Prof. Dr. Ulrich Hansen
Corrensstraße 24 48149 Münster
Tel.: +49 251 83-33590
Fax: +49 251 83-36100



The effect of inertia in Rayleigh-Bénard convection

Thermal convection is one of the dominant processes governing transport of mass and heat in geophysical systems. One example is the Earth´s outer core which builds the driving engine for the geodynamo. Other examples are atmospheric and oceanographic circulations and creeping flows in the viscous Earth´s mantle.

In thermal convection the importance of mechanical inertia and thus the strength of non-linearity in the momentum equations can be expressed by the Prandtl number in the sense that the importance of mechanical inertia increases with decreasing Prandtl number. The Prandtl number is a material parameter and measures the importance of diffusive transport of momentum relative to diffusive heat transport. Geophysical systems show a wide range of Prandtl numbers. For the Earth´s outer core, mainly consisting of molten iron, a Prandtl number between 0.01-1 is realistic. Water has a Prandtl number of ~10, whereas molten magmas have a Prandtl number around 100. Finally the Earth´s mantle can be characterized by a nearly infinite Prandtl number.

The aim of this study is to get a better understanding of how convective flows are affected by mechanical inertia. To do so I use a numerical model which describes buoyancy driven convective flows in a planar three-dimensional geometry, the so-called Rayleigh-Bénard configuration. Here the fluid is enclosed in a box which is heated from below and cooled from above. The only external force which acts on the fluid is buoyancy due to thermal expansion. I use this comparatively simple configuration because it is suitable for a better understanding of the problem first to try to isolate the effect under consideration from other influences, like complicated geometry, special boundary conditions or additional forces due to e.g. rotation.

Die Grafik "http://earth.uni-muenster.de/dyn/img/snap100.jpg" kann nicht angezeigt werden, weil sie Fehler enthält.

Snapshots of the temperature field illustrated by the temperature iso-surface for a non-dimensional value of T=0.6 (the temperature varies between 1 at the bottom and 0 at the top of the box) and temperature cross-sections, for the Prandtl numbers (a) Pr=0.025 and (b) Pr=100. At low Prandtl numbers (Pr=0.025) the iso-surface indicates that the thermal structure depends on a large-scale recircularisation cell with one warm up-welling near to a sidewall and one cold down-welling on the opposite wall. In the high Prandtl number case (Pr=100) the thermal flow pattern is characterized plume-like structures which are distributed over the whole box.

Impressum | © 2008 Institut für Geophysik
Prof. Dr. Ulrich Hansen
Corrensstraße 24
· 48149 Münster
Tel.: +49 251 83-33590 · Fax: +49 251 83-36100