PANEL DISCUSSION-WAVE RESISTANCE 



Nonlinear and Viscous Effects in Wave Resistance 



J. N. Newman, Panel Chairman 

 Massachusetts Institute of Technology •; 



Cambridge, Massachusetts 02139 



INTRODUCTION 



In recent years there has been increasing evidence of the shortcomings in 

 existing techniques for predicting the wave resistance of surface ships. Theory, 

 as represented by the classical approach of Michell, and experiments carried 

 out with the Froude hypothesis, have been known to be in poor agreement, espe- 

 cially at low Froude numbers. But the main impact of recent investigations, and 

 particularly the direct experimental measurements of viscous and wave drag, 

 has been to suggest that the fault may rest with both the theoretical and experi- 

 mental techniques. This premise has now led to a broad questioning of the 

 classical assumptions that wave resistance could be considered entirely as an 

 inviscid mechanism and theoretically analyzed using the linearized theory of 

 water waves. Relaxing either assumption involves a compounding of the ana- 

 lytical complexities, so that progress has been slow, and we must not expect 

 any major breakthroughs to occur in the next few years, but sufficient advances 

 have recently been made that it is timely to discuss and report on our progress 

 at this time. 



The following brief summaries are categorized under the three headings 

 Nonlinear Effects, Viscous Effects, and Miscellaneous. Acknowledgment is due 

 to the participants in the panel discussion on wave resistance. Of necessity, 

 their contributions have been severely abbreviated in this report. 



NONLINEAR EFFECTS 



The classical Michell theory assumes that the ship hull is geometrically 

 thin, and the boundary conditions both on the hull and on the free surface are 

 linearized with only the leading (first) order terms retained. For many years 

 the relative importance of these two linearizations has been discussed, and 

 some investigations were aimed at the more tractable extension of including 

 nonlinear effects from the hull boundary condition. The work of Sizov (1961) has 

 stimulated several investigations of the complete second- order solution. These 

 have included the two-dimensional treatments of submerged cylinders by Tuck 

 (1965) and Salvesen (1966), and in three dimensions the analysis of the sub- 

 merged sphere by Kim (1968), the spheroid by Chey (1968), and the parabolic 

 strut by Eng (1968). All of these references contain actual calculations, and 

 in some cases experimental confirmation is included as well; the importance of 



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