94 Linear Theories — Viscous 



where u and v are the x and y velocity components, p is pressure, / is the 

 CorioHs parameter, p is density, and K^ and Ky are the horizontal and 

 vertical coefficients of eddy viscosity. We assume iCg to be constant and 

 uniform. 



These equations may be integrated from the surface z = Zq to a depth 

 z= —h beneath which both the currents and the horizontal pressure 

 gradients vanish: ^^ 



p=r^pdz, (19) 



M^= r° pudz, (20) 



^I^^r' pvdz. (21) 



Now the integrals of the pressure gradients are given as follows: 



^« dp , dP , 8zq 



" f!rf.=«/-^(..)|«. (23) 



-h^y 8y Sy 



There seems to be little reason to make use of the complete integral of the 

 horizontal shearing-stress terms. We shall assume that 



and that 



where 



/•2„ /Q2 52 \ /g2 Q2\ 



ASK^. 

 The vertical shearing-stress term integrates very simply: 





Ky£\dz = T^, (26) 



dz = Ty, (27) 



where t^ and Ty are the x and y components of the wind stress applied at the 

 surface. The integrated equations of motion are: 



8P / 52 32 \ 



-*'^=-a^+^(s5+a^^j^'+^- <28) 



8P / a2 52 \ 

 +^./=-^+^(a-.+g-^)j^.+r.. (29) 



