Frontal collision of internal solitary waves of first mode

• Published in: Wave motion 2018-03, Vol.77, p.229-242
• Main Authors: Terletska, K., Jung, K.T., Maderich, V., Kim, K.O.
• Format: Article
• Language: English
• Subjects: Amplitudes; Collision dynamics; Collisions; Computational fluid dynamics; Fluids; Head-on collision; Interface stability; Internal solitary waves; Kelvin-Helmholtz instability; Navier-Stokes equations; Numerical modelling; Phase shift; Solitary waves; Studies; Thin films; Wave dispersion; Wave interaction; Wave power
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2017.12.006

The dynamics and energetics of a frontal collision of internal solitary waves (ISW) of first mode in a fluid with two homogeneous layers separated by a thin interfacial layer are studied numerically within the framework of the Navier–Stokes equations for stratified fluid. It was shown that the head-on collision of internal solitary waves of small and moderate amplitude results in a small phase shift and in the generation of dispersive wave train travelling behind the transmitted solitary wave. The phase shift grows as amplitudes of the interacting waves increase. The maximum run-up amplitude during the wave collision reaches a value larger than the sum of the amplitudes of the incident solitary waves. The excess of the maximum run-up amplitude over the sum of the amplitudes of the colliding waves grows with the increasing amplitude of interacting waves of small and moderate amplitudes whereas it decreases for colliding waves of large amplitude. 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%. 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. •Frontal collision of internal solitary waves is studied numerically.•Collision results in a wave phase shift growing with wave amplitude.•Nonlinear components of runup for waves of small and large amplitudes differs.•Collision of waves of large amplitude leads to the shear instability.•Collision of small and large amplitude waves triggers the shear instability.