SECOND-ORDER WAVE THEORY FOR 

 SUBMERGED TWO-DIMENSIONAL BODIES 



Nils Salvesen 



University of Michigan 



Ann Arbor, Michigan 



{now at Naval Ship Research and Development Center 



Washington, D.C.) 



ABSTRACT 



The main object of this work has been to investigate the importance of 

 nonlinear free-surface effects on flow past submerged two-dinnensional 

 bodies. For a foil-shaped body the surface waves and the wave resist- 

 ance have been obtained both experimentally and analytically, including 

 second-order effects. 



Second-order wave theory has previously only been applied to sub- 

 merged circular cylinders and only the wave resistance and the lift 

 have been computed correct to the second order. This work therefore 

 presents the first computations of wave profiles correct to the second 

 order in wave amplitude for free- surface flow past a body. It is also 

 the first time an experimental verification of the second-order wave 

 theory has been carried out. 



The wave profiles have been nneasured by a capacitance wire, and the 

 wave resistance data have been obtained by three techniques: (a) drag 

 measurements, (b) wave survey, accounting for second-order effects, 

 and (c) second-order wave theory. 



The work clearly proves the importance of the effect of nonlinearity at 

 the free surface. At low speeds the second-order theory predicts wave 

 heights several times the size given by the linear theory. 



The results show, for low and nnoderate speeds, amazingly good agree- 

 ment between second-order theory and experiments both for the wave 

 resistance and the wave elevations. Especially encouraging is the ex- 

 cellent agreement at the very low speed, where the difference between 

 linear and second-order theory is large. The theory gives less satis- 

 factory agreement with experiments at high speeds, however. 



Useful information and data are included on wave breaking for snnall 

 submergences. 



595 



