Turbulence modelling of a lock-release oil slick

The motion of a lock-release oil slick as an immiscible two-fluid gravity current is numerically studied by a finite difference algorithm based on the Volume of fluid (VOF) method for the basic formulation and a rigid cover approximation for the open free surface. Detailed numerical simulation with careful model validation reveals the existence of turbulence and the adaptability of the renormalization group ( RNG) k - epsilon model for the Reynolds-stress closure in the case of the oil slick. The time evolution and spatial distribution of the mean velocity, turbulence kinetic energy and turbulent viscosity are characterized. The mechanism for the transition from an initial gravity- inertial phase to a second gravity-viscous phase is shown to be the relaminarization effect of the initially highly turbulent slick. Compared well with known theoretical analyses and experimental observations, the turbulence modeling results in self-similar spreading laws in terms of the fact that the oil slick passes through the initial gravity- inertial phase with the front speed decreasing as t (- 1/3) ( where t is the time measured from lock release) and the second gravity- viscous phase with the front speed decreasing as t (-5/8).