SECT. 3 J 



PYNAMIOS OF OtVKAN CUHKKNTS 



337 



As the gc()}H)tent.ial cannot he ])reci.sely estahhshed at any ])ressiire surface 

 within the ocean, the geostrophic ecjuations are usually a])phed in the form 

 given in (40). The geopotential anomaly (39) can be evaluated from observa- 

 tions of temperature and salinity as a function of depth. Absolute velocities 

 cannot be found unless a reference velocity is established on some isobaric 

 surface by independent methods. If the velocity at an isobaric surface Pr is 

 known, the velocity at any other surface is given by 



f[v{0)-v{Pr)]-mO)-v{P)] =f[v{P)-v{Pr)] = M^(^^) " ^ ^(^)] 



dx 



(42) 



Fig. 1. A schematic diagram showing the separation of the velocity into barotropic (vb) 

 and barochnic (vg) components. Frictional layers at the surface and bottom are not 

 shown. 



Velocity differences from one isobaric surface to another, computed from 

 (41), are often referred to as relative geostrophic velocities. In deep water, 

 where horizontal differences of density are small, differences of geopotential 

 anomaly from one point to another become relatively insensitive to depth of 

 the reference isobar. It is convenient, therefore, to introduce the term baroclinic 

 velocity to indicate the relative geostrophic current between the upper part of 

 the ocean and the deep water. The barotropic velocity can be considered uniform 

 with depth and equal to the deep-water velocity. This separation of the velocity 

 into baroclinic and barotropic modes allows us to examine the behaviour of 

 multi-layered and continuously-stratified models of the ocean in a more 

 systematic manner. The separation into barotropic and baroclinic components 

 is shown schematically in Fig. 1. 



B. The Vertically Integrated Equations of Motion 



In order to write the vertically integrated equations of motion in convenient 

 form, we shall introduce components of mass transport, U and V, representing 



12— s. I 



