464 



Tides in Estuaries 



we have T= 5h 30 min = 19,800 sec, V = 7-45 and c = 108 m/sec, which gives S= 25 km, 

 a point still below Brunsbiittel. According to the observations, with normal head water and tidal 

 range, the Elbe water has no seawater at low water at Brunsbiittel, at high water near Gluckstadt. 

 This equation should, however, be used cautiously, for it ignores the stratification of fresh water 

 and sea water within the river current. In reality, the tide causes a mixing of the two kinds of 

 water, through which fresh water is transported more rapidly downstream, and sea water further 

 upstream than if the streamlines of the separate layers were completely parallel. 



Table 78. Tidal currents in the Rivers Elbe and Weser 



(According to Franzius) 



The tidal curves of the tidezone often show irregularities caused by the 

 important shallow water tides (harmonic and combined tides); often there is 

 a double, in rare cases a triple high water. The latter case is known to happen 

 in the Forth River up to Stirling and is called "Leaky". The tidal curve of 

 Southampton also shows three secondary maximas which for 3 full hours 

 keep the high water level which is so very useful for navigational purposes. 

 In the Seine there are also two secondary high waters, even a third one near 

 Isigny, and at Le Havre. Similar phenomena occur in the estuary of the 

 Sao Francisco and of the Paranagua at the coast of Brazil, where there are 

 four high waters in 24 h, two higher and two lower, which are called "meias 

 mares". Such irregularities are always connected with particularly shallow 

 water. 



2. Theoretical Considerations Regarding River Tides 



If a channel with a uniform cross-section and a level bed opens up into 

 a sea with tides, its water-masses will be forced by these tides to co-oscillate 

 at the mouth. As in estuaries the water depth is small and decreases gradually 

 upstream, the periodical variations in water level in the river will hardly be 

 of the form of a standing wave, as is the case with deeper, canal-like adjacent 

 seas. The effect of the friction will give it the character of a progressive wave 

 travelling up the river. As the velocity of propagation with small water depth 

 is very small, it can happen, in the case for great, long rivers, that, before 

 a tide wave reaches the tide mark, a new wave has already arrived in the 



