Unsteady Radial Flow of Oil Being Discharged from a Source on the Ocean

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Abstract
SUMMARY The problem considered is that of calculating the uncoupled stratified flow associated with a suddenly initiated and uniformly sustained source of mass flux and/or energy flux. A solution is constructed from the critical flow conditions using the Method of Characteristics. Such a solution provides maximum discharge for given head. It is remarked that this solution tends towards a steady state defined simply by constant energy head. A trial calculation suggests that this steady state solution can be employed for finite time, to a good approximation. The approximate solution then consists of a centred simple wave extending from the line r=r0 where r0 is the radius at which the flow becomes critical for given mass and energy flux, to a line , where λ is a relative density of the oil and h0 is the critical depth of the oil layer.

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