Gary T. Jarvis

Continental collisions in wide aspect ratio and high Rayleigh number two‐dimensional mantle convection models

Distinct rigidly moving oceanic and continental plates of finite thickness are incorporated into a two-dimensional numerical model of mantle convection. We investigate upper mantle convection in models having aspect ratios as great as 24 and compare our findings with the results of earlier studies which were limited to aspect ratio 4 models. In addition, we implement models of whole mantle flow by specifying high Rayleigh number convection and thinner nondimensional plates. We are thus able to compare the results of continental collision models which include similarly sized continents in the cases of upper and whole mantle convection. For each case considered we model a pair of identical continents being carried toward a site of plate convergence by underlying counterrotating mantle convection cells. Upon collision, the continents form a motionless, rigid, model supercontinent, while oceanic plate material continues to recycle through the mantle. Following the continental collision, our models of upper mantle convection exhibit a reorganization of the convective planform below the model supercontinent into a smaller wavelength mode which is unable to generate the net stress needed to break apart the continent; alternating compressive and tensile deviatoric stress associated with the small scale flow results in a low integrated stress. In contrast the large scale of whole mantle convection enables flow reversals to produce shear stresses acting in a common direction over extensive areas of the base of a continent, the integrated effect of which is capable of causing continental rifting. The conventional view of the role of thermal blanketing in continental rifting does not apply in the whole mantle convection scenario.

Mantle convection models of continental collision and breakup incorporating finite thickness plates

Abstract A two-dimensional numerical model has been developed to study mantle convection during continental collision and breakup. The model incorporates rigidly moving continental and oceanic plates with distinct thermal and mechanical properties, and finite thickness. We systematically investigate the influences of continental width, diffusivity, thickness and internal heating on continental collision and breakup. In addition, we consider the influence of different degrees of internal heating in the mantle. For each case considered we model a pair of identical continents being carried towards a site of plate convergence by underlying counter-rotating mantle convection cells. The continents collide at the mid-plane of the model to form a motionless, rigid, conducting supercontinent whereas oceanic plate material continues to recycle through the mantle. We find that changes in the mechanical boundary conditions at the upper surface are important factors in initiating flow reversals below the supercontinent. More generally, our findings, based on 144 models, are that the following factors favour the initiation of flow reversals below the supercontinent: wider continents, lower thermal diffusivity of continental plates, thicker plates and continental crustal heating. Furthermore, lower percentages of internal heating in the mantle are necessary to sustain and promote the subcontinental flow reversals in our models.

Mantle convection flow reversals due to continental collisions

Rigidly moving continental and oceanic plates with distinct thermal and mechanical properties, and finite thickness, are included in a two-dimensional numerical model of mantle convection. Model plates typically span six vertical increments of a finite difference mesh. We model two identical continents being carried towards each other by a pair of underlying, counter-rotating, mantle convection cells. Upon meeting at the model mid-plane the model continents form a motionless, rigid, conducting, “supercontinent” along a portion of the upper boundary, while the model oceanic plates continue to move and recycle through the mantle. The resulting changes in the mechanical boundary conditions at the upper surface prove to be important factors in facilitating flow reversal below the supercontinent, leading to a subsequent dispersal of the individual continental blocks. We find the following factors to favour the development of sustained flow reversal below our model supercontinent: wider continents, lower thermal diffusivity of continental plates, thicker plates and lower proportions of internal radiogenic heating within the mantle.

Effects of curvature, aspect ratio and plan form in two- and three-dimensional spherical models of thermal convection

Abstract Three-dimensional models of thermal convection in a spherical shell are presented for five different cases, each characterized by a unique ratio, f, of the radii of the inner and outer bounding surfaces. These solutions are compared to comparable two-dimensional solutions in axisymmetric spherical, cylindrical and Cartesian coordinates. All solutions were obtained with a Rayleigh number of 105, stress free, isothermal boundaries and no internal heating in a constant property Boussinesq fluid of infinite Prandtl number. Similarities and differences between three-dimensional and two-dimensional curvilinear models are discussed in terms of scales and stability of the flow patterns, mean radial temperature profiles and heat transport. It is shown that diagnostic statistics such as mean temperature and Nusselt number may be scaled from one degree of curvature to another for both three- and two-dimensional curvilinear models, provided the aspect ratio and plan form of the flow solutions are comparable....

A numerical study of thermal convection between rigid horizontal boundaries

Abstract A sequence of two-dimensional numerical models of Benard convection between rigid horizontal boundaries is presented. Steady solutions were obtained in the Rayleigh number range 5125.5≦R≦512550 or 3≦R/Rc ≦300 for constant property, and infinite Prandtl number, Boussinesq fluids with unit aspect ratios. At higher values of the Rayleigh number time-dependent flow was found to occur. The rigid boundary convection solutions are compared with the predictions of boundary layer theory (blt) for rigid boundaries, laboratory experiments (between rigid boundaries), previous numerical solutions at lower R, and with numerical solutions of convection at high Rayleigh number between free boundaries. The predicted variation of the Nusselt number, Nu, with Rayleigh number, agrees well with laboratory studies, and is in excellent agreement both with previous numerical studies in the lower range R/Rc ≦20, and with bit predictions at high R. Finally, the rigid boundary scheme is used to model both the stress distri...

Low-wavenumber signatures of time-dependent mantle convection

Abstract Spectral analysis is applied to idealized two-dimensional numerical models of mantle convection. Examining the spectral signature of known model temperature fields represents the forward problem corresponding to the inverse problem of inferring the unknown temperature field in the mantle from the spectral components of lateral heterogeneity obtained by seismic tomography. Previous two-dimensional Fourier analyses of steady convection cells indicate that, with current levels of resolution, tomographic techniques have a much better chance of detecting horizontal boundary layers than vertical plumes. From an examination of the shape of the spectral envelopes of the power spectrum of lateral heterogeneity at various depths in steady convection cells, it has been suggested that evidence for thermal boundary layers in the mantle may be contained in the published spectral amplitudes of lateral heterogeneity. This possibility is expanded on in the present study. Here we examine the effects, on the spectral signature of lateral heterogeneity, of averaging the model temperature field over vertical intervals of a few hundred kilometers, of large amounts of internal heating, of time-dependent flow and of aspect ratios greater than unity. The vertical averaging is an attempt to mimic the finite vertical resolution of tomographic inversions. The various complications considered here are found to render the distinction between the spectra of lateral heterogeneity, inside and outside of thermal boundary layers, less clear than in the simpler models considered previously. Nevertheless, the boundary layer spectra continue to contain significant information on the dominant scale of the model flow solutions.

Curvature, heat flow and normal stresses in two-dimensional models of mantle convection

Abstract Predictions of surface heat flow and normal stresses at the boundaries from two-dimensional finite-difference models of mantle convection in curvilinear coordinates are compared with similar predictions from plane layer models. Curvature effects are parametrized in terms of f , the ratio of the radii, or f a , the ratio of the areas, of the inner and outer bounding surfaces of the model solutions. Suites of numerical solutions with values of f ranging from 0.1 to 1.0 are presented for both cylindrical shell and axisymmetric spherical shell geometry. For either shell geometry it is shown that heat flow decreases with decreasing f according to a simple geometrical scaling factor which depends only on the ratio f . Results from the two shell geometries agree for common values of f a . In cylindrical geometry it is shown that decreasing f leads to an asymmetry in the distribution of normal stresses (which produce topography) at the upper surface relative to the lower surface. In the constant-viscosity models studied here, this asymmetry results in a maximum normal stress at the lower boundary which exceeds that at the upper boundary by about 60% for values of f appropriate to the whole mantle. Thus, curvature alone contributes to producing differences in the magnitude of stresses at the two bounding surfaces, although this contribution may be small compared with those of varying material properties, such as viscosity.

The period of the free core nutation: towards a dynamical basis for an ‘extra-flattening’ of the core-mantle boundary

Abstract Indirect observations and theoretical predictions for the period of the free core nutation (FCN) differ by anywhere from 15 to 30 days, and various effects have been invoked in attempts to explain this difference. The favored explanation remains as much as 5% departure in the flattening of the core-mantle boundary (CMB) from that of its hydrostatic reference figure. This 5% ‘extra-flattening’ of the CMB is not seen at the Earths surface, where the difference is only about 0.5%. In contrast to the a posteriori model adjustments used to determine this up to 5% value, and the kinematic results available from viscous flow modeling using the seismically determined lateral heterogeneity in density data, we consider this problem from the perspective of a forward-modeling dynamical study. More specifically, we investigate the related problem of flow-induced surface and CMB topography, arising from convection in the mantle. As such, we have completed a comparative and systematic study of relative surface and CMB topography resulting from numerical models of mantle convection. When effects resulting from boundary curvature are isolated, it appears that the magnitude of CMB topography produced is insufficient in producing a significant extra-flattening of the CMB. However, results concerning effects solely resulting from a depth-dependent mantle viscosity profile, indicate that this factor may indeed lead to enhanced topography at the CMB of the magnitude required to produce the extra-flattening there.