2010
DOI: 10.1017/s0022112010000601
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Fully nonlinear higher-order model equations for long internal waves in a two-fluid system

Abstract: Fully nonlinear model equations, including dispersive effects at one-order higher approximation than in the model of Choi & Camassa (J. Fluid Mech., vol. 396, 1999, pp. 1–36), are derived for long internal waves propagating in two spatial horizontal dimensions in a two-fluid system, where the lower layer is of infinite depth. The model equations consist of two coupled equations for the displacement of the interface and the horizontal velocity of the upper layer at an arbitrary elevation, and they are corre… Show more

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Cited by 22 publications
(26 citation statements)
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“…[13][14][15][16][17], and references therein). In the general case, an analytical study of this system requires quite lengthy calculations, especially when fully nonlinear dispersive approximations of higher orders are considered [16][17][18][19][20][21][22][23][24]. In the present work, it will be shown that in the case ǫ ≪ 1 (the so called Boussinesq limit), there exists an elegant and remarkably short way how to derive fully nonlinear dispersive models of high orders.…”
mentioning
confidence: 91%
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“…[13][14][15][16][17], and references therein). In the general case, an analytical study of this system requires quite lengthy calculations, especially when fully nonlinear dispersive approximations of higher orders are considered [16][17][18][19][20][21][22][23][24]. In the present work, it will be shown that in the case ǫ ≪ 1 (the so called Boussinesq limit), there exists an elegant and remarkably short way how to derive fully nonlinear dispersive models of high orders.…”
mentioning
confidence: 91%
“…This situation with internal waves is in contrast with the exact description of 2D surface waves of constant vorticity [30], where at least numerical implementation is simple and efficient with a fast Fourier transform. That is why the problem of simplified description for moderately steep interfacial waves has attracted much attention in last years [16][17][18][19][20][21][22][23][24]. Here we suggest a simple procedure for the Boussinesq case.…”
mentioning
confidence: 99%
“…The results showed some differences between this model and the Euler-RL solution for a deep-configuration case. Debsarma, Das & Kirby (2010) improved the deep-water model of Choi & Camassa (1999) and Camassa et al (2006), and increased the approximation to O( 2 ) terms, where = h 2 /λ. Some differences between the Euler-RL solution and the results given by Debsarma et al (2010) for the deep-configuration case were observed.…”
Section: Introductionmentioning
confidence: 99%
“…By including higher order terms and more accurate vertical velocity distributions, the BE has been improved so that the linear dispersion can be extended to deep water conditions [2][3][4][5][6][7][8][9][10]. Recently, new forms of BE have been developed with higher-order accuracy, which extends the applicability ranging from shallow to deep waters [11,12]. BE is usually modified by adding dissipation terms or the artificial viscosity in momentum equations to account for energy dissipation of wave breaking in the surf zone [13].…”
Section: Introductionmentioning
confidence: 99%