All-lOl 8 



density. The equations of motion in each layer are then inte- 

 grated over the depths of the respective layers and the non- 

 linear terms are neglected, V/e also neglect shear forces at 

 the bottom of the lov;er layer and at the interface. No assump- 

 tion is made concerning the vertical distribution of velocity , 

 but instead, we hope to solve for the integrated velocities 

 (i.e., the transports) in each layer. This case is referred to 

 as the two-layer problem. Unfortunately, it is much too diffi- 

 cult to handle analytically, and consequently we must consider 

 a second problem, 



(ii) The maiiner of performing the integration in this case 

 will lead to a considerably simplified problem which allows us 

 to stipulate a more general density distribution than that in 

 (i). The density is specified as a continuous function of depth 

 and the ocean is divided into three layers, A layer of constant 

 density, Pq, lies above the surface z = T(x,y,t). From z = T 

 down to z = T - d (d is constant) the density increases linearly 

 with depth from Po to the value P _j^» Below z = T - d, the den- 

 sity has the constant value, p . 



We assume that there is a depth z = - h(x5y,t) belov; 

 which the velocities may be considered negligible (in some 

 suitably defined sense). The pressure gradients will then also 

 be negligible below z = - h. As a consequence of this assumption 

 and the previous assumption of hydrostatic pressure, a relation- 

 ship exists between the surface z = T and the free surface 



* Compare this with caie~Tii). 



