Viscous mountain spreading over an underthrust plate
= Viscous mountain spreading over an underthrust plate
{title2=$q=Uh-\rho gh^3h_x/(3\mu)$}
For a Newtonian layer with density $\rho$, <dynamic viscosity> $\mu$, thickness $h$ and a plate moving at $U$, a stress-free roof and no-slip base give $q=Uh-\rho gh^3h_x/(3\mu)$. Zero net mountain-material <volume flux> produces $h^3=9\mu Ux/(\rho g)$ when the contact height vanishes. Very near its idealized contact line the slope violates the <lubrication approximation>.