Convection Cells With Accumulating Crust: Models of Continent and Mantle Evolution

Abstract

Numerical calculations of two component cellular convection with a lighter component diffusing down from the top are a simple model of the convection of rocky planets with a crust. The crust either is mixed down, floats along the top as blobs (continents separated by ocean basins), or forms layers. The calculations are for very viscous fluid with density variations from temperature and the lighter component representing the crust. If variations are approximately the same size, the lighter component collects along the top into H‐shaped blobs/clusters that have a flat midsection with two lobes on each end. Elevations are calculated for a free upper surface and the shape resembles continent and ocean floor topography with level interiors and thickening (mountains) at the edges produced by sinking at the margins. Between each pair of clusters, thermal and concentration boundary layers resemble ocean basins with spreading centers. Convection is unsteady but introducing internal decay of the lighter concentration produces steady flow. Internal heating produces similar results along with periodic drifting and merging of blobs like some geological cycles. The fact that these features arise without phase changes or viscosity variation implies that blobs of continent‐like crust might be widely found on rocky planets.

Converging material with two bulges

“…As shown in figure 2, the double bulges appear within certain parameter ranges, and they change the simple bulge with one maximum to a clump with two bulges separated by a central region of relatively constant thickness. Whitehead (2023) has arguments about why this is an interesting first approximation for a simple continent with thickening (like mountains) at the margins next to subduction zones. A cold root under it and a uniform tabular interior are additional features of this model that are possessed by real continents.…”

“…It is useful to review the calculation for both figure 2 and other results (Whitehead 2023). First, the layer of lighter material along the top is supplied by downward diffusion at the top boundary of a compositional concentration in a numerical code for cellular convection.…”

“…Then, a Poisson equation solver operating on the curl of (3.2) is used to determine the vorticity, and then it operates on (3.4) to determine the streamfunction. The code to do this (in MATLAB) is easily simplified from the code in the supporting information of Whitehead (2023).…”

“…This would seem to be the principal balance for the formation of continents on the surface of the Earth: convergence of continental crusts by mantle convection balanced by the natural spreading of the lighter crust. Numerical studies had surprising new results (Whitehead 2023) whereby a single bulge of light fluid over a downwelling location splits in two. The fluid mechanics needed for the double bulges are the subject of this study.…”

“…Section 2 has a brief review of the convection study leading to figure 2 as reported previously (Whitehead 2023). The primary purpose of the review is to illustrate the physical meaning of the four governing parameters, although some motivating issues connected with continents and mantle convection are mentioned as well.…”