SECT. 3] DYNAMICS OF 0(1EAN CITRRENTS 335 



been neglected are small for the scales of motion considered in the general circu- 

 lation of the ocean. However, these terms are not always negligible at the 

 extremes of the scale range and should always be examined for significance in 

 specific applications of the equations. 



A. Geostrophic Currents 



Except near boundaries of the ocean, where sharp horizontal and vertical 

 gradients of velocity can be developed, the opposition of the pressure gradient 

 and Coriolis forces is the major dynamical restriction to be satisfied by the 

 steady flow. Geostrophic currents, which are defined by assuming an exact 

 balance of pressure gradient and Coriolis forces, can yield useful approxima- 

 tions to the actual currents in regions removed from solid boundaries and the 

 free surface of the ocean. 



The theory and application of the geostrophic velocity approximation has 

 been discussed at length by Sverdrup et al. (1942). The theory is redeveloped 

 here in slightly revised form to serve as an introduction to the subsequent 

 discussion of geostrophic mass transport. 



Gravitational acceleration can be expressed in terms of a potential, 0, defined 

 so that its difference at two levels is equal to the work per unit mass required 

 to move a body from one level to the other. The co-ordinate z has been chosen 

 parallel to the direction of action of gravitational acceleration so that is a 

 function of z only. Surfaces of constant z correspond to surfaces of constant 

 gravitational acceleration potential (geopotential). The geopotential is related 

 to height z by the equation 



d0 = g dz. (29) 



Thus, the geopotential at any level z is 



0{z) = <^o + 



gdz, (30) 



where 0o is the geopotential at the origin of the co-ordinate system (2 = 0). 



The geopotential can be expressed in terms of specific volume of sea-water 

 and pressure by means of the hydrostatic equation 



adP = -gdz = -d<P. (31) 



Integrating (31), we obtain 



0(P)-0(Po) - - r adP. (32) 



The geopotential relative to the surface of the ocean (P = 0) is 



0{P) = 0(0)- r adP. (33) 



jo 



