Internal Waves 537 



Groen (1948) has presented an extension of Fjeldstad's theory, in which 

 he also considers the short waves. For a special density increase with depth 

 (two essentially homogeneous layers separated by a transition layer) the 

 computations are carried out until their end analitically. The width of the 

 transition layer which can be chosen arbitrarily, enters the computation as 

 a free parameter. It is rather remarkable that there exist for a given 

 density distribution a lower limit for the period of internal waves. This 

 minimum period seems to be the period of "eigen" or free oscillations of 

 the disturbed stable density distribution about its equilibrium position. This 

 eigen-period is rather small and is for a density increase of Aq = 10 -4 per 

 metre of an order of magnitude of some minutes. This should be those 

 stability oscillations already mentioned and discussed above (see p. 531). 



2. Observations of Internal Waves in the Oceans; Testing of the Theory 



(a) Internal Tide Waves in the Open Ocean 



The magnitude of the vertical displacement of the water-masses can be 

 computed from variations of a conservative property of water as temperature, 

 salinity, oxygen content, etc. This can be done without too much effort, if 

 the horizontal gradient of this property is very small. If this property is S, 

 then the condition, that S remains unchanged, will be: 



dS „ 8S dS 8S n 



-^- = or — +U— + W— = 0. 

 dt ot ox oz 



If 5 = S (z)-\-S 1 (x, z, t), and if es/dx is small and w = drj/dt, then 



*— „|? or l — a^j. (XVI.37) 



The vertical displacement /; can be obtained best where the vertical grad- 

 ient of the property can be determined readily and exactly. This is the 

 usual method whereby the vertical amplitudes of internal waves have been 

 computed from observations of temperature and salinity repeated at short 

 time intervals from an anchored ship. 



Not all the variations in oceanographic properties, which are being ob- 

 served in the various depths, can be attributed to internal waves, even if 

 these changes occur more or less periodically. At the boundaries of neigh- 

 bouring water-masses oceanographic properties change rapidly within a short 

 distance (fronts). Advances of one water-mass against the other cause oscil- 

 lations of these properties. The boundary layers between such water bodies 

 are rarely in equilibrium with the existing currents. The disturbances mani- 

 fest themselves in unperiodical or periodical oscillations of the isolines of 

 the various properties. They then simulate internal waves, and have little 

 to do with true internal waves. In stratified water-masses there occur also 

 periodical oscillations in the slope of the isosteres. They resemble internal 



