Charaateristios of Ship Boundary Layers 



velocity profile , the cross-flow angle, and the shear-stress coefficient 

 are not in accord with these data. If the energy integral equation is 

 also used to obtain an auxiliary equation, then an additional assump- 

 tion concerning the dissipation coefficient comes into question. 



Two significant ship boundary-layer phenomena, the generation 

 of secondary flows and possibly of vortices at the bilges near the bow 

 and at a wave crest along the hull. Indicate that cross -flow angles 

 may become large, so that the small cross-flow assumption would be 

 inappropriate. The possibility that the cross-flow may change in 

 sense and that the velocity profiles may become S- shaped both at the 

 bow and along the wave profile on the hull must also be taken into 

 account. 



Lines of principal curvature are recommended as the basis of 

 the orthogonal coordinate system for treating ship boundary layers 

 because, in contrast with alternative choices, this system rennains 

 orthogonal even in the thick boundary layer at the stern, and because, 

 unlike the streannline coordinates, the former system does not change 

 as the draft, trim, and the Froude and Reynolds numbers are varied. 

 For this reason, equations for determining the lines of principal 

 curvature have been included. 



Since integral miethods seenn to be wedded to the use of stream- 

 line coordinates, the recommendation that these be replaced by the 

 lines of principcil curvature implies that a differential method must 

 be adopted. One such method, based on the work of Bradshaw, 

 Ferriss and Atwell [ 3l] for a two-dimensional boundary layer, has 

 been extended to the case of a three-dimensional surface by Nash [ 32] , 

 An alternative approach based on determining the vorticity in the 

 boundary layer, strongly promoted by Lighthill [ IJ , motivated the 

 derivations of the vorticity equations in principal-curvature coordi- 

 nates and the integral equations of a vortex sheet for irrotational 

 flow about a three-dimensional form. Considerable further develop- 

 ment is required for application of these vorticity equations to a tur- 

 bulent three-dimensional boundary layer. 



Lastly it should be remarked that presently we cannot deter- 

 mine the outer flow about a ship form with sufficient accuracy for 

 reliable boundary-layer calculations due to a combination of errors 

 due to linearization of the free-surface boundary conditions, approxi- 

 mate satisfaction of the hull boundary condition, and the effects of 

 viscosity on the wave making. In comparison with the outer-flow 

 approximation for the flow about a body without a free surface, the 

 effects of viscosity are experienced much farther upstream along the 

 body because of the phenomenon of interference between waves 

 generated near the bow and stern. Because of the strong interaction 

 between the outer flow and that in the boundary layer and wake, it 

 appears to be necessary to develop an iteration procedure, alter- 

 nating between these regions, which hopefully would converge to a 

 solution for the flow about a ship form. 



469 



