J. Fluid Mech. (2003), vol. 478, pp. 287–298. c  2003 Cambridge University Press DOI: 10.1017/S0022112002003233 Printed in the United Kingdom 287 Laminar starting plumes in high-Prandtl-number fluids By EDOUARD KAMINSKI AND CLAUDE JAUPART Institut de Physique du Globe de Paris, Universit´ e Paris 7 – Denis Diderot, Paris, France (Received 25 April 2002 and in revised form 1 August 2002) Experimental studies of laminar axisymmetric starting plumes are performed to investigate the dependence of the flow on the Prandtl number, focusing on large Prandtl numbers. Thermal plumes are generated by a small electric heater in a glass tank filled with viscous oils. Prandtl numbers in the range of 7–10 4 were investigated. Experimental conditions are such that viscosity variations due to temperature differ- ences are negligible. Plumes ascend in two different regimes as a function of distance to source. At short distances, the plumes accelerate owing to the development of the viscous boundary layer. At distances larger than about five times the heater size, the ascent velocity is constant and increases as a function of the Prandtl number, as predicted by theory for steady plumes. This velocity is, within experimental error, proportional to the steady plume centreline velocity. 1. Introduction Thermal convection phenomena play a key role in many natural systems such as the atmosphere, the ocean, magma chambers and the Earth’s mantle. At one end of the spectrum, geological flows involve fluids with very large Prandtl numbers (larger than 10 3 for magmas and at least 10 23 for the Earth’s mantle) and are routinely studied in the limit of infinite Prandtl number. In this limit, inertial effects are neglected, but the validity of this approximation has not been thoroughly tested for laminar thermal plumes. Theory for steady laminar plumes is well-established. Scaling arguments indicate that the vertical velocity is constant (Batchelor 1954). Numerical results are available up to a Prandtl number of 10 (e.g. Fujii 1963; Brand & Lahey 1967; Worster 1986) and an asymptotic analysis for large Prandtl numbers may be found in Worster (1986). These analyses are valid for the plume stem far from the leading edge (the cap) and do not specify the cap behaviour. How the ascent velocity of a plume cap compares with that of the steady stem below is not known. As regards starting plumes, existing laboratory studies (Shlien 1976; Moses, Zocchi & Libchaber 1993) do not allow an assessment of the Prandtl number dependence. Coulliette & Loper (1995) found differences between their numerical calculations for very large, but finite, Prandtl number and those of Olson, Schubert & Anderson (1993) at infinite Prandtl number. One consequence is that it may not be possible to make quantitative comparisons between numerical models for infinite Prandtl number and laboratory experiments. Our initial motivation for the present work was to study various aspects of mantle plume dynamics in the laboratory. In a viscous oil with a Prandtl number of 10 3 , we found that starting plumes were much faster than allowed by the scaling law of Moses et al. (1993). This raised the question of how to extrapolate experimental results to