amount of turbulence depends on the dimensions of the turbulent field as 

 considered in the formula for the Reynolds number, 



R- PUL 



where p is density, 



u is horizontal velocity of flow, 

 L is linear extension of flow, and 

 u, is the coefficient of viscosity. 



In stirring processes more complex and effective than pure horizontal 

 flow, the duration of wind stress must also be taken into account. Ey 

 choosing the wave parameters, fetch and duration are introduced automati- 

 cally — their part in wave development is relatively well known. 



The velocity and vertical extension of pure wind current also depend 

 on the fetch and duration of the wind and can be assumed to be proportional 

 to the dimensions of spectral components of the wind sea. If only wave 

 parameters are used for determination of the mixing parameter, the pure 

 wind current factors may be considered as having been incorporated in the 

 mixing parameter. The problem is thus simplified sufficiently to permit 

 experimentation in determination and prediction of the mixed-layer thick- 

 ness. 



Wave height or amplitude, period, length, and steepness are expected 

 to contribute to the problem. Length and period are naturally interdepend- 

 ent; therefore, only one of these must be considered. Spectral distribution 

 of steepness in a wind sea is difficult to determine; however, it is a 

 function of the spectral distribution of height and length and is therefore 

 partly accounted for by use of these parameters. 



The mixed-layer thickness is finally considered to be a function of 

 wave amplitude A, wave length X, and a mixing parameter k, h = f (A,X,k), 

 which is valid at the interface between the mixed layer and the thermo- 

 cline. k cannot be expected to remain constant. Since it applies to the 

 bottom of the mixed layer, it must be dependent on mixed-layer thickness 

 and on the wave parameters. In addition, its value depends on the sta- 

 bility in the thermocline. 



The relation describing orbital motion in trochoid waves 



2irh 



k 



Ae ~ < 6 ) 



includes most of the parameters, if h is considered to be a fixed value 

 under given surface conditions and if stability in the thermocline is 

 constant? The above function, k(A,h, X), was adopted in view of the 

 generally accepted theory that orbital motion of particles due to waves 

 and the velocity of the pure wind current both decrease exponentially 

 with depth and are proportional to the wave parameters. 



2k 



