Generation of second mode solitary waves by the interaction of a first mode soliton with a sill

Abstract

Abstract.Results of an experimental and theoretical study of the interaction of a first mode internal solitary wave with a localised bottom topography (sill) are presented. Laboratory experiments have been performed in a 10m long and 0.33m wide channel filled with a stratified fluid. The interface between the two layers (fresh and salt water) is diffuse and has a finite thickness. Soliton-type disturbances of the interface having characteristics of the first baroclinic mode are generated at one channel end. They move along the channel and encounter an underwater obstacle (sill) in the middle of the channel, where they break into reflected and transmitted waves. Two types of internal waves are produced by the interaction: a fast first mode internal soliton and a slower (by a factor of approximately 3) second mode soliton-like wave.A numerical model, based on the two-dimensional NavierStokes equations in the Boussinesq approximation, is used to reproduce the laboratory experiment. The detailed analysis of the horizontal and vertical structures of transmitted and reflected waves showed that the fast reflected and transmitted waves observed in the experiment can be interpreted as a first mode internal solitary wave whose characteristics are very close to those of the K-dV solitons. It is also demonstrated that the slow speed waves, generated during the interaction behind the first fast wave have vertical and horizontal structures very close to the second mode internal K-dV solitons.

A weakly nonlinear model for multi-modal evolution of wind-generated long internal waves in a closed basin

“…Hüttemann and Hutter (2001) observed emergence of solitary waves of the second vertical mode when a mode-one soliton ran over a sill in a long laboratory channel. At the same time, Vlasenko and Hutter (2001) simulated the twodimensional Navier-Stokes equations in the same configuration as Hüttemann's experiment, and detailed structure of the flow field was obtained, confirming that both the first and the second mode solitons are very close to those obtained by Korteweg-de Vries (KdV) theory.…”

Combined Effect of Rotation and Topography on Shoaling Oceanic Internal Solitary Waves

“…However, the numerical solution is fully nonlinear and includes rotation effects that are not considered in the theory and may contribute to the numerical observation. There have been several previous reports of a secondmode disturbance [see Vlasenko and Hutter (2001), Vlasenko and Alpers (2005), and sections 5.4.3 and 6.4 of the monograph by Vlasenko et al (2005), for instance], excited by interaction of a first-mode ISW with topography, but this would seem to be the first identification of such a disturbance as a breather where background rotation is involved.…”

Convex and concave types of second baroclinic mode internal solitary waves

“…Deeper in the water column, the opposite displacement occurs, creating what has been described as a bulge-shaped, double-humped, varicose, or sausage-type wave (Davis and Acrivos, 1967;Stamp and Jacka, 1995;Ostrovsky and Stepanyants, 2005;Moum et al, 2008). Pioneering investigations have described this type of wave, including theoretical investigations (Benjamin, 1967;Davis and Acrivos, 1967;Akylas and Grimshaw, 1992;Vlasenko, 1994;Grimshaw, 1997), laboratory experiments (Davis and Acrivos, 1967;Kao and Pao, 1980;Maxworthy, 1980;Honji et al, 1995;Stamp and Jacka, 1995;Vlasenko and Hutter, 2001;Mehta et al, 2002;Sutherland, 2002), numerical analyses (Tung et al, 1982;Terez and Knio, 1998;Rubino et al, 2001;Vlasenko and Hutter, 2001;Rusås and Grue, 2002;Stastna and Peltier, 2005;Vlasenko and Alpers, 2005), and field observations (Farmer and Smith, 1980;Konyaev et al, 1995;Imberger, 1998, 2001;Antenucci et al, 2000;Boegman et al, 2003;Duda et al, 2004;Yang et al, 2004;Bougucki et al, 2005;Sabinin and Serebryany, 2005;Moum et al, 2008;Shroyer et al, 2010).…”