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

Overview of Research Activities in the second year Task 4. Improvement and validation of numerical nonhydrostatic models for lakes. 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 4.2 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 Subtask 4.3 Validation study of numerical models by using analytical solutions and laboratory experimental data Task 4. 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 Subtask 5.1 Numerical modeling of the transformation of short-period internal waves over underwater obstacles

Subtask 4.2 Improvement and adaptation of 3D numerical nonhydrostatic model for lakes 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 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 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 The algorithm “wetting-drying” was implemented in the model to describe lake dynamics

Description of non- hydrostatic model

Governing equations

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

Generalisation of sigma system

Quasi Z-coordinate system Quasi Z system system system

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. 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. 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.

Parameters of numerical experiments

Experiment E

t=0 s t=25 s t=65 s t=80 s

Experiment F

t=0 s t=25 s t=35 s t=45 s

Internal solitary wave passing over an obstacle

Initial salinity profile

Results of experiment

Results of calculation

Density

Vorticity

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.

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

Laboratory experiment

Numerical simulation

Plane view of interface

Comparison of non-hydrostatic and hydrostatic model

Experiments G and H

Experiment G non-hydrostatic modelling

Experiment H Hydrostatic modelling

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. 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.