SECT. ■)] TinKs 7a§ 



9. Internal Tides 



A few remarks must be made concerning internal tides. In the foregoing it 

 has always been assumed that the density of sea-water is constant. In the open 

 sea as well as in the ocean there is often a stratification characterized by an 

 upper and lower layer. These discontinuity layers are not at rest, records of 

 temperature and/or salinity pointing to remarkable oscillations, sometimes with 

 tidal periods ; the amplitudes of these oscillations may be many times larger 

 than that at the sea-surface. Defant (1932) has shown that in an infinite non- 

 rotating ocean tidal forces cannot directly generate internal tides. In essence 

 Haurwitz (1950 and 1954) came to the same conclusion. Fjeldstad (1935) 

 treated the problem of internal waves in waters of continuously varying 

 density. Defant (1952) gave a summary. Recently Rattay (1960) discussed 

 internal tides caused by variations of depth at, for example, the edges of 

 continental shelves. Although these internal tides are often observed in the 

 open sea, the observations available are not so numerous as tidal observations 

 in coastal areas. This may be the reason why valuable qualitative explanations 

 of this phenomenon exist based on hydrodynamics while a lack of methods, 

 capable of treating these problems quantitatively, remains. Later on it is 

 possible that the difference methods will also become applicable in this field. 



The symbols used in this chapter are : 



X, v/ = horizontal co-ordinates (normally .c = East, ^ = North direction) 



t = time co-ordinate 



M, v = components of velocity taken as means in a vertical line, in x, i/ direction 



respectively 

 ^ = elevation above mean sea-level 

 li =mean depth 

 a = speed of the tidal motion 

 / =geostrophic factor 

 i = \/ - 1 



a = mean radius of earth 

 (p, A = latitude and longitude 

 CO = angular speed of the rotation of the earth 

 A =the Laplacian 

 I = mesh-size in x, y grid 

 T =time step 



References 



Airy, G. B., 1842. Tides and waves. Encycl. Metrop., 5. 



Bartels, J., 1957. Encyclopedia of Physics, Berlin, 48; Geophys., 2, 734. 



Bowden, K. F., 1955. Physical oceanography of the Irish Sea. Fish. Invest., Lond., 



Ser. 2, 18, No. 8. 

 C'hrystal, G., 1904. Some results in the mathematical theory of seiches. Proc. Roy. Soc. 



Edinburgh, 25. 328-337. 

 Collatz, L., 1955. Numerische Beliandlung von Dijferentialgleichungen. Springer, Berlin. 

 Courant, R. and D. Hilbert, 1924. Methoden der mathematischen Physik. Springer, Berlin. 

 Defant, A., 1919. Untersuchungen iiber die Gezeitenerscheinungen in Mittel- und Rand- 



meeren, in Buchten und Kanalen. Teil I.-IX. Denkschr. Akad. Wiss. Wien. Math.- 



nat. Kh, S. 96. 



