Simple scaling relations in geodynamics: the role of pressure in mantle convection and plume formation

Scaling relations are important in extrapolating laboratory experiments to the Earth's mantle. In planetary interiors, compression becomes an important parameter and it is useful to explore scallings that involve volume. I use simple volume scaling relations that allow one to extrapolate laboratory experiments and upper mantle behavior, in a thermodynamically self-consistent way, to predict lower mantle behavior. The relations are similar to the quasi-harmonic approximation. Slabs and plates have characteristic dimensions of hundreds of kilometers and time constants of 100 million years, but the volume scalings predict order of magnitude higher values in the deep mantle. The scaling relations imply that the deep mantle is a sluggish system with ancient features. They imply irreversible chemical stratification and do not favor the plume hypothesis.