Limitations to Length of Contained Oil Slicks

The drag forces exerted by a current passing beneath a contained oil slick cause it to thicken in the direction of the flow. In rivers and channels of finite depth this process cannot continue indefinitely and ultimately, if the slick is of sufficient length, an instability develops at the oil-water interface making the retention of more oil impossible. A theory is developed which enables the ultimate or critical length, volume, and profile of a contained oil slick to be expressed as a nondimensional function of the Froude number of the river flow and interfacial and boundary friction coefficients. Laboratory experiments were performed which verify the dynamics of the theoretical model and enable magnitudes of the interfacial friction coefficient to be calculated. The interfacial stress is markedly increased if waves develop at the interface.