Viscous Gravity Current — Lubrication Theory

A viscous fluid spreading under gravity on a flat surface is governed by the thin-film (lubrication) equation: ∂h/∂t = (1/3μ)∇·(h³∇p) where p = ρgh. The Huppert (1982) similarity solution gives nose position x_N ∝ t^(1/5) for constant volume.

1.0
1.0
2.0