WIT Press



Free (open access)


Volume 5 (2010), Issue 3



Page Range

242 - 253

Paper DOI



WIT Press




Labeled ‘the all-time breakthrough in geology’, plate tectonics brought a revolution in Earth Science 40 years ago. This theory links movements of lithospheric plates to processes taking place deep inside the Earth. The assumption of rigid surface plates enables one to describe the surface kinematics in terms of two components: the horizontal divergence (ridge-trench system) and the radial vorticity (transform faults and plate spin). The horizontal divergence and the radial vorticity are directly related to the poloidal (vertical motion around a lateral axis) and toroidal (lateral motion around a vertical axis) scalar fields, respectively. Surprisingly, kinetic energy in present-day plate motions is partitioned approximately equally between horizontal divergence (poloidal) and radial vorticity (toroidal) parts. I work with a time-dependant 3D spherical convective code where plates are coupled dynamically to the mantle. This method, which ensures the retrieval (to within ±10%) of the main global observables at the Earth’s surface (mean plate velocity, global heat flux and potential temperature under oceanic ridges), is unique and provides new opportunities to tackle questions such as the coupling between plates and the deeper mantle. I made experiments with different plate geometry on top of the 3D spherical code. When I plot the degree variance of the poloidal and toroidal components of the surface velocity field, only a geometry close the observed presentday geometry shows almost the same toroidal to poloidal ratio that exists at present-day. It suggests that only a geometry close to the one which is observed at present-day can reproduce an equipartition between the poloidal and toroidal components of plate motions. Further, O’Connell et al. (Toroidal-poloidal partitioning of lithospheric plate motions. Glacial Isostasy, Sea Level and Mantle Rheology, eds R. Sabadini & K. Lambeck, Kluwer Academic Publishers: Dordrecht, 1991) presume that, since the toroidal velocities are not involved in the heat transfer, the convective process develops a dynamical structure reducing the loss of kinetic energy, so that the partitioning essentially depends on the plate distribution. The constructal theory is covariant (the shape is changing in relation to the flow) as is plate tectonics. Plate motion reconstructions show that the geometry and plate motions are evolving slowly and probably maintain a lowest relative toroidal power through time. The constructal theory can be used to explain why the present-day confi guration of plates is optimal for the Earth’s mantle flow dynamics as the surface plate motions are indeed representative of the large-scale convective flow in the mantle.


plate tectonics, mantle convection, plate motion reconstruction, constructal theory