Internal solitary waves: propagation, deformation and disintegration

Grimshaw, Roger; Pelinovsky, Efim; Talipova, Tatiana; Kurkina, Oxana

doi:10.5194/npg-17-633-2010

Cited by 162 publications

(149 citation statements)

References 71 publications

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“…In many cases of the vertical distribution of density and shear flow the coefficient of the quadratic nonlinear term is small (for instance, it is zero for a two-layer flow with equal thicknesses), and the cubic nonlinear term should be accounted in the same order of perturbation theory as the quadratic nonlinear term. This combined Kortewegde Vries equation is called the Gardner equation, and it is very often used to model the solitary internal waves in the ocean with real stratification (Grimshaw et al, , 2010a), or to demonstrate that modulation instability leads to the formation of rogue internal waves (Grimshaw et al, 2010b;Talipova et al, 2011), or to describe transformation of the internal tide in the coastal zone . In the latter case in the initial stage of the transformation dispersion effects are negligible (Smyth and Holloway, 1988;Sakai and Redekopp, 2007;Zahibo et al, 2007) and so the dispersionless Gardner equation can be chosen as an appropriate model:…”

Section: Dispersionless Gardner Equation For Long Internal Wavesmentioning

confidence: 99%

Fourier spectrum and shape evolution of an internal Riemann wave of moderate amplitude

Kartashova

Pelinovsky

Talipova

2013

Nonlin. Processes Geophys.

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The nonlinear deformation of long internal waves in the ocean is studied using the dispersionless Gardner equation. The process of nonlinear wave deformation is determined by the signs of the coefficients of the quadratic and cubic nonlinear terms; the breaking time depends only on their absolute values. The explicit formula for the Fourier spectrum of the deformed Riemann wave is derived and used to investigate the evolution of the spectrum of the initially pure sine wave. It is shown that the spectrum has exponential form for small times and a power asymptotic before breaking. The power asymptotic is universal for arbitrarily chosen coefficients of the nonlinear terms and has a slope close to –8/3

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Section: Dispersionless Gardner Equation For Long Internal Wavesmentioning

confidence: 99%

Fourier spectrum and shape evolution of an internal Riemann wave of moderate amplitude

Kartashova

Pelinovsky

Talipova

2013

Nonlin. Processes Geophys.

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“…We are guided by numerical solutions of Kortewegde Vries (KdV) type equations that incorporate both weak nonlinear and weak dispersive effects. The state of the art of the evolution of internal solitary waves (ISWs) across the continental shelf is reviewed in Grimshaw et al (2010). Grimshaw et al (2004) simulated the transformation of ISWs across the North West Shelf of Australia, the Malin shelf edge and the Arctic shelf; Holloway (1987) discussed the evolution of the internal tide in a two-layer ocean on the Australian North West Shelf.…”

Section: Introductionmentioning

confidence: 99%

Simulations and observation of nonlinear internal waves on the continental shelf: Korteweg–de Vries and extended Korteweg–de Vries solutions

O’Driscoll

Levine²

2017

Ocean Sci.

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Abstract. Numerical solutions of the Kortewegde Vries (KdV) and extended Korteweg-de Vries (eKdV) equations are used to model the transformation of a sinusoidal internal tide as it propagates across the continental shelf. The ocean is idealized as being a two-layer fluid, justified by the fact that most of the oceanic internal wave signal is contained in the gravest mode. The model accounts for nonlinear and dispersive effects but neglects friction, rotation and mean shear. The KdV model is run for a number of idealized stratifications and unique realistic topographies to study the role of the nonlinear and dispersive effects. In all model solutions the internal tide steepens forming a sharp front from which a packet of nonlinear solitary-like waves evolve. Comparisons between KdV and eKdV solutions are made. The model results for realistic topography and stratification are compared with observations made at moorings off Massachusetts in the Middle Atlantic Bight. Some features of the observations compare well with the model. The leading face of the internal tide steepens to form a shock-like front, while nonlinear high-frequency waves evolve shortly after the appearance of the jump. Although not rank ordered, the wave of maximum amplitude is always close to the jump. Some features of the observations are not found in the model. Nonlinear waves can be very widely spaced and persist over a tidal period.

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“…Similar to the case 1, the characteristics and energy loss of the amplitude-modulated wave packet for the case 5 were also similar with the breather definition. Noted that the breather solution exist only if the cubic nonlinearity coefficients in Gardner equation is positive (Lamb et al, 2007), but the configuration of the stratification in our simulation results a negative cubic nonlinearity coefficient in Gardner equation (Grimshaw et al, 2010;Talipova et al, 2011) and it means the breather is not allowed The oscillating tail was frequently observed in similar studies (Carr et al, 2015;Olsthoorn et al, 2013;Stastna et al, 2015). Its generation was related to the shear, and the tail was sustained by continuous energy input.…”

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confidence: 63%

The evolution of mode-2 internal solitary waves modulated by background shear currents

Zhang¹,

Xu²,

Qun³

et al. 2018

Preprint

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Abstract. The evolution process of mode-2 internal solitary waves (ISWs) modulated by the background shear currents was investigated numerically. The forward-propagating long wave, amplitude-modulated wave packet were generated during the early stage of modulation, where the amplitude-modulated wave packet were suggested playing an important role in the energy transfer 15 process, and then the oscillating tail was generated and followed the solitary wave. Five different cases were introduced to assess the sensitivity of the energy transfer process to the Δ, which defined as a dimensionless distance between the centers of pycnocline and shear current. The forward-propagating long waves were found robust to the Δ, but the oscillating tail and amplitude-modulated wave packet decreased in amplitude with increasing Δ. The highest energy loss rate was observed when Δ = 0. In the 20 first 30 periods, ~36% of the total energy lost at an average rate of 9 W m -1 , it would deplete the energy of the solitary wave in ~4.5 h, corresponding to a propagation distance of ~5 km, which is consistent with the hypothesis of Shroyer et al. (2010), who speculated that the mode-2 ISWs are "short-lived" in the presence of shear currents.

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Internal solitary waves: propagation, deformation and disintegration

Cited by 162 publications

References 71 publications

Fourier spectrum and shape evolution of an internal Riemann wave of moderate amplitude

Fourier spectrum and shape evolution of an internal Riemann wave of moderate amplitude

Simulations and observation of nonlinear internal waves on the continental shelf: Korteweg–de Vries and extended Korteweg–de Vries solutions

The evolution of mode-2 internal solitary waves modulated by background shear currents

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