One limitation of most previous studies has been that the horizontal dimensions of the plates considered are from 1 to 4 with respect to the fluid depth. These values are too small given the true scales of typical continental plates and the mantle: the horizontal sizes of supercontinents are of the order of 20000 km, whereas the thickness of the entire mantle is 2900 km. Thus the horizontal dimensions of real continental plates with respect to the thickness of the fluid layer are 6-7. Previous studies have shown that an upwelling develops beneath the center of the plate. However, in the case of a horizontally extensive plate, upwelling under the center of the plate may be impeded because the associated large-scale convection cell may be resisted by shear stress in the vertical direction. An upwelling may therefore tend to appear near the margins of the plate, rather than beneath its centre, and the horizontal scale of the associated cells might be smaller than previously thought.

Due to the phase change in mantle materials at depths of ~670 km, it has been suggested by some authors that convective motion is restricted to the upper part of the mantle (e.g. Honda 1997). In that case, the horizontal size of the continental plates is even larger than in the case of whole-mantle convection: in relation to an upper mantle thickness of 670 km, the horizontal size of supercontinents is about 30, and that of the present-day Eurasian continent about 15.

Lowman and Jarvis (1996) investigated mantle convection with a horizontally extensive plate using numerical methods. They considered a plate with a horizontal size of 12 for upper mantle convection alone. Their results show that for Ra=255000 upper mantle convection, upwellings emerge near the margins of the plate rather than beneath its center. They did not consider other Rayleigh numbers, and only considered plates of horizontal dimension 4 in the case of whole-mantle convection.

In this study, we investigate the horizontal cell sizes of mantle convection induced by continental plates of larger horizontal dimension than considered in previous numerical studies and laboratory experiments. In the following sections, we describe the model configurations and governing equations and present the results of numerical experiments. By applying boundary-layer theory, we then estimate the temperatures beneath the plates, the velocity amplitude, and the horizontal cell sizes. The final section discusses the limitations of our study and its application to upwelling in the earth's mantle.

Figure 1: Mantle convection and a continental plate