부산대학교 도서관

Rocky planets and large rocky satellites begin their evolution as relatively hot planetary bodies, both in the interior and on the surface. Heat released during planetary accretion is thought to have resulted in temperatures well in excess of the solidus of silicates, with radiogenic heating also playing a major role. In many cases this results in a partially molten mantle, known as a magma ocean. Both fully solid mantles and magma oceans are noted for their complex fluid dynamics, in particular involving the convection of fluids with strongly temperature-dependent viscosities. Because of the dominant surface cooling of planets, typical mantle modelling involves a mode of convection featuring a thick surface boundary layer known as the stagnant lid - a cool region with a correspondingly high viscosity. Recently the stagnant-lid model of mantle convection has been extended to the cooling of magma oceans. The viscosity of partially molten magma is most sensitive to temperature, pressure and solid fraction, which are in turn controlled by the phase diagram. However, in a well-mixed partial melt the solid fraction is itself a function of density and pressure. As the viscosity of a pure solid silicate is generally over 20 orders of magnitude in excess of that of a pure melt, it is the solid fraction that plays the most important role in the viscosity of a partial melt. The main effects of temperature and pressure on viscosity are through their control of melt fraction via the phase diagram. In turn, this large contrast in viscosity controls the convective heat flux that drives much of the development of planetary structure. In this thesis we investigate the evolution of the thickness of stagnant lids while taking the resulting pressure dependence of viscosity into account, and research the effects on other variables over the course of the early evolution of rocky planets. In the introduction, Chapter 1, we review the modelling of planetary lithospheres from a fluid-dynamical perspective, the observations of dichotomies in planetary crusts, and those of planetary magnetic fields. Then in Chapter 2 we investigate both the symmetric evolution and the subsequent stability of a pressure-dependent planetary stagnant lid to spherically asymmetric perturbations to its thickness. The close link between the thickness of the early stagnant lid of a small rocky planet and the thickness of its later crust suggests that this instability may play an important role in amplifying small initial perturbations to produce the large crustal dichotomy seen in some planetary bodies. The wider implications of this instability for the evolution of planets is then examined in Chapter 3. We find that our asymmetric instability is most relevant to Earth's Moon, while also comparing to Mars and Mercury, and we compare numerical growth rates and temperature profiles to the quasi-steady examples from our theory. In Chapter 4 we focus on a symmetric form of this instability together with the effects of changes to interior temperature on the core-mantle-boundary heat flux. Given the close relationship between the latter and the strength of the core dynamo, we deduce that under some circumstances a planet may undergo late increases to its magnetic field intensity, offering a potential explanation for the longevity of the Lunar core dynamo seen in the palaeomagnetic record. Finally, in Chapter 5, we conclude with some summary remarks on the implications of this work for the formation and evolution of planetary bodies, and describe some potential future directions.