A Simplified Model for the Interaction Between the Boundary Layer and Longitudinal Vortices

Abstract

This paper represents a simplified model of the flow in the boundary layer (B.L.)developing on ships with bilge vortices. The simplified flow model is a combination of the B.L. developing on a flat plate and the trailing vortex produced by the edge of sweptback wing. B.L. suction is applied to reduce the B.L. thickness to half its original value to simulate scale effect. The B.L. deformation due to the vortex effect is calculated assuming that the volocity components normal to the vortex line is due to the potential effect of the vertex and that the stream-wise component is constant on the same stream line. The calculated value are compared with experiments, and the results are summarized as: 1) The simplified flow model creates a similar velocity distribution to that which occurs around the stern of full ships. 2) The calculated velocity patern is similar to the measured one except near the vortex core. 3) The scale effect on the deformed B. L. and the flat plate B.L. is found to be different. This may be attributed to the rolling up of the B.L. and the existance of a secondary vortex which appears above the main one. Such secondary vortex may strongly affects the main vortex lateral position. 4) The asymptotic solution on the trailing vortex by Batchelor is found to be a good approximation to the vorticity diffusion, but its application to the velocity distribution on this flow model is not recommended.