Numerical simulations of thermal convection in rapidly rotating spherical fluid shells

Details Numerical simulations of thermal convection in rapidly rotating spherical fluid shells Numerical simulations of thermal convection in rapidly rotating spherical fluid shells

Jan 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phdt........88s&link_type=abstract

Ph.D. Thesis California Univ., Los Angeles.

Computer Science

Numerical Analysis

Free Convection, Meridional Flow, Numerical Analysis, Numerical Stability, Spatial Resolution, Zonal Flow (Meteorology), Cylindrical Bodies, Geothermal Anomalies, Rotating Fluids, Spherical Shells

Scientific paper

Numerical simulations of thermal convection in rapidly rotating spherical shells of Boussinesq fluid were carried out with a nonlinear, three-dimensional, time-dependent spectral-transform code. The basic state is hydrostatic, spherically symmetric, and independent of time. The numerical methods, the numerical stability, and the adequacy of the spatial resolution were examined by a benchmarking study. A sequence of bifurcations from the onset of a steadily propagating convective state, to a periodic state, to a quasi-periodic state and thence a chaotic state was found. Convective solutions at each stage along the route to chaos were studied. The emphases are on the three dimensional and time-dependent convective structures and associated mean zonal flow. The spherical shell is heated from both below and within. The boundaries are isothermal and stress-free. The consequences of imposing a spatially varying temperature anomaly on the upper surface of a spherical shell on thermal convection in the shell was also explored. The spherical shell is heated from below and cooled from above. The lower boundary is isothermal and both boundaries are rigid and impermeable. The results show that the patterns and amplitudes of the convective motions and associated mean zonal and meridional flows depend largely on the pattern and amplitude of the imposed thermal anomaly. The purpose is to illustrate the influence of thermal conditions in the lower mantle on motions in the Earth's liquid outer core. Finally, numerical simulations at both high Taylor and Rayleigh numbers were carried out. The spherical shell is heated from below and cooled from above. The boundaries are isothermal and stress-free. Columnar rolls that are quasi-layered in cylindrical radius and associated banded mean zonal flow are obtained. The quasi-layered convective structure and the banded zonal wind are consequent upon both the high Taylor and Rayleigh numbers.

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