Thermochemically driven convection in a rotating spherical shell

Abstract

S U M M A R YWe present a numerical study on convection in a rotating spherical shell that explores the influence of the two possible driving sources in planetary iron cores: temperature differences exceeding the adiabatic gradient and compositional differences that arise from the rejection of light elements at the inner core freezing front. Similarly, both effects play an important role in driving convection in Earth's outer core but their individual contribution remains uncertain. Dynamically, both components significantly differ in terms of their diffusion timescales since heat diffuses much faster than chemical elements. To investigate the influence of the driving mechanisms on the convective flow pattern, we consider different scenarios including the two extreme cases of purely thermally and purely compositionally driven convection and the more likely situation of a joint action of both sources. We solely focus on implications resulting from the given difference in the thermal and chemical diffusivity. For the present, we disregard the effects that might arise from the more realistic case of distinct thermal and chemical boundary conditions. We show that the driving mechanism strongly affects the resulting flow pattern, for example, differential rotation and global quantities such as mean energy and transport efficiencies. Additionally, we use a selected case for a specific comparison of two different codes based on a pseudospectral and a finite volume formulation, respectively.

The onset of thermo-compositional convection in rotating spherical shells

“…The case of purely thermal convection corresponds to α = 0, the case of purely compositional convection is obtained at α = π/2 and the typical co-density approach is corresponds to α = π/4 with Pr = Sc. We also remark that our parametrisation has several advantages over previous parametrisations such as the once proposed by Breuer et al (2010) and Trümper et al (2012). These authors considered a total Rayleigh number constructed simply as the sum of the thermal and compositional Rayleigh numbers.…”

Planetary Dynamos

“…Even possible interactions between thermal and compositional buoyancies have not yet been taken fully into account (Breuer et al, 2010;Busse, 2002b;Glatzmaier and Roberts, 1996;Simitev, 2011). Even possible interactions between thermal and compositional buoyancies have not yet been taken fully into account (Breuer et al, 2010;Busse, 2002b;Glatzmaier and Roberts, 1996;Simitev, 2011).…”

“…It must be kept in mind that Ganymede is the largest satellite in the solar system, which exceeds even Mercury in size. But see also the discussion by Breuer et al (2010). Even a capture of Ganymede into a resonance in its more recent history would not have supplied sufficient heating (Showman and Malhotra, 1999).…”

On the inhomogeneity of the transition surface layer of the solid core of the earth

“…A mathematical analysis [7] shows that the afore mentioned flows change significantly during the rota tion of the liquid core. In particular, due to the strong influence of the Coriolis force, additional convective flows arise.…”

“…Since is much larger than the velocity because of the diffi culties related to the filtration in the porous layer, the continuous material flows in the equatorial plane in Figs. 2 and 3 (the plots are drawn according to [7]) are not circular. Both heavy and light components are present here; however, the heavy component (iron) is 2 Aubert et al [5] indicated the leading role of the magnetic, vis cous, and gravitational torques, which also cause the weak rota tion of the solid core with respect to the lower mantle (by approximately 8° for 100 million years.…”