All-101 11 



where V/ ' , P ', w ^ and n are constants and x^ (Fig, 1) is the 

 east-west component of the stress. The above form for the wind- 

 stress may be considered as the general term of a Fourier series 

 expansion so that the wind-stress may be generalized for the 

 linear problem. However, for our numerical example, we have 

 chosen w to give a period of one year and n as 2ti;/s where s is 

 the north-south length of the ocean (0 <_ y < s). The wind- 

 stress component t: is assumed identically zero. Since the wind - 

 stress is prescribed in such a manner that its y derivative 

 vanishes at y = 0,3^ it appears reasonable to demand that these 

 boundaries be streamlines and that the normal derivatives of 

 the velocities vanish there. 



The one-layer problem is solved by the following proce- 

 dure. The equations are non-dimensionalized. The non-dimen- 

 sional velocities and free surface height are expanded in per- 

 turbation series with the non-dimensional time parameter as the 

 perturbation parameter. Each resulting set of equations is 

 then solved by application of the boundary layer technique* 



The conditions for the validity of the expansion restrict 

 the time variation to a maximum frequency of seasonal oscilla- 

 tion. In the numerical example, yearly frequency is assumed 

 and the perturbation terms of second-order and higher are 

 neglected. The error involved in neglecting the second-order 

 term as compared to the zero-order term is about 5^, and it is 

 about 20^ as compared to the first-order term. The remaining 

 physical parameters are given values which correspond roughly to 

 those of the North Atlantic Ocean, 



