Large amplitude internal solitary waves over a shelf

Abstract

Abstract. Dynamics of large amplitude internal waves in two-layers of shallow water is considered.It is demonstrated that in laboratory experiments the subsurface waves of depression over a shelf may be simulated by internal symmetric solitary waves of the mode 2 ("lump-like" waves). The mathematical model describing the propagation and decaying of large internal waves in two-layer fluid is introduced. It is a variant of Choi-Camassa equations with hydrostatic pressure distribution in one of the layers. It is shown that the numerical scheme developed for the GreenNaghdi equations in open channel flows may be applied for the description of large amplitude internal waves over a shelf.

Outcomes of the Special Issue on Extreme and Rogue Waves

“…The total height of the waves is very large and they must be considered as a significant factor controlling the environment in this basin. Gavrilov et al (2011) presented the results of laboratory experiments with large-amplitude internal waves in a twolayer fluid. A mathematical model describing the propagation and decaying of large internal waves in a two-layer fluid is introduced.…”

Mass and momentum transfer by solitary internal waves in a shelf zone

“…In dimensionless variables (H = 1, ρ + = 1,b = 1), the two-layer shallow water equations representing the model 2 (Eq. 16 in Gavrilov et al, 2011) take the form…”

“…In the domain (0 < y < H ) symmetric internal waves of the second mode can be considered as the waves of depression, so to describe their dynamics we use the model 2 from Gavrilov et al (2011). Let H be the reference length,b = (ρ − ρ − )g/ρ + be the reference buoyancy and ρ + be the reference density.…”

“…Mathematical models using two-layer scheme of flow have been analyzed in Gavrilov et al (2011). One of them was the full nonlinear model, taking into account the nonhydrostatic effects in both layers (model 1, Choi and Camassa, 1999).…”

“…One of them was the full nonlinear model, taking into account the nonhydrostatic effects in both layers (model 1, Choi and Camassa, 1999). The further simplification of the model has been achieved by using the hydrostatic pressure distribution in one of the layers (models 2 and 3 in Gavrilov et al, 2011). It was shown by comparing exact solutions for models 1-3 that the generation and propagation of large amplitude solitary waves in a two-layer fluid in the channel of finite depth is governed by nonhydrostatic effects in an outer layer.…”