D28: Internal seiche mixing study - Hydromod

σσ
Integrated Water Resource Management for Important Deep European Lakes and their Catchment Areas
EUROLAKES
D28: Internal seiche mixing study
σ
10
9
8
7
6
5
4
3
2
1
0
0 5 10 15 20
Figure 36 : Dependency of the dimensionless eigen-frequencies
FP5_Contract No.: EVK1-CT1999-00004
Version: 1.2
Date: 24.08.2004
File: D28.doc
F
σn ωn
ω
Page 55 of 92
= on the rotation
( 0)
1
( 0)
F = f /ω for 15 modes of internal seiches in Upper Lake Constance on the basis of a
number
1
two-layer constant equivalent depth model (Figure 35) The vertical dashed lines indicate the dates
for which the calculations of the 1991 report were done. The circles refer to Figures 38, 41, 44, 47
and Figure 50 through Figure 55.
( 0)
Since the stratification enters into ω 1 proportionally to the phase velocity according to
(8), the rotation number F increases, when either the stratification as given in (2) or the
equivalent depth he diminish. The latter is effectuated by reduction of h1, the thickness of
the surface layer. As mentioned above, the influence of the size of the lake is, by the
way, detected with the help of (3) in terms of the length L in a rectangular basin. In this
case the rotation number is proportional to L.
With constant Coriolis frequency the rotation number F depends (inversely) on the
( 0)
( 0)
value of ω 1 . As discussed above, ω 1 decreases with the length of the basin and with
decreasing phase velocity. In other words, the larger and the less stratified the lake is,
the larger is the influence of the earth rotation.
At low F the internal seiches resemble standing oscillations. With increasing F the effect
of rotation becomes dominant and the structure of the oscillations takes the form of a
rotating wave propagating around amphidromic points, where the amplitude of vertical
displacements is zero. The number of amphidromic systems for the lower order modes
is generally identical with the modal number.