Internal Waves 521 



and the ratio becomes 



-^X. (XVI. 15) 



Q 



Greenhill (1887) has treated the case of several superposed strata of dif- 

 ferent densities. Particularly important is perhaps the result that, for instance, 

 if there are three layers, the discontinuity surfaces can oscillate with opposite 

 phases, so that wave crests (-troughs) at one boundary surface correspond 

 to the wave troughs (-crests) at the other boundary surface. For further 

 theoretical problems see also Solberg's paper (1928) in which are also treated 

 the conditions in case of wedge-shaped layers. 



Internal waves can also be generated in a wave tank in which two layers 

 of different densities, each with a different colour, are superposed. Sandstrom 

 (1908, p. 6) has made such tests in stratified water. In his paper are also in- 

 dicated the precautions to be taken in order to obtain sharp discontinuity 

 surfaces (see also Defant, 1923, p. 83). 

 (b) Internal Waves Having the Character of Surface or "Short" Waves 



The equations (XVI. 10) to (XVI. 15) apply to "short" waves, whose wave- 

 length is small compared to the water depth. As the potential energy necessary 

 for the development of these internal waves at boundary surfaces is very 

 small, any slight pressure disturbances or tangential stresses at the surface 

 of a stratified water-mass will suffice to develop respectively to maintain 

 internal waves at an internal boundary surface. Consequently, these short 

 internal waves must be a frequent phenomenon, not easily recognized because 

 it is not a simple matter to detect them. 



The phenomenon of "dead water" is related to these short internal waves. 

 Where rivers flow into the fjords or where ice melts (drift-ice in polar areas) 

 there is frequently a relatively thin layer of fresh or nearly fresh water spread- 

 ing over the lower layer of higher salinity (heavier water). When the weather is 

 calm and the tides recede so that the layers in the superposed water-masses 

 are maintained, it happens that slow moving vessels are "stuck" in the water 

 and make very little headway. It has been found that frequently an increase 

 in the force of the wind, or the passing-by of another ship at full speed, can 

 make the "dead water" vanish. 



This phenomenon was especially observed by Fridjof Nansen during his 

 polar cruise. His vessel "Fram", with its heavy construction and its weak engine 

 and little speed, proved to be Very sensitive to the "dead water". The phe- 

 nomenon has been observed also in the Baltic and in the Kattegat; there is, 

 however, no doubt that it always occurs where a thin layer of light 

 water is superposed on heavier water and when the vessels have a relatively 

 slow speed. Interesting cases have been described by Meyer (1904, p. 20). 

 A slight increase in the speed of the vessels already seems to be sufficient 

 to overcome the effect of the "dead water" on the vessels. 



