Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 4 1 1997 10.5194/npg-4-19-1997 http://www.nonlin-processes-geophys.net/4/19/1997/ http://www.nonlin-processes-geophys.net/4/19/1997/npg-4-19-1997.html http://www.nonlin-processes-geophys.net/4/19/1997/npg-4-19-1997.pdf 19 27 0000-00-00 The global characteristics of the three-dimensional thermal convection inside a spherical shell J. Arkani-Hamed Earth and Planetary Sciences, McGill University, Montreal, Quebec, Canada The Rayleigh number-Nusselt number, and the Rayleigh number-thermal boundary layer thickness relationships are determined for the three-dimensional convection in a spherical shell of constant physical parameters. Several models are considered with Rayleigh numbers ranging from 1.1 x 10<em>²</em> to 2.1 x 10<em>⁵</em> times the critical Rayleigh number. At lower Rayleigh numbers the Nusselt number of the three-dimensional convection is greater than that predicted from the boundary layer theory of a horizontal layer but agrees well with the results of an axisymmetric convection in a spherical shell. At high Rayleigh numbers of about 10^<em>5</em> times the critical value, which are the characteristics of the mantle convection in terrestrial planets, the Nusselt number of the three-dimensional convection is in good agreement with that of the boundary layer theory. At even higher Rayleigh numbers, the Nusselt number of the three-dimensional convection becomes less than those obtained from the boundary layer theory. The thicknesses of the thermal boundary layers of the spherical shell are not identical, unlike those of the horizontal layer. The inner thermal boundary is thinner than the outer one, by about 30- 40%. Also, the temperature drop across the inner boundary layer is greater than that across the outer boundary layer.