330 Forces and their Relationship to the Structure of the Ocean 



problems arising with oceanic currents. This applies to the dynamics of moving 

 ""non-homogeneous'' media in which the effects of friction are considered unimportant. 

 This method of treating problems of oceanic movements has the particular advantage 

 that it takes into account the total ejfect of the mass field on the water movements 

 including all their smaller details. It can only be used in its simpler form by neglecting 

 friction; in general, however, at a distance from the boundary surfaces the friction 

 does not change to any large extent the nature of the currents set up by the internal 

 forces. 



{a) Circulation for an Earth at Rest and for a Rotating Earth 



In the presence of (/?, a) solenoids, motions are always initiated the nature of which 

 is that of a circulation, i.e., motions following in the most simple case a closed path. 

 In a moving fluid a continuous chain of material elements may lie in a closed curve s. 

 The velocity component of one of these small elements tangential to the curve s 

 shall be F<. The sum of all these components along the curve s is defined as the 

 circulation C of the curve s 



C = & Vt ds, (X.42) 



where ds is a linear element of the curve s. An expression for the change of C in time is 

 easily obtained from the equations of motion (X. 1 6) (stationary Earth, frictionless 

 motion). 



(X.43) 



Since normally the external forces (gravity) have a potential, the first integral vanishes 

 and the equation becomes 



— = -^ ^ y.dp = N, (X. 44) 



where A'^ is the number of isobaric-isosteric unit solenoids, enclosed by the curve s 

 (see p. 307 equation (IX. 1 1)). Assuming that the curve s lies in a plane, then: 



(1) The circulation is constant with time (dCldt = 0) if a is constant over the whole 

 of the space under consideration (homogeneous sea) or if it is a function of 

 pressure. The isobaric and the isosteric surfaces then coincide and the mass 

 distribution is barotropic. 



(2) A circulation acceleration will be present if the specific volume is dependent not 

 only on the pressure but also on other properties of the water (temperature, 

 salinity). The mass field is then baroclinic. Form equation (IX. 12) for a curve 

 5 in a dynamic section formed by two vertical lines, the physical sea-level (/? = 0) 

 and an isobaric line at depth p^, the number of solenoids enclosed will be 

 given by the diff'erence in dynamic depths of the isobar p^ at the two stations. 

 This gives 



dC 



-^ = N= Da- D,. (X.45) 



