A high-order nonlinear Boussinesq-type model for internal waves over a mildly-sloping topography in a two-fluid system

Liu, Zhongbo; Han, Peixiu; Fang, Kezhao; Liu, Yong

doi:10.1016/j.oceaneng.2023.115283

Cited by 2 publications

(2 citation statements)

References 29 publications

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“…The use of Boussinesq-type models for wave propagation and evolution on the impermeable seabed [20,21] has been fully developed, and some representative types of these equations include the extended Boussinesq-type models, with improved linear dispersion/shoaling characteristics [22][23][24][25]; the second-order nonlinear Boussinesq-type models [26,27]; the so-called fully nonlinear Boussinesq-type models [28][29][30][31][32]; and the extremely dispersive and nonlinear Boussinesqtype models [33][34][35][36]. More recently, using the methods proposed in the literature [30,33,35,37], a Boussinesq-type model for interfacial waves over a two-density system has been proposed.…”

Section: Introductionmentioning

confidence: 99%

High-Order Boussinesq Equations for Water Wave Propagation in Porous Media

Wang,

Liu,

Fang

et al. 2023

Water

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To accurately capture wave dynamics in porous media, the higher-order Boussinesq-type equations for wave propagation in deep water are derived in this paper. Starting with the Laplace equations combined with the linear and nonlinear resistance force of the dynamic conditions on the free surface, the governing equations were formulated using various independent velocity variables, such as the depth-averaged velocity and the velocity at the still water level and at an arbitrary vertical position in the water column. The derived equations were then improved, and theoretical analyses were carried out to investigate the linear performances with respect to phase celerity and damping rate. It is shown that Boussinesq-type models with Padé [4, 4] dispersion can be applied in deep water. A numerical implementation for one-dimensional equations expressed with free surface elevation and depth-averaged velocity is presented. Solitary wave propagation in porous media was simulated, and the computed results were found to be generally in good agreement with the measurements.

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Section: Introductionmentioning

confidence: 99%

High-Order Boussinesq Equations for Water Wave Propagation in Porous Media

Wang,

Liu,

Fang

et al. 2023

Water

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“…The Boussinesq-type (hereafter BT) models [8][9][10][11] are phase-solving and have many advantages in terms of computational efficiency and nonlinear wave interactions. There are many sophisticated versions of Boussinesq-type models (e.g., FUNWAVE, based on the equations of Wei and Kirby [12]; MIKE21 BW, based on the equations of Madsen and Srensen [13]), and the BT models have been significantly enriched and widely applied in the modelling of coastal waves and currents in complex bathymetric configurations [14][15][16]. Some of these models have been presented to couple either a one-dimensional BT wave model [17][18][19] or a two-dimensional BT wave model [20][21][22][23][24][25], with the sediment transport and morphological model presented.…”

Section: Introductionmentioning

confidence: 99%

A Beach Profile Evolution Model Driven by the Hybrid Shock-Capturing Boussinesq Wave Solver

Wang,

Fang,

Liu

et al. 2023

Water

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An existing Boussinesq wave model, solved in a hybrid format of the finite-difference method (FDM) and finite-volume method (FVM), with good merits of stability and shock-capturing, was used as the wave driver to simulate the beach evolution under nearshore wave action. By coupling the boundary layer model, the sand transport model, and the terrain updating model, the beach evolution model is established. Based on the coupled model, the interaction process between sandbars and waves was simulated, reproducing the process of the original sand bars diminishing, new sandbars creating, and finally disappearing. At the same time, the formation and movement process of sand bars under solitary and regular waves are numerically simulated, in the breaking zone, the water bottom has a larger shear stress, which promotes the sediment activation, transport and erosion formation, and near the breaking point, the decrease of sand-carrying capacity is the main reason for the formation of sandbars, the numerical model can accurately describe the changes in the shoreline profile under wave action.

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A high-order nonlinear Boussinesq-type model for internal waves over a mildly-sloping topography in a two-fluid system

Cited by 2 publications

References 29 publications

High-Order Boussinesq Equations for Water Wave Propagation in Porous Media

High-Order Boussinesq Equations for Water Wave Propagation in Porous Media

A Beach Profile Evolution Model Driven by the Hybrid Shock-Capturing Boussinesq Wave Solver

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