2021/05/17 by J. S. Knibbe, Tim Van Hoolst, Knibbe, Jurrien Sebastiaan +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Astro and Planetary Science #Earth and Planetary Astrophysics (astro-ph.EP) #FOS: Physical sciences #Geomagnetism and Paleomagnetism Studies #Geophysics (physics.geo-ph) #Planetary Science and Exploration
paper · pdf · doi:10.48550/arxiv.2105.07651
openalex publication_date 2021/05/17 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We present a new numerical scheme for one-dimensional conduction problems of\na spherical shell. The scheme adopts a solution of the conduction equation in\neach interval of the chosen discretization that is valid if the fluxes at\ninterval boundaries are constant in time. This piece-wise steady flux (PWSF)\nnumerical scheme is continuous and differentiable in the space domain, which is\nconvenient for implementing the numerical scheme in an energy-conserved thermal\nevolution model of a planetary core in which a conductive stratified layer\ndevelops below the core-mantle boundary when the heat flux is subadiabatic. The\ninfluence of a time-variable stratified region on the general evolution of the\nplanetary body is examined, in comparison to imposing an adiabatic temperature\nprofile for the core. By considering stratification in a planetary core where\nthe heat flux is subadiabatic, radial variations in the cooling rate are\naccounted for whereas otherwise the distribution of energy in the core is fixed\nby the imposed adiabat. During the growth of the thermally stratified region,\nthe deep part of the core cools more rapidly than the outer part of the core.\nTherefore, the inner core grows to a larger size and the temperature and heat\nflux at the core-mantle boundary are higher and larger, respectively, if a\nstratified region is considered. For the Earth, the implications are likely\nvery minor and can be neglected in thermal evolution studies that are not\nspecifically interested in the stratified region itself. For Mercury, these\nimplications are much larger. For example, the age of the inner core can be\nunderestimated by several billion years if thermal stratification is neglected.\nConsideration of thermal stratification in the core of Mercury also increases\nthe mantle temperature, leads to a larger heat flux into the lithosphere, and\nprolongs mantle convection.\n