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Tectonic Geodynamics: Thermal Convection

The following movies show thermal convection in the infinite Prandl number, laminar flow limit as appropriate for the Earth’s mantle. The movies were produced with the finite element code Citcom by Moresi and Solomatov (1995) as modified by Allen McNamara. 

Figures 8.1a-d - Isoviscous, bottom heated models

The aspect ratio of the computational domain is four (4 x 1 , 2D), there is no internal heating, fixed thermal boundary conditions on the top and bottom (heating from below) and free slip along the boundaries. Ra is the Rayleigh number which fully describes system behavior for these examples.

 

Figure 8.1a Subplot depicts temperature contours with velocity fields and temperature profiles at Rayleigh number (R a) = 1 * 10 to the 5th power. Increasing R a values show finer convective patterns and sharper gradients.
Figure 8.1b Subplot depicts temperature contours with velocity fields and temperature profiles at Rayleigh number (R a) = 1 * 10 to the 6th power. Increasing R a values show finer convective patterns and sharper gradients.
Figure 8.1c Subplot depicts temperature contours with velocity fields and temperature profiles at Rayleigh number (R a) = 1 * 10 to the 7th power. Increasing R a values show finer convective patterns and sharper gradients.
Figure 8.1d Subplot depicts temperature contours with velocity fields and temperature profiles at Rayleigh number (R a) = 1 * 10 to the 8th power. Increasing R a values show finer convective patterns and sharper gradients.

Isoviscous, bottom-heated thermal convection for different Rayleigh numbers, Ra, as indicated. Graphs on the right show horizontally averaged temperatures, (罢虃), in terms of their temporal mean (line) and variation (whiskers, over a constant number of 25 snapshots). Thickness of top boundary layer estimate is indicated.

Figures 8.2a-c - Isoviscous, mixed and internal heating models

Fig. 8.2a Subplot depicts temperature contours, velocity fields, and temperature profiles. R a = 1 * 10 to the 7th power; H = 15. Increasing height (H) intensifies convection, altering patterns and reducing gradients.
Fig. 8.2b Subplot depicts temperature contours, velocity fields, and temperature profiles. R a = 1 * 10 to the 7th power; H = 30. Increasing height (H) intensifies convection, altering patterns and reducing gradients.
Fig. 8.2c Subplot depicts temperature contours, velocity fields, and temperature profiles. R a = 1 * 10 to the 7th power; H = 30; Qsub(CMB) = 0,. Graph shows limiting boundary flux alters patterns and reduces gradients.

Snapshots from mixed (a鈥揵, 膜 鈮� 0) and pure internal (c, QCMB = 0) heating, isoviscous thermal convection. See Fig. 8.1c for the purely bottom-heated cases.

Figures 8.4a-e - Temperature and depth-dependent viscosity

Fig. 8.4a Subplot 1 of 5 depicting mantle convection with varying parameters. Increasing R a and E values modify temperature contours and velocity fields. Higher H and eta m values introduce finer convection cells and sharper gradients.
Fig. 8.4b Subplot 2 of 5 depicting mantle convection with varying parameters. Increasing R a and E values modify temperature contours and velocity fields. Higher H and eta m values introduce finer convection cells and sharper gradients.
Fig. 8.4c Subplot 3 of 5 depicting mantle convection with varying parameters. Increasing R a and E values modify temperature contours and velocity fields. Higher H and eta m values introduce finer convection cells and sharper gradients.
Fig. 8.4d Subplot 4 of 5 depicting mantle convection with varying parameters. Increasing R a and E values modify temperature contours and velocity fields. Higher H and eta m values introduce finer convection cells and sharper gradients.
Fig. 8.4e Subplot 5 of 5 depicting mantle convection with varying parameters. Increasing R a and E values modify temperature contours and velocity fields. Higher H and eta m values introduce finer convection cells and sharper gradients.

Snapshots from temperature-dependent (E 鈮� 0), mixed heating (H 鈮� 0), thermal convection, where some models also have a viscosity jump of 畏lm = 50 at the upper/lower mantle equivalent depth. Effective Rayleigh numbers are Raeff ~ 107 for all, where Ra for d) and e) are adjusted for the viscosity jump. Compare with Figs. 8.1 and 8.2, but depth averages here also show mean viscosity, log10(畏). Note that in some regions, 罢虃  > 1 for c), since internal heating allows for temperatures larger than those imposed at the lower boundary.

Figures 8.7a-e - Effects of phase transitions

Fig. 8.7a Subplot 1 of 5 depicting convection patterns influenced by phase transitions. Variations in R a, density contrasts, and thermal parameters modify cell structures, flow intensity, and temperature profiles.
Fig. 8.7b Subplot 2 of 5 depicting convection patterns influenced by phase transitions. Variations in R a, density contrasts, and thermal parameters modify cell structures, flow intensity, and temperature profiles.
Fig. 8.7c Subplot 3 of 5 depicting convection patterns influenced by phase transitions. Variations in R a, density contrasts, and thermal parameters modify cell structures, flow intensity, and temperature profiles.
Fig. 8.7d Subplot 4 of 5 depicting convection patterns influenced by phase transitions. Variations in R a, density contrasts, and thermal parameters modify cell structures, flow intensity, and temperature profiles.
Fig. 8.7e Subplot 5 of 5 depicting convection patterns influenced by phase transitions. Variations in R a, density contrasts, and thermal parameters modify cell structures, flow intensity, and temperature profiles.

Snapshots from convection with simplified phase changes at 410 km and/or 660 km. Based on computations without phase transitions, Figs. 8.1 and 8.4, the nondimensionalized reference temperatures for the phase transitions are 罢虃 = 0.5 and 罢虃 = 0.72, for E = 0 and E = 3, respectively. The P parameters, eq. (8.17), are P410 = 0.033, P660 = 鈥�0.041, P660 = 鈥�0.061, P410 = 0.033/P660 = 鈥�0.061, and P660 = 鈥�0.061 for cases a)鈥揺), respectively.