**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.