The surface stress due to the wind formula adopted in the form of 

 Equation (6) is 



T = pk W^ = pk WJWl (9) 



where W is the wind velocity. For convenience is using standard observa- 

 tions, the wind velocity is taken to be at 30 feet above the wave surface, 

 based on 10-minute averages. The square of the wind velocity is written 

 in Equation C9) as w|w| to retain the proper sign consistent with the 

 coordinate system employed. In the example calculations presented, the 

 dimensionless coefficient k is taken as a function of the wind speed as 

 implied by the Van Dorn (1953) relation for wind stress. Thus, it is 

 assumed that 



k = K for W ^ W 



W 2 ' ^'^^ 



k = K^ + K^ (1~) for W > W^ 



— f\ —ft 



where the constants K and K„ are 1.1 x 10 and 2.5 x 10 , respectively, 

 and W is a critical wind speed taken as 14 knots (about 16 miles per hour), 



Finally, surface-stress equations for introduction into Equations 

 (4) and (5) can be written as: 



T - 



•^^ = k W cos 6 

 P 



CIO) 



-5Z. = ic W sin 6 

 P 



where is the angle between the x-axis and the wind vector. 



Equations (4) and (5) can now be written as follows: 



IS = 1 f V + k W^ cos e (11) 



9x gU 



-^ = k W^ sin 9 - K V^ D"^ (12) 



ot 



Thus, two simple differential equations are obtained which can readily be 

 resolved by the method of numerical integration. However, simplifying the 

 more complete hydrodynamic relations (i.e., Equations (1), (2) and (3) for 

 the storm- surge problem, results in formulas which are restricted to 

 certain classes of problems. 



14 



