The horizontal cell sizes of mantle convection induced by the effects of continental plates

Junko Matsumoto and Shin-ichi Takehiro (Faculty of Science, Kyushu University)

Abstract:

We investigate numerically and analytically the horizontal cell sizes of mantle convection induced by continental plates, especially those of larger horizontal dimensions than considered in previous numerical and experimental studies.

The numerical model we employ is a two-dimensional Boussinesq fluid model whose domain has an aspect ratio of 12. A continental plate is represented as a rectangular zero-velocity region near the model domain’s upper surface. Numerical time integrations are performed for cases in which the dimensionless horizontal extents of the plate are 4, 5, and 6 and the Rayleigh numbers are Ra=10⁴, 10⁵ and 10⁶. The Prandtl number and the thickness of the plate are fixed to 10 and 0.1, respectively. The calculations demonstrate that convection cells extending beyond the regions below and adjacent to the plate always develop, with upwelling occurring below the plate and downwelling outside it. However, the horizontal scales of the convection cells in the cases of Ra=10⁵ and 10⁶ are completely different from that in the case of Ra=10⁴. In the latter situation, the aspect ratio of the convection cell is nearly 1 and upwelling occurs below the margin of the plate, whereas when Ra=10⁵ and 10⁶, the convection cells are horizontally elongated and upwelling takes place below the center of the plate.

We estimate the difference in average temperature between points below and outside the continental plate by applying boundary-layer theory to the thermal convection problem. The velocity amplitude of the convection induced by the horizontal temperature difference is evaluated as a function of the Rayleigh number and the horizontal scale of the convection cell. By comparing this velocity amplitude with that of intrinsic thermal convection induced by the vertical temperature difference, the maximum horizontal size of the convection cell can be expressed as a function of the Rayleigh number. It is shown that convection cells with larger horizontal scales emerge for the larger Rayleigh numbers, a finding consistent with the results of previous numerical experiments.

The estimated maximum horizontal sizes of the convection cells are about 10 and 30 for Ra=10⁵ and 10⁶, respectively. These values suggest that convective upwelling of the convection cell that extends beyond the margin of a supercontinent can be generated beneath the center of the continent itself in the case of whole-mantle convection, while in the case of upper mantle convection the upwelling occurs beneath the continent’s margin.