Viscous Gravity Current — Lubrication Theory & Barenblatt Self-Similarity

Viscosity μ: 1.0
Initial volume Q: 1.0
Gravity g: 1.0
Speed: 1×
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Lubrication equation: ∂h/∂t = ∂/∂x[h³/(3μ) · ∂/∂x(ρg·h)]. The Barenblatt self-similar solution h(x,t) = t^(−1/5)·H(x/t^(1/5)) gives a spreading front ∝ t^(1/5) for fixed-volume release. Conservation of volume: ∫h dx = Q = const.