= Inertia criterion for an inclined viscous film
{title2=$UH^2/(\nu L)\ll1$}
For a film of thickness $H$, axial length $L\gg H$, and <velocity> $U$, the ratio of convective inertia to transverse viscous stress in <lubrication theory> is $UH^2/(\nu L)$. On a small incline of slope $\theta$, <lubrication gravity-current flux> gives $U\sim g\theta H^2/\nu$ when $H\ll\theta L$, and $U\sim gH^3/(\nu L)$ when $H\gg\theta L$. The respective criteria are $g\theta H^4/(\nu^2L)\ll1$ and $gH^5/(\nu^2L^2)\ll1$. Unsteady inertia also requires $H^2/(\nu T)\ll1$ if the evolution timescale $T$ is independent of $L/U$.
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