538 Internal Waves 



waves only superficially. Let us assume for simplicity only two superposed 

 water bodies. If the water-masses are in stationary equilibrium then the system 

 and currents must satisfy the Margules relation (see vol. I). For instance, the 

 lower water-mass is at rest u = 0, h = the height of the boundary surface 

 at the distance L from its intersection with the horizontal, a and a the specific 

 volume of the lower and upper water-mass, and /= 2cosin cp, then, accord- 

 ing to Margules' relation, 



h = - ; u . 



g a —a 



If the current changes, h changes also, if the steady state is to be maintained and 



dh = ; du . 



g a -a 



When 



/ = 10- 4 , -?— = 10 3 and du' = 20 cm/sec , 

 a —a ' 



dh = 2 x 10 -3 L or at a distance of L = 10 km, dh = 20 m. The boundary 

 surface will be 20 m higher or lower than before. For a point in the vicinity 

 of the boundary surface, this variation will cause considerable changes in 

 the oceanographic properties. The periodic variations of the tidal currents 

 for example will cause periodic changes in the slope of the isosteric surfaces 

 (normal to the current direction). But such variations are not internal waves 

 in the strict sense of the word, even if they occur periodically. 



The first hydrographic observations repeated at short intervals over a long 

 period made by Helland-Hansen and Nansen (1909) proved the existence 

 of true internal waves. The main waves have often besides meteorological 

 influences also tidal periods. They appear especially where there is a well- 

 developed discontinuity layer of density (see Defant, 1938, p. 9). Otto Petterson 

 pioneered in these observations by studying the waters in the Great Belt between 

 the Baltic and the Kattegat; while working from an anchored ship he found 

 such waves with semi-diurnal period. The problem of internal waves at discon- 

 tinuity surfaces of the density in the free ocean was first investigated on the 

 "Michael Sars" Expedition in the Atlantic Ocean. Later it was studied on the 

 anchor stations of the "Meteor" Expedition 1925-27 in the tropical and sub 

 tropical regions of the Atlantic Ocean, on the anchor stations of the "Snel- 

 lius" Expedition 1929-30 in the Indonesian waters, and on the anchor stations 

 of the later cruises of the "Meteor" 1937-8. In addition to the temperature 

 and salinity observations in short intervals, also current measurements were 

 taken in various depths. Thus there exist already from many points in the 

 free ocean homogeneous observations on internal waves. The analysis of 

 this material has demonstrated that internal waves exist everywhere and are 

 not limited to discontinuity surfaces. They appear also when the density 



