Abstract: Plate reorganizations (changes in plate motion direction) are a poorly understood phenomena of plate tectonics. The most well known reorganization occurred at approximately 43 million years ago and was recorded by the bend in the Hawaiian-Emperor seamount chain, although plate reorganizations have also been documented in the Paleozoic based on continental paleomagnetic evidence. We have documented a mode of convection in 3D Cartesian mantle convection models with strong dynamic plates, where the direction and magnitude of plate motion driven by changing convection patterns, changes over a short interval of time. Changes in plate motion occur in nearly periodic to random time intervals depending on the size of the plates, the amount of internal heating, and other parameters. Analyzing this behavior, we find that internal heating is critical because plate reorganizations in the models are driven by the growth of a hot region of fluid in the relatively isolated core of the plate-scale flow pattern. These hot regions result from internal heating and drive flow opposing the plate-scale flow. Flow driven by the hot region decreases the shear tractions aligned with the direction of plate motion and results in a decrease in plate velocity. Eventually the tractions on the base of the plate, resulting from the flow generated by the hot buoyant region, weaken the plate scale flow leading to a reorganization event. Because this behavior is controlled by the growth of a hot region of fluid near the downwelling flow, we predict that there will be an increase in heat flow and shallowing of the ocean floor near downwellings before a plate reorganization occurs.
| Rapid changes in the direction of tectonic plate motion are well documented. The most familiar evidence for changes in plate motion is the bend in the Hawaiian-Emperor seamount chain shown at the right. In addition to this, there are other documented changes in plate motion. An explanation for changes in plate motion based on the dynamics of the convective system that drives plate motion has not been established. The numerical convection calculations presented here document a phenomenon that drives rapid reversals in plate motion in 2D models and rapid reorganizations in plate velocity in 3D models. This phenomenon occurs in a convective regime that requires 1) plates and 2) internal heating. | 
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We model an infinite Prandtl number, Bousinesq fluid with a depth-dependent Newtonian viscosity. The uniform velocity of tectonic plate interiors and the corresponding discontinuities in velocity at plate boundaries are emulated by prescribing surface boundary conditions on velocity in accordance with a force balance approach. The viscosity of the Earth's plates has been approximated by specifying a layer of high viscosity extending from the surface to a depth of roughly 150 km. The viscosity of the high viscosity plates is 1000 times greater than that of the underlying layer.
We specify a static plate geometry, however, each plate moves at a velocity such that the integrated shear stress due to thermally induced buoyancy is balanced by the integrated shear stress due to the specified motion of the plates (Gable et al., 1989, King et al., 1992). The integration is performed over the base of the viscous plates and results in a vanishing net force on each plate (force balance). During each model run, plate velocities dynamically adjust in order to satisfy the force balance criterion.
| The model on the right is characterized by single cell flow and periodic flow reversals. The non-dimensional temperature is color coded with red being the warmest temperature and blue being the coldest. Green represents a temperature of 0.5 Clearly, due to internal heat sources, most of the box is warmer than 0.5 Note the solid ornage region beneath the cold plate and downwelling. From these images, you can clearly follow as a) flow moves in a counter-clockwise direction,b) then slows, c) reverses to a clockwise direction and d) slows again as the warm region cuts off the cold downwelling and e) reverses back to counter clockwise and f) the cycle continues. A buildup of heat supplied by internal heat sources occurs along side the downwellings. The buoyancy associated with this heat buildup drives flow in the opposite direction to the plates. Incidentally, the time-series of the heat flow, rms velocities, or internal temperature are a simple function with only one or two harmonics and exactly periodic. | 
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| The temperature fields and surface velocity profiles on the right are taken from from an aspect ratio 12 calculation with a depth-dependent viscosity and uniformly distributed internal heat sources. The model has periodic (i.e, wrap around) boundary conditions and incorporated four plates with widths 4D, 4D, 2D, and 2D where D is the depth of the fluid. The Rayleigh numbers specified for the model are RaT =108 and RaH = 1.5 x 109. Panels a) and r) depict the entire aspect ratio 12 solution domain while panels b)-q) present only the right-hand portion of the solution space shown in a). Time series of the surface (red) and basal (green) heat flux are shown to the right of the temperature fields and include dashed horizontal lines that indicate the times corresponding to each of the temperature field panels. | 
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| The figure on the right shows the time series of the plate velocites (dashed lines VP1, VP2, VP3, and VP4) and the plate convergence velocities at the plate boundaries (solid lines VB12, VB23, VB34, VB41) the geometry of the plates is shown by the solid black lines at the top of the figure. The calculations are scaled such that the nondimensional velocity of 10,000 scales to approximately 10 cm/yr. The plate boundary convergence velocity is calculated by taking the difference in the velocity of the plate to the left of the boundary and the velocity of the plate to the right of the boundary. Positive values (shaded) in the plate boundary convergence velocity therefore correspond to convergent plate boundaries and negative values correspond to divergent plate boundaries. | 
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Author Contact
Carl W. Gable, MS F649 EES-5 Geoanalysis, Los Alamos National Lab, Los Alamos, NM 87545, United States, gable@lanl.gov
Julian P. Lowman, Department of Physical and Environmental Sciences, University of Toronto at Scarborough, Toronto, ON, M1C 1A4, Canada e-mail: lowman@utsc.utoronto.ca
Scott D. King, Dept. of Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN 47907, United States, sking@purdue.edu
This material is based upon work supported by the National Science Foundation under Grant No. 9726013.