Viscous Gravity Current — Lubrication Theory

A dense fluid spreading under gravity on a surface. Lubrication theory: ∂h/∂t = (g/3ν)∂/∂x(h³∂h/∂x). Self-similar solution: radius ~ t^(1/2) (2D) or t^(1/3) (axisymmetric).

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Time: 0.00 Max h: 0.00 Nose radius: 0.00 Theory x_N ~ t^1/2