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, 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

N. .. Vs-ra-for-various-?-?,

, 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

N. .. Vs-ra-for-various-?-+,

, 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

.. .. Time,

A. , 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

A. , 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

A. , Heat flux coefficient as a function of the phase change numbers and Nusselt number as a function of Rayleigh number, p.155

A. , 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

A. , 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