304 The Geophysical Structure of the Sea 



exaggeration of the vertical scale is required to show the slope of the lines in a better 

 way. The geometrical depth, the dynamic depth or the pressure can all be used as the 

 vertical co-ordinate. Such graphic representations are termed dynamical vertical cross- 

 sections, in short dynamic sections. 



4. The Pressure Field and its Relationship to the Mass Field. Solenoids 



The internal stress in a liquid such as the ocean is characterized by the pressure per 

 unit area. In a liquid in equilibrium, due to the absence of any resistance to deforma- 

 tion, this pressure acts perpendicular to any arbitrarily oriented surface through the 

 liquid and is equal for any point and in all directions. This state is denoted as hydro- 

 static stress state. The water masses in an ocean at rest is subject to the influence of 

 gravity and the static pressure p at a depth h is defined as that force produced by the 

 weight of a water column of unit cross-section extending from this depth to the surface 

 of the sea. This does not take into account the atmospheric pressure at the surface 

 of the water so that p is defined solely as the water pressure. Thus 



P = pmgh, 



where Pm is the mean density of the water column /;. The dimensions of p is 

 [g cm^^sec"^]. According to (IX. 3) the dynamic depth D can be substituted in place 

 of the geometric depth /; so that 



P = PmD. (IX.7) 



The pressure of a column of pure water (p„j = 1) of a height of 1 dyn. m is defined 

 as 1 decibar. This is a tenth part of a bar which is defined as 10^ dyn/cm^ and is the 

 pressure of a column of pure water of lOdyn.m. The practical pressure unit "one 

 atmosphere", is only about 1% greater than one bar. Fractions of the bar in addition 

 to the decibar are the centibar and the millibar. The latter corresponds to a water 

 pressure of one dynamical cm of pure water and is equivalent to a pressure of 0-75 

 mm of mercury. 



For an ocean of pure incompressible water the following rule applies: The numerical 

 value of "sea pressure" expressed in decibars is the same as that of the depth in dy- 

 namic metres at which this pressure is exerted. Since p^ in the sea is not very diff'erent 

 from 1 this rule also applies in very close approximation for sea-water. From equation 

 (IX. 7) is obtained 



D = a^p, (IX.8) 



where a,„ is the mean specific volume of the water column. If p or a vary, equations 

 (IX. 7 and 8) will be replaced by the integral forms 



\ pdD and Z) = a 



p=\pdD and D=\adp, (IX.9) 



where the integrals must be extended over the whole water column h. For numerical 

 calculations the integral is split up into sums for the thinnest possible layers with 

 approximately constant density or specific volume (see later). 



The relationships between pressure, geometrical and dynamic depth and the vertical 

 distribution of specific volume and of density are shown in Table 110 for a homo- 

 geneous sea at 0°C and 35%o salinity (standard ocean). 



