All-101 89 



Appondix 3 . Hydrostatic P r essure Assumption . 



The results in the main body of the report are based on 

 the assumption that the vertical equation of motion can be 

 approximated by the hydrostatic pressure equation. Although 

 this approximation is probably sufficiently accurate for the 

 problem under consideration, it may warrant a few further 

 remat^ks. 



Consider the steady, linearized problem. The equations 

 of motion with a linearized Coriolis term are 



. R yv' = - 1 9E + AAu' + i -|-(A. ^' ) (D 



^^ P ax p 8z az 



Byu- = - i |£ + AAV +1 |~(A. f^' ) (2) 



^■' p9y paziaz 



and the continuity equation is 



alaiiU + 9le.v'J. + alpwll = o (3) 



ax ay Sz 



Equations (1) and (2) can be multiplied by the density 

 to yield 



where we have written AA(pu') for ApAa' and AA (pv') for 

 ApAV . This approximation is certainly permissible since 

 these terms represent, in the first instance, only very rough 

 approximations to the true state of affairs in turbulent motion. 



