SEAWAY 



89 



39 Directional Wave Spectrum Measurement From 

 Ships at Sea. Apparently no method of measuring tlie 

 directional wave spectrum on ships has been proposed 

 to date. Nevertheless, effort sliould he applied to this 

 problem. 



40 Energy Transport in Irregular Waves (Section 

 8.8). The static concept of the wave-energy spectra 

 may not be adequate in problems of the energy transfer 

 from wind to waves. Thought nuist be given to the 

 mathematical and physical conseciuences of the energy 

 transport by irregular waves. Defined with respect to 

 harmonic-wave components by the classical theory, the 

 energy-transjiort concept should be generalized by 

 statistical theory. The work suggested by this project 

 can be considered as a further development of Longuet- 

 Higgins' (19J)6, 1957) work with particular emphasis on 

 flow (or transjiort) of energy in \'arious directions. 



41 Waves of Extreme Steepness and Their Proper- 

 ties. In the analysis of danger(.)us ship stresses it is 

 important to know the ma.ximum steepness of ocean 

 waves of various lengths. A maximum height-to-length 

 ratio of 0.14 and a minimum inehuled angle of 120 deg 

 at the crest are indicated by classical theory (Section 3.2 

 of Appendix A) for simple gravity waves. A minimum 

 included angle of 90 deg is indicated (Taylor, 1953) for 

 standing waves. 



(o) Thefiretical research is needed to establish the 

 maximum steepness and the mean wave height for short- 

 crested irregular waves. Concei\ably, the interaction of 

 various wave trains may bring about the reduction of the 

 120 deg angle. This angle is reduced to 90 deg for 

 standing waves which are represented mathematically 

 by a summation of two simple wave trains. 



(6) Ship-stress analysis requires not only knowledge 

 of the wave steepness as a function of wave length but 

 also of the pressm-e distribution in waves. The methods 

 by which the limiting crest angles were determined in 

 simple gravity waves involved only local conditions and 

 not the general flow description. A project in evalua- 

 tion of pressure distributions in wa\'es of limiting steep- 

 ness is therefore reconimended both for long-crested and 

 for short-crested irregular waves. While the problem 

 may prove to be prohibitively difficult for sharp-crested 

 waves, the computations for Stokes' waves (Section 3.1 

 of Appendix A) are simple and will yield valuable data. 



(c) The spectral sea description is based on the linear 

 superposition of simple wave trains and, strictly speak- 

 ing, is valid only for very low waves. Development of a 

 nonlinear statistical wave description is needed to repre- 

 sent the waves approaching limiting steepness. This 

 project consists of: (i) the basic de\-elopment of nonlinear 

 methods and (ii) their application to typical sea spectra. 

 In defining the latter, Bowden's, Section 3.1 Umitation of 

 the wave steepness by the balance of the energy received 

 from wind and di.ssipated in waves and Phillips' (1958) 

 definition of sharp wave crests by the condition that 

 rj = —g may be useful. 



(d) Expressions for the wave slopes are available in the 

 statistical work of Pierson and Longuet-IIiggins. These, 



however, are based on the linear theory. A study of 

 storm-wave records (for instance, Darbyshire's, 1955) is 

 recommended in order to verify empirically the degree of 

 agreement lietwcen large wave slopes as observed and as 

 derived from linear spectra. Wave steepness appears to 

 be connected with wave age, c/U, so that small-scale 

 data, as in Cox and Munk's, Section 4.3 sun-glitter meas- 

 urements, are not applicable to the present project. It 

 must be based on full-.scale storm conditions. 



42 Shape of Wind-Driven Waves. The sliape of 

 wind-driven storm waves may l)e of significance in 

 evaluating the bending moments acting on ships in 

 waves. The increased steepness of leeward slopes can 

 be expected to cause appreciable increase in the bending 

 moments. Three subprojects are indicated here: 



(a) Efforts to formulate and solve the problem theo- 

 retically. 



(b) Empirical e\'aiuation of tlie increase of the ob- 

 served leeward slopes of storm waves over the slopes pre- 

 dicted from linear spectra. 



(c) Empirical modification of the descriptive spectnun 

 formulation (such as Voznessensky and Firsoff's, Section 

 6.6) to generate an unsymmetric wa\'e form. 



43 Restricted-Water Waves. Increa.sed steepness of 

 storm waves progressing into restricted waters (reduced 

 depth, channel constriction, head current) may cause 

 increase of ship stresses and is, in fact, suspected to be 

 the cause of certain ship failures. Theoretical and 

 empirical studies of the properties of these wa\'es are 

 desired. It is necessary to know the pressure-distribu- 

 tion pattern in these waves as well as their forms. The 

 increase of sea severity near steep shores (for instance 

 in the Bay of Biscay) is well known to mariners. It can 

 generally be attributed to the standing-wa\'e system 

 caused by wave reflections from shore, but a more thor- 

 ough quantitative investigatif)n of the wave properties 

 is needed. 



44 Natural and Ship-Wave Interaction. The inter- 

 action of ship-made waves with natural wind waves can 

 often lead to weird wave forms, excessive wave steepness 

 and dangerous surf-like breakers. Two particular cases 

 of interference-caused wa^'es can be cited: 



«) Interference of the following sea with the trans- 

 verse stern wa\'e of a ship. This may lead to the break- 

 ing of a large wave over a ship's stern (Alockel, 3- 

 1953). 



6) Interference of a ship's bow waves with obliciue or 

 beam seas. The interference breakers can often he seen 

 over a large distance in the directions of the oblique liow 

 and stern ship waves. This interference often increases 

 ship wetness and may be dangerous for a ship's super- 

 structure. A ship in a formation may be endangered by 

 the combined interference of its own and other ships' 

 waves with ocean waves. 



Theoretical and experimental work on the properties 

 of interference waves is recommended. This study can 

 be expected to lead to the development of operational 

 rules for increase of safety of fast (naval) ships operating 

 in formation in rough weather. 



