Table 4. Coefficients of eddy viscosity (turbulence 



coefficients) M(p) [cm-1 g sec-1] in different 

 stages of wave development at a wind velocity 

 of V = 10 m/sec. 



p 0.15 0.25 0.317 0.367 0.45 0.55 0.65 0.7 1.0 1.15 1.25 1.37 



M(p) 5.85 8.15 10.1 12.0 15.8 22.1 30.9 36.5 99 202 326 511 



4) Energ y equations 



A steady supply of energy by wind is necessary to cover the 

 losses of energy by virtual friction in turbulent wave motion. Only 

 in the case where the energy supply exceeds the energy dissipation 

 may the sea grow. Let E be the mean energy of the wave motion per 

 unit area of the sea surface, A the supplied energy and D the dis- 

 sipated energy per unit surface area. Then, for the total energy 

 E-A per unit crest width of a wave with wave length A , 



f^ (E A) = (A - D) . (41) 



This equation states that the individual change of wave energy with 

 time equals the difference between the supplied energy and the energy 

 lost by friction and turbulence. Associated with the wave motion 

 is a flow of energy in the direction of wave propagation. This 

 energy flow per unit time across a vertical "control-section" of 

 unit width and a depth below which the wave motion is negligible, is 



cE = J pgaV , (42) 



where C is the velocity of wave propagation (phase velocity) if 

 we consider deep water waves. The average energy per unit area of 

 a wave with the amplitude a = H/2 equals 



E = I gpa^ . (43) 



74 



