562 Internal Waves 



When s = c 2 = the velocity of free internal waves, then resonance exists 

 for forced internal waves. In other words, the amplitude of internal tide 

 waves will be very large. This is not the case for the normal tides at the sur- 

 face, for which 



D^e^-gQi^ + h)]. 



D b remains a large number when e = c 2 . 



Therefore, the rotation of the earth provides a factor which is able to 

 increase the amplitudes of internal waves, and internal waves will thus be 

 a larger wave motion than the tide at the surface (see also the paper by 

 B. Haurwitz, The occurrence of internal tides in the ocean (1954)). 



From (XVI. 43/) is obtained as resonance wave length of internal waves 



AthJhg 



yid 



-P) Q 2 (h 1 +h 2 ) 



and, if the frequency of the semi-diurnal or diurnal tides is taken for a, X R 

 as a function of latitude. With wave lengths of this magnitude, internal tidal 

 waves with great amplitudes can always be expected (see Krauss, 1957). 



5. The Stability of Internal Tide Waves Internal Breakers 



The vertical displacements with a tidal period of the discontinuity layer 

 of density occur in most cases in symmetrical form, according to the ob- 

 servations. Examples are the anchor stations "Meteor" 254 (see Fig. 216) 

 and "Meteor" 385 (see Figs. 224 and 225). These tide waves do not show 

 any decay. Their wave profiles are symmetrical, but there are cases where 

 this does not occur, like internal tide waves on the continental shelf or in 

 shallow straits. A typical example are the internal tide waves in the Straits 

 of Gibraltar at springtide. At neap tide, when the discontinuity layer is well- 

 developed between the Atlantic upper current flowing eastward and the 

 Mediteranean under-current flowing westward, these internal waves proceed 

 entirely in a normal fashion and the wave profile is symmetrical. The Danish 

 research vessel "Dana" carried out repeated hydrographic casts on Station 

 1 138 (8-10 October, 1921, 35°59'N., 5°30'W.). Working up this station, Jacob- 

 sen and Thomson (1934) showed for this period a regular internal tide wave 

 with a range of 43 m and of a phase of 07 lunar hours after high water in 

 Gibraltar. The connection between this internal wave and the surface tide 

 within the Strait can be easily explained in this case. The increase of the 

 velocity of the current (main current plus tidal current) in the upper layer, 

 which occurs simultaneously with a decrease in the velocity of the lower 

 current, causes a sinking of the discontinuity layer. A decrease in the velocity 

 of the upper current, together with an increase in the velocity of the lower 

 current, on the other hand, causes a lifting of the discontinuity layer. At 

 neap tide and under normal weather conditions, this internal tide wave occurs 



