Effects of a realistic mantle thermal conductivity on the patterns of 3-D convection

A physical model describing the temperature and pressure dependences of mantle thermal conductivity has recently been provided by A.M. Hofmeister [Science 283 (1999) 1699-1706]. We have studied numerically the influences of such a temperature- and pressure-dependent thermal conductivity on 3-D constant viscosity convection. A large aspect-ratio box of 4 x 4 x 1 has been taken for Rayleigh numbers greater than 10⁴ to 10⁶. The power-law index governing the phonon contribution to the thermal conductivity controls the style of convection. For silicates, the pattern of convection is quite different from that of constant conductivity, whereas the pattern of convection associated with conductivity of oxides is close to the case for constant conductivity. Both Boussinesq and extended-Boussinesq models with viscous and adiabatic heatings have been examined. Major effects of variable thermal conductivity on mantle convection are: (1) heating up of the lower mantle; (2) longer-wavelength Boussinesq convection; (3) shorter wavelength for extended-Boussinesq convection; (4) thick stable plumes with large plumeheads; (5) thicker thermal boundary layer of around 500 km at the base of the mantle. The contributions from the new terms due to the variable conductivity in the energy equation have magnitudes several times that of chondritic heating at the boundary layers. A large region of superdiabatic lower mantle with about a 400 to 600 K excess is caused by variable thermal conductivity. This finding has an interesting implication on the recent seismic finding of a lighter density in the deep portion of the lower mantle.