Mathematical simulation on the oil slick spreading and dispersion in nonuniform flow fields

The viscous fluid boundary layer equations were adopted to characterize the velocity distribution across the vertical section of the oil slick on moving water. The velocity profile was found to be the combination of linear and parabolic distribution. A numerical model including spreading and dispersion was developed to describe the oil slick's early movement in the open and ice-covered water. The flume test was conducted to determine the dispersion coefficients (K_x) and the effects of velocity and wave height on the slick's dispersion were also investigated. In the open water, K_x increased from 4.34 cm²/s to 20.08 cm²/s as the velocity changed from 3 cm/s to 12 cm/s. A coefficient β that characterized K_x fluctuated at 1.5 when wave heights were between 20 mm and 70 mm. Under ice, the slick didn't move until the velocity exceeded 6 cm/s and K_x increased from 2.69 cm²/s to 5.64 cm²/s as the velocity changed from 6 cm/s to 12 cm/s. β remained 0.4 when wave heights were between 20 mm and 60 mm. The model performed very well in predicting the slick's position and length during the gravitation-inertia phase for the two situations when relevant dispersion coefficients were input.