Parametrization of heat transport by non-Newtonian convection

Abstract

SUMMARY We study the heat transport e⁄ciency of the 2-D steady convection in a box (aspect ratio~1) with a power-law creep which may be important for mantle convection. Eiects of pressure- (depth) and temperature-dependent creep are also studied. To analyse the heat transport, we use the local Rayleigh (Ral) and Nusselt (Nul) numbers, which are de¢ned by the values characterizing each thermal boundary layer except the length scale. The commonly used de¢nition of the Rayleigh and Nusselt numbers is only useful when the top and bottom thermal boundary layers show similar behaviour. Our de¢nition has the advantage of treating each thermal boundary layer separately. By choosing an appropriate temperature drop and viscosity, we ¢nd that the Ral^Nul relation of non-Newtonian £uid is in good agreement with that of Newtonian convection with a constant viscosity for most cases. Generally, the viscosity weighted by the strain rate is an appropriate viscosity for the range of Rayleigh number (10 4 *10 7 ) studied. However, it appears that this weighting becomes unsuitable at higher Rayleigh numbers. Strongly temperature-dependentcreep