The dynamics of an insulating plate over a thermally convecting fluid and its implication for continent movement over convective mantle

Abstract

Continents exert a thermal blanket effect to the mantle underneath by locally accumulating heat and modifying the flow structures, which in turn affects continent motion. This dynamic feedback is studied numerically with a simplified model of an insulating plate over a thermally convecting fluid with infinite Prandtl number at Rayleigh numbers of the order of $10^{6}$. Several plate–fluid coupling modes are revealed as the plate size varies. In particular, small plates show long durations of stagnancy over cold downwellings. Between long stagnancies, bursts of velocity are observed when the plate rides on a single convection cell. As plate size increases, the coupled system transitions to another type of short-lived stagnancy, in which case hot plumes develop underneath. For an even larger plate, a unidirectional moving mode emerges as the plate modifies impeding flow structures it encounters while maintaining a single convection cell underneath. These identified modes are reminiscent of some real cases of continent–mantle coupling. Results show that the capability of a plate to overcome impeding flow structures increases with plate size, Rayleigh number and intensity of internal heating. Compared to cases with a fixed plate, cases with a freely drifting plate are associated with higher Nusselt number and more convection cells within the flow domain.

An insulating plate drifting over a thermally convecting fluid: the effect of plate size on plate motion, coupling modes and flow structure

“…The existence of this convection cell was further confirmed in the three-dimensional (3-D) geometry in the recent numerical simulation results of Mao et al. (2019). Moreover, these recent results reveal three different plate--fluid coupling modes in both 2-D and 3-D geometries as the plate size varies.…”

“…Moreover, the present study adopts a Rayleigh number of 5 × 10 7 , much higher than the value of 10 6 adopted in the study of Mao et al. (2019). Although much more time consuming for the numerical simulation, the present Rayleigh number is more consistent with the value generally attributed to the Earth, which is ~10 7 –10 9 (Whitehead & Behn 2015).…”

“…Numerical simulations using dynamically determined boundary conditions provide answers to some of the above questions (e.g. Gurnis 1988; Zhong & Gurnis 1993; Phillips & Bunge 2005; Whitehead & Behn 2015; Mao, Zhong & Zhang 2019). Rather than using water as the convecting fluid as in the laboratory experiments, these numerical simulations assume an infinite Prandtl number for a better approximation to the very large Prandtl number (~10 23 ) of the Earth.…”

“…On its way, the plate modifies the impeding flow it encounters and maintains a single convection cell underneath it by forming new hot upwelling near its trailing edge (Mao et al. 2019). These results provide a more complete picture for the possible plate--fluid interaction.…”

“…Despite the revelation of three different modes (Mao et al. 2019), the transition to the UMM lacks quantification and theoretical explanation. Can the critical plate size for the UMM be predicted?…”