SImulation details for Frasson et al. (2025) "Geomagnetic dipole stability and zonal flows controlled by mantle heat flux heterogeneities"

Input and output parameters of the simulations presented in Frasson et al. (2025).

Parameters:

• nu: Viscosity
• Omega: Rotation rate
• D: Width of the outer core
• eta: Magnetic diffusivity
• g_o: Acceleration of gravity at the top of the core
• F_i: Buoyancy flux at the bottom of the core
• kappa: Codensity diffusivity
• rho_0: Reference outer core density
• U: RMS flow amplitude
• B: RMS magnetic field amplitude

List of inputs:

• lmax: Maximum spherical harmonic degree
• mmax: Maximum spherical harmonic order
• Nr_OC: Number of nodal points in the radial direction within the outer core
• Nr_IC: Number of nodal points in the radial direction within the inner core
• dns: True for direct numerical simulation or False for hyperdiffusive treatment
• gprof: Radial profile of the acceleration of gravity
• bc_icb: Flow boundary condition at the ICB
• bc_cmb: Flow boundary condition at the CMB
• GC: Gravitational coupling
• CC: Inner Core conductivity
• rratio: Aspect ratio of the outer core
• E: Ekman number E=nu/(Omega*D^2)
• Pm: Magnetic Prandtl number Pm=nu/eta
• Ra: Rayleigh number Ra=g_o*F_i*D^2/(4*pi*kappa*nu^2*rho_0)
• Pr: Prandtl number Pr=nu/kappa
• pattern: Heterogeneous heat flux pattern at the top of the core
• dqo/qi: Peak-to-peak amplitude of the heat flux pattern normalized by the ICB heat flux

List of outputs:

• duration (dip. decay time): Duration of the simulation in dipole decay time unit
• f_dip: Amplitude of the magnetic dipole at the CMB (l=1) relative to the total magnetic field at the CMB
• E_mag: Magnetic energy
• E_kin: Kinetic energy
• M*_Za: Modified energy ratio (see Frasson et al. 2025, https://doi.org/10.1093/gji/ggae457)
• ell_u: Characteristic degree of the flow
• ell_b: Characteristic degree of the magnetic field
• Ro_l: Local Rossby number Ro_l = U*ell_u/(pi*Omega*D)
• Rm: Magnetic Reynolds number
• Elsasser: Elsasser number Elsasser=B^2/(rho_0*Omega*mu_0*eta)
• Ro_ml: Local magnetic Rossby number (see Soderlund et al. 2025, https://doi.org/10.1093/mnras/staf1081)
• f_ohm: Fraction of ohmic dissipation

Reference:

Frasson, T., Schaeffer, N., Nataf, H. C., & Labrosse, S. (2025). Geomagnetic dipole stability and zonal flows controlled by mantle heat flux heterogeneities. Geophysical Journal International, 240(3), 1481-1504.