Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 344 / 2 / f

Inertia dominates viscosity whenequivalently when the imposed root-mean-square velocity gradient satisfies ${\tau }^{-1}\ll t_0^{-1}$. In the inertial-capillary regime,The corresponding Reynolds number isThe geometry is therefore not fixed as the stirring rate changes. Slower stirring permits much larger domains, and the growth of ${\Lambda }^2$ more than offsets the reduction of $U/\Lambda$. This is why the inertial regime occurs at low imposed velocity gradient in this self-adjusting coarsening problem.