Browsing by Author "Weller, Matthew B."

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    Mixed heating velocity scaling input files
    (Rice University, 9/29/2020) Lenardic, Adrian; Seales, Johnny; Moore, William B.; Weller, Matthew B.; Earth, Environmental, and Planetary Sciences
    The input files were used to explore the effects of mixed heating on convective velocity scaling
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    Scaling relationships and physics for mixed heating convection in planetary interiors: Isoviscous spherical shells
    (Wiley, 2016) Weller, Matthew B.; Lenardic, Adrian; Moore, William B.; Lunar and Planetary Institute
    We use a suite of 3-D numerical experiments to test and expand 2-D planar isoviscous scaling relationships of Moore (2008) for mixed heating convection in spherical geometry mantles over a range of Rayleigh numbers (Ra). The internal temperature scaling of Moore (2008), when modified to account for spherical geometry, matches our experimental results to a high degree of fit. The heat flux through the boundary layers scale as a linear combination of internal (Q) and basal heating, and the modified theory predictions match our experimental results. Our results indicate that boundary layer thickness and surface heat flux are not controlled by a local boundary layer stability condition (in agreement with the results of Moore (2008)) and are instead strongly influenced by boundary layer interactions. Subadiabatic mantle temperature gradients, in spherical 3-D, are well described by a vertical velocity scaling based on discrete drips as opposed to a scaling based on coherent sinking sheets, which was found to describe 2-D planar results. Root-mean-square (RMS) velocities are asymptotic for both low Q and high Q, with a region of rapid adjustment between asymptotes for moderate Q. RMS velocities are highest in the low Q asymptote and decrease as internal heating is applied. The scaling laws derived by Moore (2008), and extended here, are robust and highlight the importance of differing boundary layer processes acting over variable Q and moderate Ra.
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    The energetics and convective vigor of mixed-mode heating: Velocity scalings and implications for the tectonics of exoplanets
    (Wiley, 2016) Weller, Matthew B.; Lenardic, Adrian
    The discovery of large terrestrial (~1 Earth mass (Me) to < 10 Me) extrasolar planets has prompted a debate as to the likelihood of plate tectonics on these planets. Canonical models assume classic basal heating scaling relationships remain valid for mixed heating systems with an appropriate internal temperature shift. Those scalings predict a rapid increase of convective velocities (Vrms) with increasing Rayleigh numbers (Ra) and non-dimensional heating rates (Q). To test this we conduct a sweep of 3-D numerical parameter space for mixed heating convection in isoviscous spherical shells. Our results show that while Vrms increases with increasing thermal Ra, it does so at a slower rate than predicted by bottom heated scaling relationships. Further, the Vrms decreases asymptotically with increasing Q. These results show that independent of specific rheologic assumptions (e.g., viscosity formulations, water effects, and lithosphere yielding), the differing energetics of mixed and basally heated systems can explain the discrepancy between different modeling groups. High-temperature, or young, planets with a large contribution from internal heating will operate in different scaling regimes compared to cooler-temperature, or older, planets that may have a larger relative contribution from basal heating. Thus, differences in predictions as to the likelihood of plate tectonics on exoplanets may well result from different models being more appropriate to different times in the thermal evolution of a terrestrial planet (as opposed to different rheologic assumptions as has often been assumed).