D28: Internal seiche mixing study - Hydromod

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Integrated Water Resource Management for Important Deep European Lakes and their Catchment Areas EUROLAKES D28: Internal seiche mixing study FP5_Contract No.: EVK1-CT1999-00004 Version: 1.2 Date: 24.08.2004 File: D28.doc Page 76 of 92 from another location, tells the following example. Take the initial information at the central position of Lake Überlingen, where amplitudes of about 12 m are of common occurrence (Bäuerle et al., 1998): From Figure 44 it is inferred that at central Lake Überlingen the amplitude of the interface displacement is about 90 % of the maximum. This in turn yields that 13.3 m is the corresponding amplitude at the very end of Lake Überlingen. Finally, in analogy to the above case of reference, we get 13.3 x 4300/1500 = 38 cm/s and 13.3 x 4300/8500 = 6.7 cm/s as vertically averaged velocities in the upper and lower layer in the Straits of Mainau, respectively, which correspond to an amplitude of 12 m measured at a central position of Lake Überlingen. Figure 52 : Current field of the eleventh internal mode in the surface-layer on 13 April 1989 with T11 = 39.8 h. The normalised maximum transport occurs at the mouth of the Bay of Constance and amounts to about 5600 cm²/s. The cross mark near the southern shore in the eastern half of the lake designates the site of the waste water intake discussed in the text. (further explanation in Figure 50) It should be mentioned that the same value of the phase velocity of long internal waves ci results from different combinations of he and ε according to the relations (1), (2), (8). Since the eigen-solutions of the problem (5) are uniquely determined for a very phase speed, ci, the respective definite transport field of the mode in question has to be evaluated with regard to he, i.e. the associated combination of h1 and h2, which fit together with ε in the relation (8). In this sense, there is a certain variety of two-layer manifestations equivalently related to a unique set of eigen-solutions. Thus, for the same maximum amplitude of a mode of them different definite transports result at a selected place, just depending on the differences allowed for by both the associated
Integrated Water Resource Management for Important Deep European Lakes and their Catchment Areas EUROLAKES D28: Internal seiche mixing study FP5_Contract No.: EVK1-CT1999-00004 Version: 1.2 Date: 24.08.2004 File: D28.doc Page 77 of 92 variations of the pair of upper and lower layer depths on one hand and the density difference, ε, on the other hand. This peculiar variety of two-layer cases covered by one set of eigenfunctions means a useful advantage, as the same calculations can be exploited for certain different two-layer approaches. The current fields of the first and ninth modes are depicted in Figure 50 and Figure 51 for the case in spring and in Figure 53 and Figure 54 for that in late summer. Additionally, the currents of the eleventh mode are enclosed in Figure 52 and Figure 55 in order to emphasize the practical use by a peculiar application, which Hollan (1995) carried out and is outlined below. Except for the reference to the amplitude normalisation the relative variation of the structures in the current fields can be detected well from the diagrams. They consist each of a pair, showing the current ellipses in the upper diagram which indicate the position of the head of the current vector when turning during one cycle of oscillation. The main axis of the ellipses shows the orientation of the predominant current during a wave cycle, while the small axis gives the maximum transverse currents a quarter of the period later than the main currents. In the lower diagram the information is compiled, which concerns the sense of rotation at a given moment. Included into this stick representation is the sense of rotation of the current vector. The illustration of the phase relation and the sense of rotation throughout the lake is secondary for a rough evaluation, as this information is more important for inspection of closely adjacent conditions. The assessment of the local intensity of the currents is very comprehensive in the upper diagram. There is remarkable variation of the intensity and relative difference between the main and the transverse currents. This is easily perceived in the different examples and left to the reader for comparison.
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D28: Internal seiche mixing study - Hydromod

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