Terletska K. Dynamics of large amplitude internal waves

Numerical simulation methods are used to study the dynamics of internal waves of large amplitudes, that are under description of the asymptotic models. An improved numerical hydrodynamic model of stratified flows was used to study the transformation of waves of large amplitudes in reservoirs with arbitrary stratification and abrupt changes in the bottom topography. Numerical simulation allowed us to find the limits of applicability of asymptotic models, to estimate energy losses during transformation over bottom inhomogeneities, wave interaction with each other, and wave breaking on the shelf. The influence of geometric parameters such as wave amplitude, fluid stratification (depth of the upper layer h1 and depth of the lower layer h2+ above the shelf or underwater obstacle), the angle of shelf inclination and the length and shape of the underwater obstacle on the transformation of the waves and energy loss on the shelf and above the bottom relief features are investigated. A new parameter B (blocking parameter) is proposed. Blocking parameter is the ratio of the height of the lower layer above an obstacle or shelf to the amplitude of an internal solitary wave that approaches it. Parameter B was used for describing the transformation of the internal solitary waves of both the first and second baroclinic modes over obstacles and abrupt changes in the bottom topography. With the help of this parameter, various types of interaction between the waves of the first and second modes were classified, both for the two-layer and for the three-layer stratification. For various types of waves, stratifications and obstacle shapes, self-similar dependences of the energy loss during the transformation of internal waves over these obstacles and bottom features were obtained. In the study of the influence of the tilt angle on the transformation of the waves, a new scenario of the non-adiabatic transformation of internal waves on an inclined bottom was described. A new mechanism of generation of breathers for internal waves in the range of intermediate wavelengths during the transformations of the second baroclinic mode with sharp changes in the bottom relief has been discovered. Unlike the waves of small and moderate amplitudes collision of ISWs of large amplitude was accompanied by shear instability and the formation of Kelvin–Helmholtz (KH) vortices in the interface layer. However, subsequently waves again become stable. The loss of energy due to the KH instability does not exceed 5%–6% from energy of incident wave. An interaction of large amplitude ISW with even small amplitude ISW can trigger instability of larger wave and development of KH billows in larger wave. When smaller wave amplitude increases the wave interaction was accompanied by KH instability of both waves. A new classification of modes of interaction of internal waves with an idealized trapezoidal shelf has been constructed. It was established the correspondence of the proposed classification with the results of laboratory and field experiments. According to the simulation results, the energy losses of the waves on the shelf were estimated and the dependence of the energy losses of the waves during transformation on the characteristics of the waves, stratification and relief was obtained. Zonal maps of regimes for the South China Sea with locations of intensive mixing on the shelf were constructed. Numerical study of degeneration of internal seiche in the deep elongated lake with spoon-like topography showed flow focusing by topography and the supercritical internal jet formation. That internal critical jet causes vortex pairs in the thermocline with like-wave wake that can be visible at the surface. Modeling of interaction of internal seiche with a North end of Loch Ness confirms possibility of the supercritical internal jet generation and subsequent internal and surface disturbances.