All-101 23 



equilibrium su.rface and v/ith the plane 2 = at the bottom of 

 the ocean, the bottom being assumed plane in this problem, A 

 layer of constant density Pp extends from the bottom of the 

 ocean to the height z = D2 + ^2 ^'^hore the constant D2 is the 

 average height of the lower layer and t]2 is the height of the 

 disturbed surface of this layer measured from the plane z = D2. 

 A layer of constant density p-, extends from the height 

 z = 'Dp "^ ^2 ^° ^^'^ free surface z = D]_ + r]-^y where D-|^ is the 

 distance from z = of the undisturbed equilibrium surface of 

 the upper layer and r\j^ is the height of the disturbed free sur- 

 face of the upper layer measured from z = D-j_, 

 Then equation (3»a) becomes 



Pi - gPi(ni + D-i - z) for the upper layer, 



^ (3.h) 



P2 - gPl^ ^ "^ •'-'1 ~ ^ " ■'^2'' "*" SP2^^2 ■*" ^2 ~ ^^ ''-^^^ '^'^® lower laye33 



(3.C) 



If we denote all quantities in the upper and lower layers 

 by subscripts 1 and 2, respectively, the equations (1), (2) and 

 (*+) 5 with expressions (3»h) and (3«g) substituted for the pres- 

 sure in the upper and lov;er layers, respectively, become 



!<.u{'J^..'^. 2QvJ sln(|) = - g ^ + i(VA,V)u^ (5) 



ri-i- 1 fiv 1 av 1 R ox p -L -^ 



at -^ 9x 1 ay 



!!i , u' --i . .; .'-li . 2X sln(L = - g !2l + l(V.A,V)v; (6) 



at 1 3x 1 ay 1 R ay p^ ^ '- 



!i , ill . !!^ = (7) 



ax ay az 



