Three-dimensional fully spectral numerical method for mantle convection with depth-dependent properties (Q1335597)

A semi-implicit fully spectral collocation method for the simulation of three-dimensional mantle convection with depth-dependent thermodynamic and transport properties is presented. The variable property Navier- Stokes equation expressed in terms of the primitive variable velocity and pressure is solved with the mass continuity and temperature equations. The periodic horizontal boundary conditions allow a Fourier expansion for the two horizontal directions. The stress-free, impermeable isothermal boundary conditions along with the depth-dependent coefficients are handled with a Chebyshev expansion in the vertical direction. Strongly time-dependent three-dimensional solutions up to a surface Rayleigh number of \(1 \times 10^ 7\) have been obtained. Strong upwellings, pulsating chaotically, are formed by the collective merging of cylindrical plumes.