Abstract
The wake left directly behind a moving ship is composed of bubbles and foam, viscous wake and propeller wake. Two regions can be clearly distinguished in the wake; the near wake and the far wake. In the near wake, there is a rapid decay of these features. In the far wake the variations are relatively gradual. The bubbles and foam rise to the surface bringing with them surfactants and dragging the water upwards. The water encounters the surface and deflects, carrying the surfactants across the wake. The surfactants are known to damp out high frequency surface waves, which makes for easy detection of ship trails from satellites. It is thus of interest to calculate the velocities of the diverted flow on the surface to understand the surfactant distribution.
The analogy of a two dimensional air bubble plume is applied on a vertical section of the wake. Away from the surface self similar solutions are obtained by numerical integration. Close to the surface, streamfunction analysis is used with a rigid surface and a nonlinear Poisson’s equation is solved numerically on a uniform grid. These solutions are then matched and crosswake velocities are estimated. This analogy has not been previously applied to a ship wake. Studies of plumes in the past have been motivated by other applications. Underwater blowouts are known to occur when drilling for oil in the sea. Plume analysis has been used to predict oil spreading and oil layer thickness. Artificial air bubble plumes have also been used to prevent ice formation, for mixing in water quality control, as pneumatic breakwaters and as barriers to prevent salt water intrusion in locks by creating a wall of rising air bubbles.