Past exam of the physics of the Earth as a Planet course of the University of Cambridge / 2014 / Paper 1 / 2 / b / Solution

Unsteady inertial force density scales as $\rho v/\tau$, whereas viscous force density scales as $\eta v/{\lambda }^2$. Using the preceding timescale givesConvective inertia has ratio $\rho v\lambda /\eta$. Since $v\sim h/\tau$, this is smaller by $h/\lambda$ for small relief. Thus the displayed estimate controls the larger inertial contribution in this model.