= Ice-floe oil painting fraction
{title2=$\min\{1,Q/(dvh)\}$}
If a <buoyant plume> of diameter $d$ supplies oil at volume rate $Q$ to an <ice floe> moving at speed $v$, the plume sweeps area $dv$ per unit time. Retaining a layer of depth $h$ over that area would require volume rate $dvh$, so <conservation of mass> gives the painted fraction $\min\{1,Q/(dvh)\}$. Discontinuous painting starts when $v>Q/(dh)$. This estimate assumes all arriving oil is retained and a constant track width equal to the plume diameter; the plume's circular cross-sectional area does not enter the swept-area rate.
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