Bow Waves and other Non-Linear Ship Wave Froblems 



and theoretical developments will give the answer to this question. 



The method presented here is applicable to other bow shapes, 

 like blunt round bows. In this latter case the bow drag appears at 

 higher order than in the completely blunt case. The extension to 

 other shapes , as well as to three-dimensional bodies is left for 

 future studies. 



IV. CONCLUSIONS 



Theoretical models of breaking wave inception and of a free- 

 surface bow drag have been derived for the case of a two-dimensional 

 gravity free -surface flow past a blunt body. In both cases the effects 

 are nonlinear and are related to the important role played by the 

 inertial term of the Bernoulli equation in the vicinity of the bow. 



The results are of the order of magnitude of those found by 

 Baba [ 1969] , but an improved verification has to be done by carrying 

 out two-dimensional experiments. The theory presented here may be 

 extended, with additional approximations, to three-dimensional flows. 



ACKNOWLEDGMENT 



The present work has been supported by the Office of Naval 

 Research under Contract No. Nonr-3349(00) , NR 062-266 with 

 HYDRONAUTICS, Incorporated. 



REFERENCES 



Baba, E. , "Study on Separation of Ship Resistance Components," 

 Mitsubishi Tech. Bui. No. 59, pp. 16, 1969. 



Carrier, F. G. , Krook, M. , and Pearson, C. E. , Functions of 

 a Complex Variable . McGraw-Hill, pp. 438, 1966. 



Dagan, G. , and Tulin, M. P. , "Bow Waves Before Blunt Ships," 



HYDRONAUTICS, Incorporated Technical Report 11 7- 14, 1969. 



Dagan, G. , and Tulin, M. P. , "The Free Surface Bow Drag of a 



Two- Dimensional Blunt Body," HYDRONAUTICS, Incorporated 

 Technical Report 117-17, 1970. 



Eggers, K. W. H. , "On Second Order Contributions to Ship Waves 

 and Wave Resistance," Proc. 6th Symp. of Naval Hydro- 

 dynamics, 1966. 



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