84 



THEORY OF SEAKEEPING 



mended. The tank should be of rectangular cross sec- 

 tion with a good wave generator, so that regular waves 

 of low steepness progress without appreciable change of 

 form and amplitude. A good absorbing beach must be 

 pro\'ided so that progressive waves are not contaminated 

 by beach reflection. The wave generator should be pro- 

 grammed to make irregular waves with a spectrum not 

 too different from a typical sea spectrum. The wa^'e- 

 energy spectriun is to be measured at two or more sta- 

 tions in the part of the tank ^^'here the good conditions 

 called for above obtain. It can be expected that the 

 difference in the spectral energy at the different stations 

 will grow as the steepness of the generated wa\'es is in- 

 creased and as an increasing number of breaking crests 

 appears. It will be remembered that the rate of energy 

 dissipation in waves is low, and therefore high accuracy is 

 neces.sary in the experiments. These towing-tank experi- 

 ments, in which no transfer of energy from wind is 

 present, will provide valuable data for separation of the 

 wind-transferred and wave-dissipated energies in the 

 master project 7). 



13 Energy Dissipation in Irregular Waves. The re- 

 sults of project 12) obtained in long-crested waves 

 should be generalized to sbort-crested waves by means 

 of the data of project 9). 



14 Energy Transmission from Wind to Waves. None 

 of the heretofore published work on the transmission of 

 energy from wind to water has presented a complete 

 solution but each has been an advance in a certain direc- 

 tion. All of these can be listed, therefore, as good 

 directions of further research: The work of 



(a) Eckart, Section 4.1, and Phillips, Section 4.2, 

 based on the random fluctuations of air pressures in a 

 gusty wind. ]\Iore ofiservations on air turbulence are 

 needed and can be obtained from project 4). 



(b) Munk, Section 4.4, based on the air pressure as a 

 function of wa\'e form and the wind \'elocity at anemom- 

 eter height. Improvement of the pressure-distribution 

 function and introduction of wa\'e-facet velocity are sug- 

 gested. Longuet-Higgins' (1956, 1957) work will be 

 valuable in defining the facet velocity. 



(c) Miles, Section 4.5, based on the air pressure as a 

 function of wave form, but evaluated by the potential 

 solution for air flow possessing a \'elocity gradient. 

 Consideration should be given to variation of the veloc- 

 ity-gradient profile with location along the wave contour 

 in order to make the solution applicable to waves of sig- 

 nificant steepness. The shape of small, usually sharp- 

 crested, wavelets carried by larger wa\'es is go\'erned by 

 the algebraic difference between the gravity acceleration 

 and the acceleration of the large-wave motions. This 

 leads to expectation of steeper wa\'elets at the crests and 

 less steep ones in the hollows of the larger carrier waves. 

 This difference can be expected to be aggravated further 

 by the higher ambient air velocity over wave crests and 

 the reduced one over troughs. These changes of local 

 water-surface characteristics can be expected to affect the 

 roughness parameter and the velocity-gradient profile. 



These should be measured on rigid models in wind tunnels 

 and also in observations of large natural waves. 



15 Air-Velocity Profile Measurements. More meas- 

 urements of the air-velocity pnjfiles over waves are 

 needed for practical implementation of Miles-based proj- 

 ects. 



General Remarks on the Pruhlem of Wave-Energy Trans- 

 mission. It should not be assumed that only mathema- 

 tically complicated work such as Phillips' and Miles' is 

 \-aluable. Useful results can be expected at all le\^els of 

 simplicity or sophistication. Generally speaking, com- 

 plex solutions have to be limited to a narrow facet of the 

 broad problem. Simpler and cruder solutions, on the 

 other hand, can usually be expected to cover wider 

 ground and to lead sooner to usable (if less refined) results 

 because they are not o^■erburdened by details regarding 

 any one aspect of the problem. Although work on re- 

 fined and sophisticated solutions must lie piu'sued in or- 

 der to gain a more complete understanding of the phe- 

 nomena, a researcher (and his sponsor) must realize that 

 refinement in an isolated facet of a problem does not 

 necessarily lead to improvement in the over-all result. 

 Quite the contrary, it often upsets the balance obtained 

 in a cruder approach. Refined solutions of individual 

 aspects of a problem are expected to produce improved 

 results only after several aspects are cleared and the 

 broader problem is covered. Meantime, sufficient re- 

 search effort should also be applied to simpler and 

 broader approaches. 



16 Combined Theory of Wave Generation by Ran- 

 dom and Wave-Correlated Pressures. The three re- 

 search projects covered under 14) apply to several indi- 

 vidual aspects of the problem. Effort should be made 

 to formulate a theory of the energy transfer from wind 

 to water in which both the random atmospheric tur- 

 bulence and the effect of the wave shape on the air- 

 pressure distribution are considered. 



17 Simple Evaluation of the Wind-Energy Transfer. 

 A relatively simple e\-aluation of the energy transfer from 

 wind to wa\'es can probably be obtained bj' neglecting 

 the drag of waves of low steepness and considering only 

 the high drag coefficient of sharp-crested waves (Motz- 

 feld. Section 2.3; Johnson and Rice, Section 2.4) to- 

 gether with the distribution probability of these waves 

 and a suitable statistical definition of the mean facet 

 velocity. It should not be forgotten that Motzfeld's 

 data apply to long-crested waves, (project 2). Calcula- 

 tions can be made for typical wave spectra. 



18 Directional Spectrum of Wind-Generated Waves. 

 The work of Phillips, Section 4.2, should be extended to 

 provide a clear statement of the directional spectrum of 

 generated waves. Certain information on the direc- 

 tional distribution of waves was given in the work of 

 Eckart. 



19 A Combined Hydromechanic and Statistical In- 

 vestigation is needed to clarify the generalization to 

 short-crested waves of the energy transfer from wind 

 initially formulated for long-crested waves. Mathe- 

 matically, short-crested waves are described by super- 



