(1) Department of Geophysics,
Faculty of Mathematics and Physics, Charles University, Prague, Czech
Republic
(2) Department of Geology and
Geophysics and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, MN USA
The issue concerning the chaoticity of thermal convection in a 2-D axisymmetrical spherical shell for the Boussinesq approximation with infinite Prandtl number has been examined. The only control parameter of this nonlinear dynamical system is the Rayleigh number Ra. We have investigated a wide range of regimes from very low up to ultra-high Rayleigh number convection (10^4 < Ra < 10^11). The very low Rayleigh number convection (Ra=1.7x10^4) is characterized by the existence of a stable steady-state; however for Ra~10^5 the convection becomes chaotic, which has been revealed by means of a 1-D wavelet analysis of the kinetic energy and surface heat flow time series. Moreover, the estimates of the attractor dimension yield surprisingly high value of about 15.
We have employed two-dimensional wavelets for examining in detail the temperature and vorticity fields. The power of the local wavelet analysis was employed to reveal the large-scale convection cells hidden in the vorticity fields and to obtain the fine details of ultra-high Rayleigh number convection (10^10).
As the Rayleigh number has been increased beyond 10^6 secondary instabilities developed in the upwellings from the interaction between the large-scale flow and the upwellings. These features have also been found in laboratory experiments (Whitehead instabilities). At Ra greater than 5.10^9, we have found a transition from whole mantle convection to more turbulent layered convection, where the plumes are restricted close to the boundary layers. It was necessary to use zooming methods and high resolution displays in addition to the 2-D wavelet analysis in the investigations of these ultra-high Rayleigh numbers.
The poster is available in JPG (850kB).
