Landweber 



remains nearly constant, 



4, The assumption that three-dimensional boundary -layer 

 problems are best treated with equations In streamline coordinates. 



A stimulating article by Llghthlll [ l] on the fundamental 

 significance of vorticlty in a boundary layer initiated the development 

 of a proposed method for treating ship boundary -layer problems. 

 This will be presented in two sections; a first in which the vortex 

 sheet on the ship hull, which generates the ir rotational flow about it, 

 is determined; a second in which the vorticlty equations for a three- 

 dimensional boundary layer, In terms of a triply orthogonal coordi- 

 nate system, are derived. The significance of the first part Is that 

 it furnishes the Initial values for the second. 



So there will be no "review"; but It still seems desirable to 

 touch upon the ship boundary-layer treatments of Lin and Hall [ 2] , 

 Webster and Huang [ 3] , and Uberol [ 4] , and the contributions In the 

 theses of Pavamaul [ 5] , Chow [ 6] , and Tzou [ 7] • 



lU NATURE OF THE SHIP PROBLEM 



In comparison with other three-dlnaenslonal boundary-layer 

 problenas, that for the ship is much more complex because of the 

 presence of a free surface at which the body is moving partly im- 

 mersed. Some ship boundary-layer problems will now be described, 



1, The first step in a boundary -layer calculation, the deter- 

 mination of the irrotatlonal flow outside the boundary layer (the outer 

 flow) is a difficult problem. Solutions employing linearized free- 

 surface boundary conditions and thin- ship theory furnish inadequate 

 approximations. The development of more accurate methods of cal- 

 culating the irrotatlonal flow about ship forms is a current research 

 problem [ 8] . 



2, At Froude numbers sufficiently low so that the free sur- 

 face may be treated as a rigid plane, (zero-Froude-number case) , 

 the three-dimensional flow about the double model, obtained by 

 reflecting the immersed portion in this plane, is of considerable 

 Interest, Methods of computing the irrotatlonal flow for this case 

 are available [8, 9] . Calculation of the viscous drag for this case, 

 and its ratio to the frlctlonal resistance of a flat plate of the same 

 length, wetted area and Reynolds number, would yield the so-called 

 form factor of the hull form which is required in one method of 

 predicting ship resistance on the basis of model tests [ 4] . 



3, The three-dimensional boundary layer is very sensitive 

 to the shape of the bow. The nature of the boundary layer near the 

 forefoot, which determines whether or not bilge vortices will be 

 generated, can also be studied at zero Froude number. Bows 



450 



