338 The Ocean at Rest {Statics of the Ocean) 



also coincide with the isobaric surfaces and with the surfaces of equal dynamic depth. 

 If the three-dimensional fields are represented by unit layers then each isobaric unit 

 layer is then composed of several equi-potential unit layers. 



As shown on p. 308 this can also be expressed as follows: In the case of static equi- 

 librium there exists at the same time a state of homotropy between the three-dimen- 

 sional fields of mass, pressure and potential; the mass field is thus barotropic. Since 

 the specific volume is lawful dependent on the temperature and the salinity the state of 

 a basic equilibrium will also include thermotropy and halotropy. 



2. Quasi-static Equilibrium and its Importance in the Dynamic Evaluation of 

 Oceanographic Observations 



Hydrostatic equilibrium in the sea occurs only when the water masses are at com- 

 plete rest. If currents are present the homotropy of the three-dimensional mass, pres- 

 sure and potential fields will be disturbed and equation (XI. 1) is no more exactly 

 satisfied, since the vertical acceleration has to be taken into account in the third 

 equation of motion (see p. 321). However, the water movements present in the sea are 

 in most cases so weak and are, moreover, almost entirely horizontal, that deviations 

 from static equilibrium will be extremely small. This means that to a close approxi- 

 mation equation (XI. 1) can be regarded as valid, and it has indeed been used to 

 calculate the pressure field (see p. 304) from the mass field given by observation. This 

 fact is of very great importance in oceanography, since it permits the determination of 

 the geophysical oceanic structure along any vertical without a knowledge of the currents 

 present. 



Over small areas of the sea (a few km^) the deviations from hydrostatic equilibrium 

 can hardly be detected. However, for larger areas of the ocean when the distance 

 between oceanographic stations is greater, the inclination of the surfaces of equal 

 specific volume relative to that of the isobaric surfaces and the inchnation of the iso- 

 baric surfaces relative to that of equal dynamic depth are clearly evident ; the oceanic 

 structure is usually baroclinic. In practice, therefore, hydrostatic equilibrium can be 

 assumed for each station as representative of a very small oceanic area and the 

 pressure field can be calculated from the mass field according to the methods already 

 described; however, this apparent static equilibrium changes step-wise in vertical 

 direction from station to station (quasi-stationary state) and the inclination of the 

 equi-scalar surfaces relative to each other manifests itself in this way (Fig. 137). 



Rapid estimation of the relative inclinations of the isobaric surfaces in a mass field 

 can be made in a simple way using the equations of equi-scalar fields and the basic 

 hydrostatic equation (Sverdrup and co-workers, 1946). The isobars and isopycnals 

 in a dynamic section are defined by the equations 



^cix+T dy = and ^^ dx + ^^ dy = 0. (XI.3) 



dx cy dx oy 



The inclination of these surfaces is thus 



dpjdx 



dpjdx ^ dpjdx 



and 



