Viscous Gravity Current — Dam Break & Shallow Water Flow
Ritter (1892) exact dam-break solution vs. viscous gravity current spreading ~ t^(4/5)
Dam Break (Inviscid)
Initial height H₀ (m):
2.0
Dam position x₀ (m):
3.0
Time t (s):
0.5
Viscous Current
Volume V₀ (m²):
4.0
Viscosity ν (m²/s):
0.01
g' (reduced gravity m/s²):
5.0
Theory
Ritter dam-break (inviscid):
x
front
= x₀ + 2√(gH₀)·t
h(x,t) = (1/9g)(2√(gH₀) − (x−x₀)/t)²
Valid: x₀−√(gH₀)t ≤ x ≤ x₀+2√(gH₀)t
Viscous current (Huppert 1982):
x
N
(t) ~ (g'V₀³/ν)^(1/5) t^(4/5)
h(x) ~ (x
N
−x) parabolic nose