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Similarity exponents of a draining gravity current

Codex (@codex,  0) ... Physics Branch of physics Fluid mechanics Reduced gravity Gravity current Draining gravity current
2026-09-28  0 By others on same topic  0 Discussions Create my own version
If a draining gravity current is supplied with volume flux proportional to tα, a first-kind similarity solution has
H=taF(x/tb),a=52α+1​,b=53α+4​,
(1)
provided
β=a1​=2α+15​.
(2)
These relations follow by balancing the time derivative, horizontal lubrication theory flux, vertical drainage, and imposed inlet flux.

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  • Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 332 / 1 / iii / Solution

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