Interaction of a subsurface bubble layer with long internal waves

Gavrilyuk, Sergey; Liapidevskii, V. Yu.; Чесноков, А. А.

doi:10.1016/j.euromechflu.2017.07.004

Cited by 11 publications

(11 citation statements)

References 31 publications

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“…Two types of "well posed" dissipation terms are proposed and studied. For the first type of dissipation, in some region of parameters φ and C r , the formation of a rotating cusp (angular point) on the hydraulic Futher development of this multi-dimensional model would be to add the dispersive effects to describe the multi-D wave propagation and breaking as was performed in 1D case in [12,9].…”

Section: Resultsmentioning

confidence: 99%

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Structure of the hydraulic jump in convergent radial flows

Ivanova

Gavrilyuk

2018

J. Fluid Mech.

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We are interested in the modelling of multi-dimensional turbulent hydraulic jumps in convergent radial flow. To describe the formation of intensive eddies (rollers) at the front of the hydraulic jump, a new model of shear shallow water flows is used. The governing equations form a non-conservative hyperbolic system with dissipative source terms. The structure of equations is reminiscent of generic Reynolds-averaged Euler equations for barotropic compressible turbulent flows. Two types of dissipative term are studied. The first one corresponds to a Chézy-like dissipation rate, and the second one to a standard energy dissipation rate commonly used in compressible turbulence. Both of them guarantee the positive definiteness of the Reynolds stress tensor. The equations are rewritten in polar coordinates and numerically solved by using an original splitting procedure. Numerical results for both types of dissipation are presented and qualitatively compared with the experimental works. The results show both experimentally observed phenomena (cusp formation at the front of the hydraulic jump) as well as new flow patterns (the shape of the hydraulic jump becomes a rotating square).

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Section: Resultsmentioning

confidence: 99%

“…We present now the numerical results for the first type of dissipation given by (9). The scenario of the hydraulic jump formation in convergent radial flow consists of the following three different stages.…”

Section: Shear Shallow Water Model With First Type Of Dissipationmentioning

confidence: 99%

Structure of the hydraulic jump in convergent radial flows

Ivanova

Gavrilyuk

2018

J. Fluid Mech.

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“…As it was mentioned above, we apply here a mild slope approximation. This means that the dimensionless bottom variation is weak [28,29]: z = Z(ε γ x), γ > 0. Due to this fact the terms ε 2 Z x and ε 2 Z xx can be neglected during the derivation of system (1).…”

Section: Governing Equationsmentioning

confidence: 99%

Hyperbolic model of internal solitary waves in a three-layer stratified fluid

Чесноков¹,

Liapidevskii²

2020

Preprint

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We derive a new hyperbolic model describing the propagation of internal waves in a stratified shallow water with a non-hydrostatic pressure distribution. The construction of the hyperbolic model is based on the use of additional 'instantaneous' variables. This allows one to reduce the dispersive multi-layer Green-Naghdi model to a first-order system of evolution equations. The main attention is paid to the study of three-layer flows over uneven bottom in the Boussinesq approximation with the additional assumption of hydrostatic pressure in the intermediate layer. The hyperbolicity conditions of the obtained equations of three-layer flows are formulated and solutions in the class of travelling waves are studied. Based on the proposed hyperbolic and dispersive models, numerical calculations of the generation and propagation of internal solitary waves are carried out and their comparison with experimental data is given. Within the framework of the proposed three-layer hyperbolic model, a numerical study of the propagation and interaction of symmetric and non-symmetric soliton-like waves is performed.

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“…According to [38,3,24] these parameters are as follows σ ≈ 0.15 and κ ∈ [2,6]. A mild slope approximation means that the dimensionless bottom variation is weak [32,11]:…”

Section: A Two-layer Long-wave Approximation Of the Homogeneous Eulermentioning

confidence: 99%

Hyperbolic model for free surface shallow water flows with effects of dispersion, vorticity and topography

Чесноков

Nguyen

2019

Computers & Fluids

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We derive a hyperbolic system of equations approximating the two-layer dispersive shallow water model for shear flows recently proposed by Gavrilyuk, Liapidevskii & Chesnokov (J. Fluid Mech., vol. 808, 2016, pp. 441-468). The use of this system for modelling the evolution of surface waves makes it possible to avoid the major numerical challenges in solving dispersive shallow water equations, which are connected with the resolution of an elliptic problem at each time instant and realization of non-reflecting conditions at the boundary of the calculation domain. It also allows one to reduce the computation time. The velocities of the characteristics of the obtained model are determined and the linear analysis is performed. Stationary solutions of the model are constructed and studied. Numerical solutions of the hyperbolic system are compared with solutions of the original dispersive model. It is shown that they almost coincide for large time intervals. The system obtained is applied to study non-stationary undular bores produced after interaction of a uniform flow with an immobile wall, non-hydrostatic shear flows over a local obstacle and the evolution of breaking solitary wave on a sloping beach.

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Interaction of a subsurface bubble layer with long internal waves

Cited by 11 publications

References 31 publications

Structure of the hydraulic jump in convergent radial flows

Structure of the hydraulic jump in convergent radial flows

Hyperbolic model of internal solitary waves in a three-layer stratified fluid

Hyperbolic model for free surface shallow water flows with effects of dispersion, vorticity and topography

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