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, Translation mode for the inner core
, Most unstable modes of convection with phase change boundary condition
,
Eigenmodes with non-penetrative top boundary, p.42 ,
Eigenmodes with flow-through top boundary, p.43 ,
, , p.44
, , p.44
, , p.45
, Neutral Rayleigh of several modes vs aspect ratio, flow-through at bottom boundary
, Neutral Rayleigh of several modes vs aspect ratio, flow-through at top boundary
, Neutral Rayleigh of several modes vs aspect ratio, flow-through at both boundaries
, Frame in a degree-one translation case
, , p.52
, , p.53
, Temperature fields and streamlines in (? ? , Ra/Ra c ) space, p.57
Temperature fields and streamlines in (? ? , ?) space, p.58 ,
Mean temperature vs Ra for various, p.59 ,
6 RMS velocity vs Ra for various, p.59 ,
,
, Temperature fields and streamlines in (? + , Ra/Ra c ) space, p.62
63 4.10 Mean temperature vs Ra for various, Temperature fields and streamlines in ,
,
, Temperature fields and streamlines in (? ± , Ra/Ra c ) space, p.68
Temperature fields and streamlines in (? ± , ?) space, p.69 ,
Idealized temperature field in the translation regime, p.70 ,
71 6.1 Temperature and composition reference profiles for the stability analysis 98 6.2 Growth time of the most unstable mode for the Earth, Mars, and the Moon ,
, Most unstable convection modes
, Destabilization timescale of several harmonics degree, p.108
, Compositional/thermal cases destabilization timescale ratio, p.109
, Growth time of the most unstable mode versus Stokes time, p.110
, Effect of the partition coefficient on the destabilization timescale, p.112
,
Dynamic topography at the boundaries ,
Instability growth rate ? as a function of Ra/Ra c, p.140 ,
A.3 Finite amplitude velocity in the translation mode, p.141 ,
142 A.5 Critical Rayleigh number and wavenumber as function of the phase change numbers ,
A.6 Variation of the maxima of profiles as a function of, p.147 ,
First unstable mode for three different values of, p.149 ,
Growth rate of deforming perturbation over a steady translating solution ,
, Range of wave numbers as function of the reduced Rayleigh number . 151 A.10 Maximum growth rate for a non-null k mode at the critical Rayleigh number for the onset of the translation mode, p.152
Heat flux coefficient as a function of the phase change numbers and Nusselt number as a function of Rayleigh number, p.155 ,
12 First unstable mode when only the bottom boundary is a phase change interface ,
, A.13 Critical Rayleigh number and wavenumber as function of the phase change number
Heat flux coefficient as a function of the bottom phase change number and Nusselt number as a function of Rayleigh number for different values of ? ? ,
, 16 Finite amplitude solution for ? ? = 10 ?2 , = 5.58 and a nonpenetrating boundary condition at the top
Velocity and temperature of translation mode, p.173 ,
, Convection modes with two phase change boundaries, p.174
175 B.4 Convection patterns with two phase change boundaries from a random noise, Thermal structure with two phase change boundaries ,
, Heat transfer efficiency with two phase change boundaries, p.178
, Convective patterns with one phase change boundary, p.180
Convection patterns with phase change at the bottom, p.181 ,
, Heat transfer efficiency with phase change at the bottom, p.182
187 List of Tables 5.1 Dimensionless parameters for the Top Magma Ocean evolution, vol.87, p.123 ,