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 16 of 92 2.4.1.3 Frequency analysis A simple decomposition of the seiches is used through a trigonometric function decomposition of the calculated temperature of the lac at the T point at –41.0 min based on the following formula: � i ( ω t + ) −αi S = C + A e cos ϕ i Where S is the simulated temperature, C a constant and i is the order of the decomposition. The first level of decomposition gave the following parameters: C = 7. 6 A1 = −0. 9 1 10800 = ϕ 267600 − t α1 = 500000 2π ω 1 = 300000 This gave a period close to 83 hours for the first mode. On Figure 15 is shown the graphical comparison between the simulated temperature at T point at –41.0m and the first level of trigonometric decomposition. For the selected period (between 200000s and 700000s) the both curve are very close. The second level of the decomposition gave the following parameters: 2 0. 12 = A 2π ω 1 = 94000 i 1 = ϕ i 7200 With this method the second mode is estimated to 26 hours. 8.5 8.3 8.1 7.9 7.7 7.5 7.3 7.1 6.9 200000 300000 400000 500000 600000 700000 Figure 15: Simulated temperature at T point at –41.0m (S in dark Blue), first level of trigonometric decomposition (in red), first plus second level in light blue. S First level 1+2
Integrated Water Resource Management for Important Deep European Lakes and their Catchment Areas EUROLAKES D28: Internal seiche mixing study 2.4.2 SIMULATED SEICHES – ANALYSIS 2.4.2.1 Rotation The Figure 16 shows the temperature iso-contour level 7.6°C at six different times at –41.0 m depth. These times are chosen in order to illustrate the rotation of the internal wave around the amphidromic point due to the coriolis forcing. The coloured stars are associated to the position of the temperature iso-contour that has the same colour. The black arrow that follow the stars explicit the wave rotation direction. The both lines Red and Purple, which are superimposed, are related to the wave period of the seiches (80 hours). The intersection of the six curve is located at the middle of the lac, determine the amphidromic point of the internal wave. FP5_Contract No.: EVK1-CT1999-00004 Version: 1.2 Date: 24.08.2004 File: D28.doc Page 17 of 92 Figure 16 : Coriolis effect on the internal wave propagation. °C °C °C °C °C °C
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D28: Internal seiche mixing study - Hydromod

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