Near-Boom Oil-Slick Instability Criterion in Viscous Flows and the Influence of Free-Surface Boundary Conditions

Abstract

Booms are often used to contain oil spills prior to various oil removal techniques. Under certain conditions, the oil droplets can leave the oil slick and enter the water. A simple balance of hydrodynamic forces on a droplet results in an instability criterion which determines whether the droplet will be swept past the boom or not. For viscous flows, it is shown here that the instability criterion consists of a term proportional to the pressure gradient along the boom, as in the potential-flow case, and a term that is inversely proportional to the Reynolds number, although the magnitude of this new term is found to be very small. The solution of viscous flow past an oil boom is obtained using the fractional-step method in a curvilinear coordinate system and the instability criterion is estimated. The influence of the approximate free-surface conditions, such as the rigid-lid no-slip, rigid-lid free-slip, and the exact free-surface condition, the instability criterion is also investigated. The different approximations of free-surface conditions are shown to influence the pressure distributions, thus resulting in different neutral stability curves.