The Unifying Role of Aspect Ratio In Cylindrical Models of Mantle Convection With Varying Degrees of Curvature

Abstract

SUMMARY A numerical model of 2-D convection rolls in a cylindrical annulus is used to examine the influence of variable roll dimensions at various degrees of curvature. Steady-roll dimensions may be characterized by either the aspect ratio, A (width:depth), or the angular extent of each roll, D [or equivalently, the angular order of the flow, l (=π/D)]. When varying the degree of curvature, either A or D may be held constant, but not both. At low Rayleigh numbers the critical Rayleigh number for the onset of convection is determined as a function of roll dimension and degree of curvature. At high Rayleigh numbers the Nusselt number and mean temperature in vigorously converting cylindrical shells are determined as functions of roll dimension and degree of curvature. It is demonstrated that comparisons between model results at different degrees of curvature (including the plane-layer limit) are most meaningful, at all roll dimensions, when A rather than D is held constant. Results from curvilinear models obtained here are strikingly similar to plane-layer results at the same aspect ratio.