 Similarity exponents of a draining gravity current

ID: similarity-exponents-of-a-draining-gravity-current

If a draining gravity current is supplied with volume flux proportional to

t^{α}

H = t^{a} F (x / t^{b}), a = \frac{2 α + 1}{5}, b = \frac{3 α + 4}{5},

provided

β = \frac{1}{a} = \frac{5}{2 α + 1} .

These relations follow by balancing the time derivative, horizontal lubrication theory flux, vertical drainage, and imposed inlet flux.

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