High-level Green–Naghdi wave models for nonlinear wave transformation in three dimensions

Zhao, Binbin; Duan, Wenyang; Ertekin, R. Cengiz; Hayatdavoodi, Masoud

doi:10.1007/s40722-014-0009-8

Cited by 34 publications

(15 citation statements)

References 21 publications

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“…High-level GN equations, applicable to wave propagation in any water depth, are obtained by assuming higher-order polynomials for the distribution of the vertical velocity along the water column. Among others, see Shields and Webster [64], Webster and Kim [72], Demirbilek and Webster [9], and more recently Zhao et al [83][84][85], for discussion on high-level GN equations.…”

Section: The Green-naghdi Equationsmentioning

confidence: 99%

“…Shields and Webster [64] investigated the applicable range for modeling a two-dimensional wave using the Level I equations used here. They determined that the Level I GN equations are appropriate for wavelengths greater than approximately 7.0h, see also Zhao et al [84,85]. The wave height of 0.2h is chosen because this wave height was used by Chakrabarti [6].…”

Section: Single Vertical Cylindermentioning

confidence: 99%

“…The Level I Green-Naghdi equations are used, for example, to determine the hydroelastic response of VLFS to solitary and cnoidal waves by Ertekin and Kim [14], Ertekin et al [20], Xia et al [78,79], Ertekin and Xia [16], and by Demirbilek and Webster [10], Ertekin and Sundararaghavan [15] to study refraction and diffraction of nonlinear waves in coastal waters and to study solitary and cnoidal wave loads on horizontal decks by Hayatdavoodi and Ertekin [30][31][32], Hayatdavoodi et al [33]. Further discussion on the recent developments on the Green-Naghdi equations, with comparisons between high-level equations and laboratory experiments, can be found in Kim et al [38], Ertekin et al [21], Zhao et al [83][84][85], among others. Theoretical models based on the Green-Naghdi and the Boussinesq equations were recently developed by Neill et al [50] to study the interaction of solitary wave with multiple in-line, vertical cylinders.…”

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confidence: 99%

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Diffraction of cnoidal waves by vertical cylinders in shallow water

Hayatdavoodi

Neill

Ertekin

2018

Theor. Comput. Fluid Dyn.

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Diffraction of nonlinear waves by single or multiple in-line vertical cylinders in shallow water is studied by use of different nonlinear, shallow-water wave theories. The fixed, in-line, vertical circular cylinders extend from the free surface to the seafloor and are located in a row parallel to the incident wave direction. The wave-structure interaction problem is studied by use of the nonlinear generalized Boussinesq equations, the Green-Naghdi shallow-water wave equations, and the linearized version of the shallow-water wave equations. The wave-induced force and moment of the Green-Naghdi and the Boussinesq equations are presented when the incoming waves are cnoidal, and the forces are compared with the experimental data when available. Results of the linearized equations are compared with the nonlinear results. It is observed that nonlinearity is very important in the calculation of the wave loads on circular cylinders in shallow water. The variation of wave loads with wave height, wavelength and the spacing between cylinders is studied. Effect of the neighboring cylinders, and the shielding effect of upwave cylinders on the wave-induced loads on downwave cylinders are discussed.

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Section: The Green-naghdi Equationsmentioning

confidence: 99%

Section: Single Vertical Cylindermentioning

confidence: 99%

mentioning

confidence: 99%

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Diffraction of cnoidal waves by vertical cylinders in shallow water

Hayatdavoodi

Neill

Ertekin

2018

Theor. Comput. Fluid Dyn.

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“…Nevertheless, the great complexity of the GN equations beyond the 1 st level has virtually prohibited their use in studies of time-dependent nonlinear flows depending on both horizontal coordinates. This led Zhao & Duan (2010), Webster et al (2011), Zhao et al (2014) and Zhao et al (2015) to simplify the higher-level GN equations by discarding high derivative terms in order to make any headway. These simplified equations are not derivable from a variational principle, so there is no guarantee of basic conservation of energy, etc.…”

Section: Introductionmentioning

confidence: 99%

On the regularity of the Green–Naghdi equations for a rotating shallow fluid layer

Dritschel

Jalali

2019

J. Fluid Mech.

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The Green–Naghdi equations are an extension of the shallow-water equations that capture the effects of finite fluid depth at arbitrary order in the characteristic height to width aspect ratio $H/L$. The shallow-water equations capture these effects to first order only, resulting in a relatively simple two-dimensional fluid-dynamical model for the layer horizontal velocity and depth. The Green–Naghdi equations, like the shallow-water equations, are two-dimensional fluid equations expressing momentum and mass conservation. There are different ‘levels’ of the Green–Naghdi equations of rapidly increasing complexity. In the present paper we focus on the behaviour of the lowest-level Green–Naghdi equations for a rotating shallow fluid layer, paying close attention to the flow structure at small spatial scales. We compare directly with the shallow-water equations and study the differences arising in their solutions. By recasting the equations into a form which both explicitly conserves Rossby–Ertel potential vorticity and represents the leading-order departure from geostrophic–hydrostatic balance, we are able to accurately describe both the ‘slow’ predominantly sub-inertial balanced dynamics and the ‘fast’ residual imbalanced dynamics. This decomposition has proved fruitful in studies of shallow-water dynamics but appears not to have been used before in studies of Green–Naghdi dynamics. Importantly, we find that this decomposition exposes a fundamental inconsistency in the Green–Naghdi equations for horizontal scales less than the mean fluid depth, scales for which the Green–Naghdi equations are supposed to more accurately model. Such scales exhibit pronounced activity compared to the shallow-water equations, and in particular spectra for certain fields like the divergence are flat or rising at high wavenumbers. This indicates a lack of convergence at small scales, and is also consistent with the poor convergence of total energy with resolution compared to the shallow-water equations. We suggest a mathematical reformulation of the Green–Naghdi equations which may improve convergence at small scales.

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“…In using a numerical method to analyze the problem of fluid-structure interaction, many researchers tend to use the potential flow theory with the assumptions of nonviscous and irrotational flow (e.g., Meng 2008;An and Faltinsen 2012;Ertekin et al 2014;Zhao et al 2014;Zhao et al 2015;Guo et al 2015b). The governing equations are reduced to Laplace's equation in the assumptions, and velocities can be obtained by velocity potential.…”

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confidence: 99%

Review of wave forces on bridge decks with experimental and numerical methods

Chen

et al. 2021

ABEN

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Massive coastal bridges were damaged in Hurricanes Ivan (2004) and Katrina (2005), and considerable efforts have been devoted to the studies of wave forces acting on bridge decks since then. When the hurricane and tsunamis approach the coastal zones, the mean water level is elevated, making it possible for the incident wave to hit the bridge deck directly. The study of wave force acting on the bridge deck is essential for the investigation of bridge failure mechanism, and a literature review of wave forces with experimental and numerical methods after Hurricanes Ivan and Katrina is presented in this paper. Though the experiments and numerical models can not fully simulate the wave-deck interaction as in realistic conditions, remarkable progress has been achieved, and some significant findings help the researchers to further understand the failure mechanism of the bridge deck. Emphasis is given to the studies that have significantly improved our understanding of the topic. Challenges associated with the existing studies and suggestions for future studies are presented for a deeper understanding of the failure mechanism of the bridge deck, and more countermeasures are expected to protect the bridge deck under extreme wave forces.

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High-level Green–Naghdi wave models for nonlinear wave transformation in three dimensions

Cited by 34 publications

References 21 publications

Diffraction of cnoidal waves by vertical cylinders in shallow water

Diffraction of cnoidal waves by vertical cylinders in shallow water

On the regularity of the Green–Naghdi equations for a rotating shallow fluid layer

Review of wave forces on bridge decks with experimental and numerical methods

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