3-D nonhydrostatic numerical modelling of strongly nonlinear internal waves

1. 3-D nonhydrostatic numerical modelling of strongly nonlinear internal waves V. Maderich, M. Zheleznyak, E. Terletska, V. Koshebutskyy, M. Morgunov IMMSP, Cybernetics Center of National Academy of Sciences, Kiev, Ukraine

2. Overview of Research Activities in the second year • Task 4. Improvement and validation of numerical nonhydrostatic models for lakes. • Subtask 4.2 Improvement and adaptation of 3D numerical nonhydrostatic model for lakes • Subtask 4.3 Validation study of numerical models by using analytical solutions and laboratory experimental data • Task 4. Numerical simulations of the degeneration of basin-scale waves and wave enhanced meromixis in lakes • Subtask 5.1 Numerical modeling of the transformation of short-period internal waves over underwater obstacles

3. Subtask 4.2 Improvement and adaptation of 3D numerical nonhydrostatic model for lakes • The 3D nonhydrostatic numerical model developed by IMMSP (Kanarska, Maderich, 2003) was further improved by use the generalized vertical coordinate (Mellor et al., 2002). • The generator of the internal solitary wave (Vlasenko, Hutter, 2001) was implemented for the internal solitary wave of large amplitude. • The algorithm “wetting-drying” was implemented in the model to describe lake dynamics

4. Description of non-hydrostatic model

5. Governing equations

6. Numerical method • 1 stage: Free surface elevation • 2 stage: Hydrostatic components of the velocity and pressure fields • 3 stage:Non-hydrostatic components of the velocity and pressure fields • 4 stage: Scalar fields

7. Generalisation of sigma system

9. Quasi Z-coordinate system Quasi Z system system

10. Subtask 5.1 Numerical modeling of the transformation of short-period internal waves over underwater obstacles • A nonlinear dynamics of the degeneration of basin-scale waves in a closed basin filled with two water layers of different density was investigated with a 3D non-hydrostatic model. The effects of shelf were simulated. • The numerical modeling of the transformation of the internal solitary waves over underwater obstacles was done. These simulations were compared with the laboratory data of IHM.

11. Parameters of numerical experiments

12. Experiment E

13. t=0 s t=25 s t=65 s t=80 s

14. Experiment F

15. t=0 s t=25 s t=35 s t=45 s

16. Internalsolitarywavepassingoveranobstacle

18. Initial salinity profile

19. Results of experiment

20. Results of calculation

21. Density

22. Vorticity

24. Current research activities in the third year • 5. Numerical simulations of the degeneration of basin-scale waves and wave enhanced meromixis in lakes • 5.2 Numerical simulation of internal waves interaction with constrictions and widenings.

25. Internal solitary wave passing through the narrowing Plane view of the laboratory flume

26. Laboratory experiment

27. Numerical simulation

28. Plane view of interface

29. Comparison of non-hydrostatic and hydrostatic model

30. Experiments G and H

31. Experiment Gnon-hydrostatic modelling

32. Experiment HHydrostatic modelling

33. Aims of activity • By comparison of the energy transformations in the hydrostatic and non-hydrostatic models to derive parameterization of the mixing in the lakes resulted from seiche motions.