Forces and their Relationship to the Structure of the Ocean 3 1 3 



the distribution of mass. Within the sea, the turbulence in the moving water masses 

 may presumably also produce changes in the physical-chemical structure of multi- 

 stratified water bodies. All these disturbances are, however, small compared with the 

 changes in mass distribution due to atmospheric influences effective at the sea surface. 

 The only internal force dependent on the mass distribution is the gradient force. 

 This force per unit volume is given by the pressure gradient G (see equation (IX. 10)). 

 The pressure force per unit mass can be obtained by multiplication with the specific 

 volume so that 



r ^P ^ "^P (X n 



dn p dn 



The pressure field also determines the field of force per unit mass, since the normal to 

 the isobaric surface gives the direction, and the thickness of the isobaric unit layers 

 gives the intensity of the pressure gradient at any point in oceanic space. 



Bjerknes (1900) by analogy with the pressure gradient introduced a "mobility 

 vector" B which gives the variations in specific volume in the direction n of increasing 

 specific volume perpendicular to the isosteric surface. 



5 = ^. (X. 2) 



dn 



The degree of concentration of the dynamic isobaths on an isobaric surface is of 

 course also a measure of the gradient force, and is at the same time also a measure 

 of the potential energy stored in the mass distribution. Figure 133 presents a section 

 through an ocean and two oceanographic stations are indicated by A and B (L km 

 apart). As a first approximation the pressure surface can be regarded as horizontal 

 and coincident with the surfaces of equal geometric depth. The surfaces of equal 

 geopotential (equal dynamic depth) are inclined relative to these so that the same 

 pressure Pn at dynamic depth Da at station A is found at the greater dynamic depth D^ 

 at station B. Di, — Da is then the difference in potential energy between A' and B'. 

 This potential difference can be regarded as a force along L which, if present alone, 

 would set the water masses in motion. The force per unit mass resulting from the 

 internal pressure difference is then 



K = ^' ~ ^°. (X. 3) 



According to (IX. 12), D^ — Da is the number of solenoids enclosed within the cross- 

 section between the two stations A and B from sea-level to the depth in question. This 

 number per unit length is thus a measure of the internal force resulting from the mass 

 distribution. 



(c) Among the secondary forces are included all those apparent forces that in them- 

 selves do not give rise to a current but which, when motion is present, are of decisive 

 importance in determining the final form of the water displacement. These include 

 the deflecting force arising from the rotation of the Earth (the Coriolis force) which 

 affects solely the direction of the water movement, the viscosity (boundary fric- 

 tion and turbulence) which affects more the velocity of a current, and finally the 

 centrifugal force, which for motion along a curved path (velocity V, radius of 



