Oil spill under sea ice

An oil spill beneath sea ice is transported by a rising buoyant plume, lateral currents and the evolving ice--water interface. A slick can be spread, trapped in ridges, incorporated into growing ice or released through brine channels and melt ponds.

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.