An understanding of the mechanism of mixing in highly viscous
convecting fluids is of crucial importance in explaining the observed
geochemically heterogeneous nature of the Earth's mantle. Using
constant viscosity numerical experiments, we describe the mixing
mechanism of time-dependent Rayleigh-Benard convection in a
three-dimensional rectangular container. Mixing is observed by
following the positions of passive tracers advected by the flow. The
major mixing mechanisms may be described in terms of the within-cell
mixing and the cross-cell mixing. The toroidal flow structure
previously observed in steady-state 3D convection systems is perturbed
by boundary layer instabilities in the time-dependent experiments, but
this toroidal flow structure allows a very efficient exchange of mass
between the boundary layers and the core of the convection cell even in
the absence of time-dependence. In similar 2D experiments, exchange of
mass between boundary layers and core of the convection cell is
entirely effected by the boundary layer instabilities. Mixing between
neighbouring cells appears much slower in 3D than in similar 2D
experiments, perhaps because the 3D cell structure is more stable
relative to the boundary layer instabilities. The inferred mixing rates
are observed to be relatively insensitive to initial tracer location,
but the timescale for mixing, tm, decreases with increasing Rayleigh
number (t_m goes approximately as Ra**(-3/2)). The timescale of mixing
is an important constraint on the large scale structure of the Earth,
because large-scale geochemical heterogeneities persist to the present
day, implying that the mantle is not well mixed.
Click on the image to watch an 1.1MB Mpeg-Movie. The movie shows
mixing in 3D time-dependent convection. The position of the hot
upwellings is indicateded by the temperature isosurface. The red patch
consists of 60x60x10 passive tracer.
This mpeg movie shows thermal convection at a Rayleigh number of 8*10**6. The temperature isosurfaces are for the nondimensional temperatures T=0.3 (blue) and T=0.7 (yellow).
The Dependence of the Style of Thermal Convection on the Prandtl Number
All the above visualisations have been created by our home-grown software 'isovis'.
Some visualizations from spherical calculations:
I also have some hypertext documentation, mostly on programing
issues, available which you can find here.
© 2003 Joerg Schmalzl All rights reserved.
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