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3-D nonhydrostatic numerical modelling of strongly nonlinear internal waves

Explore the development and validation of 3-D nonhydrostatic models for lakes, including simulations of wave degeneration and meromixis. Investigation of basin-scale wave dynamics and interaction with obstacles. Improvement of internal wave modeling using advanced numerical methods.

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3-D nonhydrostatic numerical modelling of strongly nonlinear internal waves

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  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

  8. Quasi Z-coordinate system Quasi Z system system

  9. 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.

  10. Parameters of numerical experiments

  11. Experiment E

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

  13. Experiment F

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

  15. Internalsolitarywavepassingoveranobstacle

  16. Initial salinity profile

  17. Results of experiment

  18. Results of calculation

  19. Density

  20. Vorticity

  21. 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.

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

  23. Laboratory experiment

  24. Numerical simulation

  25. Plane view of interface

  26. Comparison of non-hydrostatic and hydrostatic model

  27. Experiments G and H

  28. Experiment Gnon-hydrostatic modelling

  29. Experiment HHydrostatic modelling

  30. 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.

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