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 38 of 92 To investigate the ability of the model to reproduce these results, we started our runs with a typical late summer stratification for Lac Léman. The response to both idealized wind fields mentioned above, each with a duration of 1 day and a wind speed roughly corresponding to 7 m/s, was analysed at point A. v ( m / s ) 0 . 0 3 0 . 0 2 5 0 . 0 2 0 . 0 1 5 0 . 0 1 0 . 0 0 5 - 0 . 0 0 5 - 0 . 0 1 - 0 . 0 1 5 0 u S i m u l a t e d b o t t o m s p e e d f o r " V e n t " v - 0 . 0 2 0 1 2 3 4 5 t ( d a y s ) v ( m / s ) - 3 x 1 0 S i m u l a t e d b o t t o m s p e e d f o r " B i s e " 1 0 - 2 - 4 - 6 8 6 4 2 0 v u - 8 0 1 2 3 4 5 t ( d a y s ) Figure 29: Time series of the x- and y-components u, v of the velocity at point A near the bottom. Left panel: with along-basin wind ‘Vent’. Right panel: with cross-basin wind ‘Bise’. Note the different velocity scales. The velocity components in x- and y-direction (see Figure 28) near the bottom are displayed in Figure 29 for both wind fields. It is evident that the cross-basin v-component is dominated by oscillations of roughly 10 hours in both cases. In particular for the ‘Bise’ situation (right panel), it is clearly visible that these oscillations are correlated to similar oscillations in the along basin u-component with a respective phase shift of 90 degrees, a clear indication for Poincaré wave activity. This correlation can also be seen, though less clearly, for the ‘Vent’ situation, where the u-component is dominated by a low frequency contribution with a ‘period’ of approximately 3 days. Spectral analysis (not shown) confirms these results, in particular the peak around 10 hours and the higher energy at low frequencies in the u-component for the ‘Vent’ forcing. Current speeds associated with the higher frequency motions are at most 1 cm/s, and only the low frequency contribution of the along basin current can reach 2-3 cm/s for the relatively strong winds applied here. We conclude that the numerical model is able to correctly predict the most important components of the currents at this location. The somewhat shorter period of the Poincaré-waves is due to the fact that the model stratification in this example was slightly stronger than the measured one, leading to higher wave speeds and shorter periods. In addition, the measured spectra (Figure 21) represent an average over many weeks with periods of varying stratification, and perfect agreement cannot be expected. The turbulence model predicts zero turbulence at the bottom. Even though this is in apparent agreement with the absence of a measured well-mixed layer near the bottom (see above), this model result should not be overemphasized: It is well known that the class of turbulence models we adopted is not suited for the prediction of laminar-
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 39 of 92 turbulent transition and strongly intermittent turbulence at very low Reynolds numbers. Both effects, however, have to be expected at the location investigated. At present, there exists no satisfactory theory for this regime of turbulent flows, and only when the boundary layer is fully turbulent, Reynolds stress models as that use here can yield reasonable results even when turbulence is rather weak. This has been shown recently by Lorke et al. (2002) for the bottom boundary layer of a small lake. 3.3.2.2 Mixing at the Entrance of the Petit Lac The dynamics of mean currents and turbulence at point B, the entrance of the S-W appendix (‘Petit Lac’, see Figure 28), is quite different. Temperature profiles measured at this point for late summer and early winter 1987 are displayed in Figure 30. For the summer period (August/September), the temperature profiles exhibit a typical structure, which is also found in other years: • a well-mixed upper layer of about 10 m thickness • a strongly stratified upper thermocline from about 10 m to 30 m • a weakly stratified lower thermocline from about 30 m to 50 – 60 m • a well-mixed bottom boundary layer of 10 to 15 m thickness Later in the year, the thermocline is slowly mixed downward and eroded by penetrative convection, as is particularly visible from the slightly unstable temperature profile in December (see Figure 30). Finally, starting from January, the whole water column at this point is well mixed until re-stratification starts in spring (not shown). Current records at the entrance of the Petit Lac for a period of the same year 1987 are plotted in the right panel of Figure 30. d e p t h ( m ) - 1 0 - 2 0 - 3 0 - 4 0 - 5 0 - 6 0 - 7 0 0 1 6 D e c T e m p e r a t u r e a t t h e e n t r a n c e o f t h e P e t i t L a c 1 7 N o v 2 8 O k t 1 0 S e p 1 8 A u g - 8 0 5 1 0 1 5 2 0 2 5 t ( d e g C ) v ( m / s ) 0 . 4 0 . 3 0 . 2 0 . 1 - 0 . 1 - 0 . 2 - 0 . 3 - 0 . 4 0 S p e e d a t t h e e n t r a n c e o f t h e P e t i t L a c 6 0 m - 0 . 5 0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 d a y s f r o m 2 1 . O k t . 8 7 Figure 30 : Left panel: profiles of temperature at the entrance of the Petit Lac for the second half of 1987. Right panel: measured in- and outflow velocities at the entrance of the Petit Lac at 10 m and 60 m depth. Outflow is positive. 1 0 m
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D28: Internal seiche mixing study - Hydromod

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