A generalized Korteweg‐de Vries model of internal tide transformation in the coastal zone

Holloway, Peter J.; Pelinovsky, Efim; Talipova, Tatiana

doi:10.1029/1999jc900144

Cited by 185 publications

(134 citation statements)

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“…Second, the horizontal variability of the density and background current field is important, particularly for the NWS situated at ~20S [Holloway et al, 1997]. Third is the cubic nonlinear effects which are often comparable with quadratic nonlinearity in tropical conditions [Holloway et al, 1999]. Fourth there is the Coriolis effect due to the Earth's rotation which influences the number and 5 amplitudes of the solitons generated from the internal tide [Gerkema, 1996].…”

Section: Generalized Korteweg-de Vries Equationmentioning

confidence: 99%

“…Fourth there is the Coriolis effect due to the Earth's rotation which influences the number and 5 amplitudes of the solitons generated from the internal tide [Gerkema, 1996]. All these factors are included in the theoretical model consisting of the generalized KdV equation [Holloway et al, 1999, 2001, Grimshaw et al, 2004. The basic equation of this model is…”

Section: Generalized Korteweg-de Vries Equationmentioning

confidence: 99%

“…For instance, the Princeton Ocean Model, based on the nonlinear primitive equations, shows a high degree of spatial variability in the amplitude and phase of internal wave currents and vertical displacements [Craig, 1988;Holloway, 1996;Holloway and Barnes, 1998]. On the other hand, weakly nonlinear and weakly dispersive models based on generalizations of the Korteweg-de Vries (KdV) equation also demonstrate the appearance of intense short-scale solitons from the internal tide on the NWS [Smyth & Holloway, 1988;Holloway et al, 1997Holloway et al, , 1999Holloway et al, , 2001Grimshaw et al, 2004]. Together these numerical and theoretical modeling studies demonstrate the important role of each of nonlinearity, dispersion, the Earth's rotation, the bottom slope and the horizontal variability of density stratification and the background current.…”

mentioning

confidence: 99%

“…The basic generalized KdV equation is briefly described in section 2. The coefficients of the model are calculated using the hydrological data on the NWS obtained by Holloway et al (1997Holloway et al ( , 1999; they are presented in section 3. Our results of numerical simulation of the solitary wave dynamics on the NWS are presented in section 4.…”

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confidence: 99%

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Modelling internal solitary waves on the Australian North West Shelf

Grimshaw

Pelinovsky

Stepanyants

et al. 2006

Mar. Freshwater Res.

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Abstract:The transformation of the nonlinear internal tide and the consequent development of internal solitary waves on the Australian North West Shelf is studied numerically in the framework of the generalized rotation-modified Korteweg-de Vries equation. This model contains both nonlinearity (quadratic and cubic), the Coriolis effect, depth variation and horizontal variability of the density stratification. The simulation results demonstrate that a wide variety of nonlinear wave shapes can be explained by the synergetic action of nonlinearity and the variability of the hydrology along the wave path.2

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Section: Generalized Korteweg-de Vries Equationmentioning

confidence: 99%

Section: Generalized Korteweg-de Vries Equationmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Modelling internal solitary waves on the Australian North West Shelf

Grimshaw

Pelinovsky

Stepanyants

et al. 2006

Mar. Freshwater Res.

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“…The model equation, dubbed here the Gardner-Ostrovsky (GO) equation (it is also known as the extended rotation-modified Korteweg-de Vries (KdV) equation), has been derived for the description of long internal waves of large amplitude [11]:…”

Section: Introductionmentioning

confidence: 99%

On Numerical Solution of the Gardner–Ostrovsky Equation

Obregon

Stepanyants

2012

Math. Model. Nat. Phenom.

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Abstract. A simple explicit numerical scheme is proposed for the solution of the GardnerOstrovsky equation ut + cux + αuux + α1u 2 ux + βuxxx x = γu which is also known as the extended rotation-modified Korteweg-de Vries (KdV) equation. This equation is used for the description of internal oceanic waves affected by Earth' rotation. Particular versions of this equation with zero some of coefficients, α, α1, β, or γ are also known in numerous applications. The proposed numerical scheme is a further development of the well-known finite-difference scheme earlier used for the solution of the KdV equation. The scheme is of the second order accuracy both on temporal and spatial variables. The stability analysis of the scheme is presented for infinitesimal perturbations. The conditions for the calculations with the appropriate accuracy have been found. Examples of calculations with the periodic boundary conditions are presented to illustrate the robustness of the proposed scheme.

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Effects of topography and Earth's rotation on the oblique interaction of internal solitary‐like waves in the Andaman Sea

Shimizu

Nakayama

2017

JGR Oceans

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High‐resolution three‐dimensional MITgcm simulations and an extended Miles theory are used to investigate the oblique interaction of internal solitary‐like waves (ISWs) in the Andaman Sea. Oblique solitary‐wave interaction is well studied in various fields of physics; however, this process in the ocean has seldom been investigated, despite the observations of its surface signature by remote sensing and potential fourfold increase of ISW amplitude by the development of a (Mach) stem. This study confirms the development of stem‐like ISWs under realistic oceanic conditions. The modeled interaction is found to be approximately consistent with the Miles theory extended to unequal incident‐wave amplitudes and small‐but‐finite incident angles. Although topography does not appear to affect the process in the deep part of the Andaman Sea, substantial topographic amplitude variation along the wave trough needs to be adjusted before comparisons with the theory. Earth's rotation has a small effect on ISW propagation due to the low latitude (≈9°N), but it does slow down the growth of stem‐like ISWs. Potential observation of the process by the next‐generation wide‐swath satellite altimeter is discussed.

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A generalized Korteweg‐de Vries model of internal tide transformation in the coastal zone

Cited by 185 publications

References 32 publications

Modelling internal solitary waves on the Australian North West Shelf

Modelling internal solitary waves on the Australian North West Shelf

On Numerical Solution of the Gardner–Ostrovsky Equation

Effects of topography and Earth's rotation on the oblique interaction of internal solitary‐like waves in the Andaman Sea

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