INTERNAL WAVES IN CHANNELS OF VARIABLE DEPTH 
Chia-Shun Yih 
Untverstty of Michtgan 
Ann Arbor, Mtchtgan, U.S.A. 
ABS TRAG. 
Internal wavesin prismatic channels of variable depth 
propagating along the channel axis are studied. It 
has been shownthat for whatever stratification of the 
fluid the frequency of the wave motion increases 
whereas the wave velocity decreases as the wave 
number increases. A general method of solution for 
anarbitrary channel isthenpresentedindetail, which 
gives the wave velocity andthe fluid motion for a given 
wave number anda given mode by successive appro- 
ximations. Finally long waves are studied in some 
detail,a few specific examples oflong wavesare given, 
and the connection of the present theory withthecla- 
ssical shallow-water theory is shown, 
I, INTRODUCTION 
Known solutions of gravity waves ina prismatic channel of 
variable depth which have a degree of general applicability are of 
three categories. For very long waves (first category) the shallow- 
water theory (Lamb 1932, p. 273-274) gives (gh) V2. asitheawaverve- 
locity, where g is the gravitational acceleration and h the average 
depth. For very short waves (second category) not confined to the 
edge region the variability of the depth is unimportant, since the mo- 
tion is confined to the region near the free surface. The third cate- 
gory is the category of edge waves, which for short waves have an ap- 
preciable amplitude only near the shores (or the edges), and are there- 
fore always affected by the geometry, specifically the slopes of the 
channel near the shore lines, however short the waves compared to 
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