Convex and concave types of second baroclinic mode internal solitary waves

Yang, Yiing Jang; Fang, Y. C.; Tang, Tie-Qiao; Ramp, Steven R.

doi:10.5194/npg-17-605-2010

Cited by 74 publications

(74 citation statements)

References 47 publications

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“…Our simulations also showed the formation of both convex and concave mode-two waves which evolved from the shoaling mode-one wave, as observed by Yang et al (2009Yang et al ( , 2010. In the simulations they were present at the depths of the observed waves.…”

Section: Discussionsupporting

confidence: 59%

“…In a pilot program Yang et al (2004) observed a single mode-two wave in 426 m deep water. Yang et al (2009Yang et al ( , 2010 analysed mooring data obtained during the VANS/WISE program which was conducted in 2005 and 2006 in the vicinity of the ASIAEX field program. Data from a mooring deployed along the 350 m isobath was analysed and showed the occurrence of many mode-two waves.…”

Section: Discussionmentioning

confidence: 99%

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Two-dimensional numerical simulations of shoaling internal solitary waves at the ASIAEX site in the South China Sea

Lamb

Warn-Varnas

2015

Nonlin. Processes Geophys.

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Abstract. The interaction of barotropic tides with LuzonStrait topography generates some of the world's largest internal solitary waves which eventually shoal and dissipate on the western side of the northern South China Sea. Twodimensional numerical simulations of the shoaling of a single internal solitary wave at the site of the Asian Seas International Acoustic Experiment (ASIAEX) have been undertaken in order to investigate the sensitivity of the shoaling process to the stratification and the underlying bathymetry and to explore the influence of rotation. The bulk of the simulations are inviscid; however, exploratory simulations using a vertical eddy-viscosity confined to a near bottom layer, along with a no-slip boundary condition, suggest that viscous effects may become important in water shallower than about 200 m. A shoaling solitary wave fissions into several waves. At depths of 200-300 m the front of the leading waves become nearly parallel to the bottom and develop a very steep back as has been observed. The leading waves are followed by waves of elevation (pedestals) that are conjugate to the waves of depression ahead and behind them. Horizontal resolutions of at least 50 m are required to simulate these well. Wave breaking was found to occur behind the second or third of the leading solitary waves, never at the back of the leading wave. Comparisons of the shoaling of waves started at depths of 1000 and 3000 m show significant differences and the shoaling waves can be significantly non-adiabatic even at depths greater than 2000 m. When waves reach a depth of 200 m, their amplitudes can be more than 50 % larger than the largest possible solitary wave at that depth. The shoaling behaviour is sensitive to the presence of small-scale features in the bathymetry: a 200 m high bump at 700 m depth can result in the generation of many mode-two waves and of higher mode waves. Sensitivity to the stratification is considered by using three stratifications based on summer observations. They primarily differ in the depth of the thermocline. The generation of mode-two waves and the behaviour of the waves in shallow water is sensitive to this depth. Rotation affects the shoaling waves by reducing the amplitude of the leading waves via the radiation of long trailing inertiagravity waves. The nonlinear-dispersive evolution of these inertia-gravity waves results in the formation of secondary mode-one wave packets.

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Section: Discussionsupporting

confidence: 59%

Section: Discussionmentioning

confidence: 99%

Two-dimensional numerical simulations of shoaling internal solitary waves at the ASIAEX site in the South China Sea

Lamb

Warn-Varnas

2015

Nonlin. Processes Geophys.

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“…An extension involving up to the fourth-order nonlinear terms was derived in Kurkina et al (2011b). The model of Yang et al (2010) involved both modes of IWs in a general three-layer ocean, the first order in nonlinearity and dispersion (Korteweg-de Vries (KdV) approximation; only mode-2 waves were analyzed). The weakly nonlinear theory for a continuously stratified fluid can be used to derive the parameters of evolution equations for IWs in a three-layer fluid Yang et al, 2010).…”

Section: O E Kurkina Et Al: Propagation Regimes Of Interfacial Solmentioning

confidence: 99%

“…The model of Yang et al (2010) involved both modes of IWs in a general three-layer ocean, the first order in nonlinearity and dispersion (Korteweg-de Vries (KdV) approximation; only mode-2 waves were analyzed). The weakly nonlinear theory for a continuously stratified fluid can be used to derive the parameters of evolution equations for IWs in a three-layer fluid Yang et al, 2010). These parameters for continuous stratification are given in the form of integral expressions including the vertical mode (whose shape is determined by the density stratification), its higher-order corrections and their derivatives (Lamb and Yan, 1996;Pelinovskii et al, 2000;Grimshaw et al, 2002).…”

Section: O E Kurkina Et Al: Propagation Regimes Of Interfacial Solmentioning

confidence: 99%

Propagation regimes of interfacial solitary waves in a three-layer fluid

Kurkina¹,

Kurkin²,

Rouvinskaya³

et al. 2015

Nonlin. Processes Geophys.

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Abstract. Long weakly nonlinear finite-amplitude internal waves in a fluid consisting of three inviscid layers of arbitrary thickness and constant densities (stable configuration, Boussinesq approximation) bounded by a horizontal rigid bottom from below and by a rigid lid at the surface are described up to the second order of perturbation theory in small parameters of nonlinearity and dispersion. First, a pair of alternatives of appropriate KdV-type equations with the coefficients depending on the parameters of the fluid (layer positions and thickness, density jumps) are derived for the displacements of both modes of internal waves and for each interface between the layers. These equations are integrable for a very limited set of coefficients and do not allow for proper description of several near-critical cases when certain coefficients vanish. A more specific equation allowing for a variety of solitonic solutions and capable of resolving most near-critical situations is derived by means of the introduction of another small parameter that describes the properties of the medium and rescaling of the ratio of small parameters. This procedure leads to a pair of implicitly interrelated alternatives of Gardner equations (KdV-type equations with combined nonlinearity) for the two interfaces. We present a detailed analysis of the relationships for the solutions for the disturbances at both interfaces and various regimes of the appearance and propagation properties of soliton solutions to these equations depending on the combinations of the parameters of the fluid. It is shown that both the quadratic and the cubic nonlinear terms vanish for several realistic configurations of such a fluid.

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“…Although mode two internal solitary waves cannot normally exist as steady travelling waves due to a resonance with mode one short waves, they can be generated as transients by interaction with topography. Yang et al (2010) report observations of mode two waves on the continental slope of the South China Sea, and apparently for the first time, found two distinct types. The usual mode two wave typically has a convex form with a bulge in the pycnocline, and this kind is that usually found, However, the observations reported here show a few cases of a mode two wave with a convex form, with a localized thinning ("anti-bulge") of the pycnocline.…”

mentioning

confidence: 99%