisen. 99 (1), 7–12.Google Scholar
Ward, N. B 1972 The exploration of certain features of tornado dynamics using a laboratory model. J. Atmos. Sci. 29 (6), 1194–1204.Google Scholar
Yih, C. S. 2007 Tornado-like flows. Phys. Fluids 19 (7), 076601.Google Scholar

Vogt et al. supplementary movie

Video sequences of the free surface at different force ratios corresponding to figure 4. The red LED inidcates the moment of the TMF spin-up.

Download Vogt et al. supplementary movie(Video)
Video 29.4 MB