790 



[CHAP. 23 



river the elevation of sea-level recorded at a gauge is needed. Up-stream the 

 freshwater input must be known ; width and cross-sections must also be pre- 

 scribed. The diiference method gives the distribution of sea-level and current 

 in time and space. The results of a number of examples from rivers flowing 

 into the south-eastern part of the North Sea are shown in Fig. 18 and compared 

 with observations for the rivers Ems, Hunte, Elbe and Eider. The differences 



Profiles from which r Existing channel profile 



curves obove and J »„ chonnel development 



''".°I,'ni*'" I 13m chonnel devebpment 



(5) (g) I ^ 0| \ (R 

 '60' 70' ■ ie'oT 1 



CUXHAVEN OTTERNDORF BRUNSBUTTELKOOC 



90 

 STADERSANO LUHEORT 

 I 

 SCHULAU 

 I 

 WITTENBERCEN 



' llJO' 'I' ' l50' ' ' ' 1401 



'|iJo' ' I' ' l50' 

 ST, PAULI K HOOf E OVER ZOLLENSPIEKER 

 II I 



ELBBRUCKEN CR. STACKDRT 



knllOS 



140km 

 CEESTHACHT 



12 IS IS 



Fig. 19. Generalized River Elbe. Upper part : distribution of tidal currents as a function of 

 time. Lower part : tidal depth as a function of time. Middle part : depth distribution 

 in the river. 



between observations and computations lead to the assumption that this 

 method is also applicable to non-linear problems, in spite of the fact that 

 Kreiss only demonstrated convergence in cases of linear systems. 



In a more mathematical way Kreiss (1957) treated the non-linear problems 

 in an elongated channel. Rose (1960) investigated tides and tidal currents as 

 functions of length, width and other parameters in numerous artificial canals. 

 Fig. 19 represents the influence of depth on the distribution of elevation and 



