= Solution
Unsteady inertial <force density> scales as $\rho v/\tau$, whereas viscous <force density> scales as $\eta v/\lambda^2$. Using the preceding timescale gives
$$
\boxed{\frac{\text{unsteady inertia}}{\text{viscosity}}
\sim\frac{\rho\lambda^2}{\eta\tau}
\sim\frac{\rho^2g\lambda^3}{\eta^2}.}
$$
Convective <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.
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