SEAWAY 



83 



roiitaniination by reflections and by water shallowness at 

 the end of the fetch. The need for a complete air-flow 

 description (velocity gradient and turbulence) at each 

 station must again be emphasized. Measurements of 

 water turbulence and mean drift \-elocities are also de- 

 sirable. 



5 Manual of Applied Boundary Layer and Turbulence 

 Theories. It is unlikely that either practical oceanog- 

 raphers or naval architects will become fully conversant 

 with all aspects of turbulence or boundary-layer theory. 

 It is desiral)le that a brief and simple exposition of these 

 theories be prepared. The primary oljjectives of such 

 exposition are to further intelligent planning of wave- 

 propagation experiments and to guide the analysis of 

 observed results (not the development of advanced 

 theories). Only relevant sections of the basic theories 

 needed in handling practical jirdblenis are to l)e discussed. 



6 Boundary Layer Over Waves. Effort should be 

 applied to establish air boundary-layer characteristics 

 over sea waves of different types. The sea types can 

 probably be roughly characterized by ///X and c/U ra- 

 tios, more completely by Voznessensky and Firsoff's 

 spectrum and most completely by the actual spectrum of 

 the measured wa\es. The project may consist of a sur- 

 vey of published data (further expanding the work of 

 Ellison, 1956) as well as analyses of the tlata of projects 

 suggested under 3) and 4) (refer to sections 2.7, 4.2 and 

 4.5). 



7 Energy Dissipation in Waves. A poor understand- 

 ing of the mechanism of energy dissipation in waves is an 

 outstanding obstacle to development of the theory of 

 wave growth under action of the wind. Two basic parts 

 of this mechanism appear to be: (a) P^nergy dissipation 

 by internal friction, and (6) energj' dissipation in wave- 

 breaking. The first was ciuantitatively, although quite 

 inadequately, investigated in the classical theory (Ap- 

 pendix A, Section 4.4 and as described in Sections 3 and 

 3.1). The second appears to exist now merely as an 

 idea. The whole subject is complicated and several 

 separate facets jarobably could be in\-estigated in dif- 

 ferent projects. Some of these will be listed in the fol- 

 lowing. The author believes that an evaluation of the 

 energy transmitted l>y wind and the energy dissi|3ated in 

 water may be obtained by analysis of the data olitained 

 from projects 3) and 4) for several sections of the fetch. 

 This iDelief is based on the apparently different rates of 

 growth of the two energies with wave steepness and with 

 absolute wave size. The effects of the two different 

 functions in the algebraic summation may be estimated if 

 their sum is evaluated at several fetch values. This 

 empirical separation of the two functions will be greatly 

 facilitated and made more certain by prior de\'elopment 

 of theoretically estalilished forms of these f\nictions. 



8 Energy Dissipation Based on von Karman. It is 

 advisable to investigate use of von Karman's (1930) 



raphers hold different views on the subject. At any rate, the 

 problems of initiation and of development of waves must be 

 separated. 



relationships in a tm'bulent fluid flow in evaluating the 

 energy dissipation in waves liy internal (turbulent) fric- 

 tion, verifying and extending the work of Bowden, Sec- 

 tion 3.1. The objective is to derive functional rela- 

 tionships between energy dissipated by waves and the 

 size and proportions of waves and then to generalize the 

 relationships found for harmonic waves to a wave spec- 

 trum. 



9 Effect of Water Viscosity in Waves. It is generally 

 known that the importance of the fluid viscosity increases 

 with increase of the velocity gradient in a fluid flow. 

 The viscosity is significant only when the velocity gradi- 

 ent is large, usually in limited regions. A project can 

 be formulated in which the velocity gradient, known for 

 the orbital water-particle velocity in harmonic waves, is 

 generalized by statistical methods to apply to wave 

 spectra. Both long-crested and short-crested waves must 

 be considered. The results of this evaluation can be 

 applied to the prolilem of energy dis.sipation in two ways: 



(a) Expression for the prol)ability of exceeding ar- 

 bitrary le\-els of water-velocity gradient can be estab- 

 lished. The energy dissipation by viscous forces can be 

 expressed in terms of \-elocity gradient by an assumed 

 (sufficiently broad) functional relationship with unde- 

 termined parameters. The parameters are to be deter- 

 mined later by analysis of the empirical data obtained in 

 project 7). 



{b) In the narrow regions of high-\-elocity gradient the 

 Xavier-Stokes' equation can be applied neglecting iner- 

 tial forces and solving for the pure viscous flow. This 

 may permit (|uantitative evaluation of the relationship 

 between velocity gradient antl the work of viscous forces. 

 The project is to be completed as under a) by estimating 

 the probability of various levels of velocity gradient, and 

 b.y applying the resultant functional relationships to the 

 empirical data of 7). 



10 Viscous Conditions at Wave Crests. The proj- 

 ects outlined under 9 can be carried out with particular 

 emphasis on the conditions at the crests of waves (in- 

 cluding wavelets) of maximum steepness. 



11 Energy Dissipation by Breaking Wave Crests. A 



rough approximation of energy losses by the breaking of 

 wave crests may be possible by the following method: 

 First conipute the wave energy in a wave spectrum by 

 a conventional linear superp(jsition theory. By the use 

 of spectral relationships for the root-mean-square of this 

 energy, determine the height of waves exceeding the 

 theoretical maximum steepness corresponding to an 

 included angle of 120 deg at the crest (this is charac- 

 terized by a water acceleration of —g). Evaluate the 

 excess of energy resulting from linear superposition over 

 the energy corresponding to limiting wave steepness and 

 assume this to rejiresent the energy lost in breaking 

 waves. Cox and jMunk's observations, Section 4.3, may 

 be used as empirical information on the increased steep- 

 ness of the leeward slopes of the wind-driven waves. 



12 Towing-Tank Measurements of Wave-Energy 

 Dissipation as a function of wave steepness are recom- 



