cnAriKR 18 



48.1 

 48.2 



48.3 



48.4 

 48.5 

 48.6 



48. 



48.8 



48.9 



Data on Theoretical Surface Waves and 

 Ship Waves 



Purpose of This Chapter 160 



ThcoreticAl Wave Patterns on a Water 



Surface IGO 



Ilognor's Conlribiition to the Krlviii W:ivc 



Systom 161 



Summary of the Troohoidal-Wavc Theory . 161 

 Elevations and Sloix-.i of the Troclioidal Wave 1 63 

 Tabulated Data on Length, Period, Velocity, 



and Frequency of Deep-Water Trochoidal 



Waves 166 



Orbital Velocities for Trochoidal Deep-Water 



Waves 166 



Data on Steepness Ratios and Wave Heights 



for Design Purposes 169 



Formulas for Sinusoidal Waves 1 70 



Standard Simple and Complcc Waves for 



Design Purposes 171 



Dolincation of a Synthetic Three-Component 



Complex Sea 172 



Tal)ulat<>d O.'ita for .\rtual Winil Waves 175 



The Zimmcrinann Wave 176 



Wind-Wave Piittcni.s and Profiles liy Modern 



Methods 177 



Comparison Between Waves in Shallow- 

 Water and in Deep Water 180 



Shallow-Water Wave Data 181 



General Data for Miscellaneous Wave.f; The 



Tsunami or Earthquake Wave 181 



Bibliography of Historic Items and Refer- 

 ences on Geometric Waves 182 



Bibhography on Subsurface Waves .... 185 



48.1 Purpose of This Chapter. .\ brief de- 

 sfriptitjn of surface and subsurface waves in 

 liquid.s, illustrated with a number of diagrams, is 

 given in Chap. 9 of Volume I. Chap. 10 discusses 

 waves and wavemaking around schematic ship 

 forms. 



Although the general and detailed discussion of 

 wavegoing is embodied in Part 6 of Volume III 

 of the book, it is convenient for a reader who uses 

 the present volume for reference purposes to 

 have available here certain theoretical and 

 obser\'ed data on natural and ship waves. 



48.2 Theoretical Wave Patterns on a Water 

 Surface. The horizontal pattern of gravity 

 waves, both divergent and transverse, set up 

 abaft a pressure point moving at steady speed in 

 a straight line over the .surface of the water, is 

 known as the Kelvin wave system. It is dia- 

 grammed in Fig. lO.B of Sec. 10.5 of Volume I. 

 Many similar figures arc publLshod in standard 

 reference works and textbooks [S and P, 1943, 

 Figs. 30 and 37, p. 27|. The manner in which this 

 geometric pattern is built up analytically and 

 graphically is explained in Sec. 10.5 and illu.strated 

 in Figs. lO.C and lO.I). \. M. Hobb shows part 

 f)f this conslnictiiin (TX.'V, 1952, Figs. 3. '24, 3.25, 

 and 3.20, pp. 58 59]. However, it has developed, 

 OS part of the analytic work on the calculation of 



100 



the wavemaking resistance of ships, described in 

 Chap. 50, that there is a definite phase difference 

 between the divergent and the transverse waves 

 of the system developed by a traveling pressure 

 point. The transverse waves are shifted ahead 

 of the positions previously predicted for them, 

 so that a plan view of the crests in the revised 

 schematic system has the appearance of the 

 intersecting arcs of Fig. 48.A of Sec. 48.3, where 

 this matter is discu.ssed in greater detail. Actually, 

 as indicated by Fig. 10. E of Sec. 10.0, the trans- 

 verse wave crests in nature appear to be more 

 nearly straight than curved. Further, the crest 

 pattern for a given moving disturbance changes 

 with water dejjth and other factors. 



A ship represents a traveling group of many 

 ])ressure disturbances. It has an entrance water- 

 line slope ('k of .sensible amount and a (inite beam. 

 It often has reverse curvature in the waterlincs, 

 either forward or aft, or both, and sonic shoulders 

 forward of and abaft amidshi])s. 



ConsidcTable interference may be expecteti 

 between the diverging waves of the original or 

 the revised Kelvin point-pre.ssure .system and a 

 ship with its stem at the .same point. Indeed, 

 \V. Hovgimrd, D. W. Taylor, and others have 

 noted wide, anil as yet uni'xplained variali<jns in 

 the cusp-line angles with the theoretical value 



