Ra. Trompert et U. Hansen, ON THE RAYLEIGH NUMBER DEPENDENCE OF CONVECTION WITH A STRONGLY TEMPERATURE-DEPENDENT VISCOSITY, Physics of fluids, 10(2), 1998, pp. 351-360
The strong dependence of the rheology of a fluid on temperature has a
great impact on the style of thermally driven convection. When the vis
cosity contrast is sufficiently large, the viscosity of the coldest fl
uid at the top of a bottom-heated box is so high that this fluid layer
becomes very stiff and a so-called cold ''stagnant lid'' develops on
top of a hot convecting layer. Studying this style of convection is re
levant for planetary mantles since the rheology of mantle material is
likely to be very strongly temperature dependent. In this paper, the R
ayleigh number dependence of stagnant-lid convection with a viscosity
contrast of 10(6) is studied numerically in two and three dimensions i
n wide Cartesian domains. Like in constant-viscosity cases, the convec
tion in the layer underneath the stagnant lid undergoes the typical tr
ansition from steady to time-dependent with the thinning of plumes and
with the appearance of boundary layer instabilities as the Rayleigh n
umber increases. A stagnant-lid style of convection was obtained in 2D
and 3D for all supercritical Rayleigh numbers considered and the inte
rior temperature appeared not to depend on the Rayleigh number. We hav
e compared our results with other theoretical and numerical results an
d we found a close agreement. (C) 1998 American Institute of Physics.