Inversion of two-dimensional numerical convection experiments for a fluid with a strongly temperature-dependent viscosity

2-D thermal convection numerical experiments are conducted for a fluid with an infinite Prandtl number, a strongly temperature-dependent viscosity, an d isothermal horizontal boundaries. The core Rayleigh number (Ra-(0) over b ar), determined with the temperature of the well-mixed interior, is in the range 5 x 10(5) < Ra ((0) over bar)< 2 x 10(7), and the ratio of the top to the bottom viscosity (Delta mu) can be as large as Delta mu = 10(6). Diffe rent convective regimes are possible, depending on the values of Ra-(0) ove r bar and Delta mu. This paper focuses on the conductive-lid regime, in whi ch convection is confined to a sublayer. First, a least-squares fit of more than 40 numerical experiments suggests that the temperature difference acr oss the lower thermal boundary layer (Delta T-1) depends mostly on the visc ous temperature scale (Delta T-v) defined by Davaille & Jaupart (1993), and slightly on the temperature difference across the fluid layer (Delta T): D elta T-1 = 1.43 Delta T-v - 0.03 Delta T. Second, a generalized non-linear inversion of the data does not support the assumptions that the temperature difference across the upper boundary layer is proportional to Delta T-v, a nd that isoviscous scaling laws can be used for describing heat Bur through the convective sublayer. Third, a generalized non-linear inversion of the data is carried out in order to avoid any assumptions on the parameters. Th is leads to the following heat flux scaling law: Nu = 3.8(Delta T-v/Delta T )1.63 Ra-(0) over bar(0.258), where the Nusselt number (Nu) is the non-dime nsional hear flux. This scaling law is different from that proposed by prev ious studies. It reproduces the data at better than 1 per cent and fits the results of previous numerical experiments very well (e.g. Christensen 1984 ). Finally, a thermal boundary layer analysis is performed. For a fluid hea ted from below, the upper and lower thermal boundary layers interact with o ne another, inducing a thermal erosion of the conductive lid. This study su ggests that the dynamics of convection is driven by the instability of the lower thermal boundary layer. Therefore, an alternative way to determine th e heat flux is to use the value of the lower thermal boundary layer Rayleig h number (Ra-delta). This value is not independent of Ra-(0) over bar, unli ke the case for an isoviscous fluid. A least-squares fit of the data leads to Ra-delta = 0.28Ra((0) over bar)(0.21). This law provides a very convenie nt way to model the thermal evolution of planetary mantles.