A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle

Gravitational braking of inner‐core rotation in geodynamo simulations

“…Here we examine the combined effects of gravitational locking and viscous deformation on the rate of inner-core rotation using the geodynamo model of Glatzmaier and Roberts [1996a]. We show that the predicted rotation rate is strongly dependent on both the amplitude of the gravitational force and the time scale for viscous adjustment of the inner core.…”

Earth's dynamo limit of predictability

“…Appropriate geodynamo simulation codes have however been available for a little more than a decade [Glatzmaier and Roberts, 1995], leading to substantial progress in our understanding of the physical mechanisms at work [Christensen and Wicht, 2007] and of what may be responsible for the current decrease of the main field [Hulot et al, 2002]. This prompted us to investigate the finite limit of predictability of such dynamos, taking advantage of the now relatively accessible CPU time those codes require to run.…”

A comparison of high-order time integrators for thermal convection in rotating spherical shells

“…A LU factorization requires the storage of block matrices with a memory size O(N 2 r (L−m+1) 2 ) for each m = 0, · · · , L, due to the change of the inner block structure during the Gaussian elimination. Therefore, the total amount of memory needed is cubic in the spherical harmonic truncation parameter L. The storage of these matrices becomes prohibitive for high resolutions when dealing with direct solvers [14,15]. However it will be seen that matrix-free methods based on Krylov techniques [23], GMRES [24] in our case, can be used efficiently, to solve the block-tridiagonal linear systems with the same memory requirements as in the Q-explicit case.…”

“…For time-integration, some authors [12,2,13], among others, use semiimplicit integration methods, namely, they treat the linear terms (except the Coriolis term) implicitly with a Crank-Nicholson scheme, and the non-linear and the Coriolis terms explicitly with an Adams-Bashforth method [14]. In [2], a mixed Euler and integrating factor technique is also considered.…”

“…At high rotation rates, though, when the Coriolis force dominates over the viscous forces, stability considerations lead to extremely small time steps. To avoid this situation, the Coriolis term can be treated implicitly [14,15]. Then the equations for a given spherical harmonic of order m are coupled for all degrees l. This implies that a large block-banded linear system has to be solved for each order m. As it was described in [15], solving them by means of direct factorization methods becomes prohibitive if relatively high resolutions are employed.…”