Experiments with a numerical model related to mantle convection: boundary layer behaviour of small- and large scale flows

For studying principle physical mechanisms relevant to mantle convection a 2-dimensional finite element model for steady state flows has been developed. A non-conforming element approach for the computation of streamfunctions and an upwind corrected scheme for solving the heat transport equation have been used. This study concentrates on the discussion of boundary layer behaviour of convective flows with constant material properties. Local mesh refinement within the boundary layers is shown to be an efficient method for determining boundary layer parameters, in particular the Nusselt number Nu. The numerical scheme allows steady state solutions to be generated for elongated convection cells without imposing stabilizing measures like a constant surface velocity (up to an aspect ratio of λ = 5 in this study). Experiments have been carried out in the range of 0.3 < λ < 5 for Rayleigh numbers 10 ⁴ < Ra < 10 ⁷. The mean surface velocity ( overlineu), boundary layer thickness ( overlineδ) and Nu deviate appreciably from the predictions of the classical boundary layer theory if flows with λ ≲ 1.8 are simulated whereas good correspondence is obtained for λ around unity. We conclude that a better agreement exists between theoretical expectation and numerically derived results for the parameter combinations Nu· overlineδ and overlineu· overlineδ² than for the individual parameters.