340 77?^ Ocean at Rest {Statics of the Ocean) 



under influence of a downward force. If it is lighter the corresponding upward force 

 will cause it to rise. The forces initiating vertical displacements can be easily found 

 from the third equation of motion in equation (X. 16). Neglecting Coriolis forces and 

 friction they are given by 



dw dp 



'dt^^~'"'8z' 



If the surrounding water masses are in hydrostatic equilibrium and have a specific 

 volume a' then 



From these two equations it follows that the enclosed water mass will be subject to 

 an acceleration given by 



dw a' — a , ^ 



The upward or downward forces (buoyance force of Archimedes) is thus proportional 

 to the difference between the specific volumes of the surrounding and the enclosed 

 water masses ; for water masses of either the same sahnity and with a temperature 

 difference of 10°C or of equal temperature and with l%o difference in sahnity, the 

 magnitude of this acceleration is about 1 cm sec~^ or about one-thousandth of the 

 gravitational acceleration. 



The nature of the equilibrium in a water column is dependent on the oceanographic 

 structure and is shown by the acceleration acting on a small quantum after vertical 

 displacement. The vertical equihbrium conditions that may occur in the ocean and 

 the calculation of the vertical stability that characterize these states have been discussed 

 in detail in Pt. I, particularly in Chap. V, 5. p. 196. It seems sufficient to refer here only 

 to the previous statements. 



In a system where there are no forces acting other than gravitational acceleration 

 and the internal forces, a dynamic vertical section showing isobars and isosteres 

 allows an immediate estimation of the direction of the water currents produced by 

 the resultant forces due to density differences. Part of such a section is given in Fig. 

 138; the isobars can be regarded as horizontal and the inclination of the isosteres 



Fig. 138. Dynamic vertical cross-section: p, isobaric; a, isosteric surfaces. Disturbed 

 equilibrium and return to equilibrium state. 



