Chapter 4

The McKenzie equations – from first principles


“I learned quite a lot of isotope geochemistry and petrology but what I didn’t know anything about was how melts were produced in the mantle and how they separated from their residues. I assumed that this was all thoroughly understood and that this was just my ignorance,” recalls McKenzie. A search of undergraduate textbooks showed that this was not the case. “I thought well, this is a branch of fluid mechanics, I understand fluid mechanics, why don’t I sit down and see whether I can see how to set up this problem from the conservation laws of mass and energy?” He derived a set of equations that described how melt can separate from its residue, laying the foundations for a new type of petrology; they are now known as the McKenzie Equations. “Fluid dynamicists like to call equations after people’s names, so that’s what it has become and I’m not at all happy with that.”

Notes & equations on the conservation of energy, from the working file for “The generation and compaction of partially molten rock” (1984).