Strongly nonlinear effects on internal solitary waves in three-layer flows

Barros, Ricardo; Choi, Woo-Young; Milewski, Paul A.

doi:10.1017/jfm.2019.795

Cited by 31 publications

(35 citation statements)

References 32 publications

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“…x , the u i 's are the layer-mean velocities, ρ i is the density of the i-th layer, and P(x, t) is the interfacial pressure. These results were generalized in Choi (2000), Barros et al (2020) to the case of n > 2 layers, together with the discussion of suitable conditions leading to systems of quasi-linear equations, which we summarize hereafter for the reader's convenience.…”

Section: Sharply Stratified N-layered Euler Fluidsmentioning

confidence: 97%

Hamiltonian Aspects of Three-Layer Stratified Fluids

et al. 2021

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The theory of three-layer density-stratified ideal fluids is examined with a view toward its generalization to the n-layer case. The focus is on structural properties, especially for the case of a rigid upper lid constraint. We show that the long-wave dispersionless limit is a system of quasi-linear equations that do not admit Riemann invariants. We equip the layer-averaged one-dimensional model with a natural Hamiltonian structure, obtained with a suitable reduction process from the continuous density stratification structure of the full two-dimensional equations proposed by Benjamin. For a laterally unbounded fluid between horizontal rigid boundaries, the paradox about the non-conservation of horizontal total momentum is revisited, and it is shown that the pressure imbalances causing it can be intensified by three-layer setups with respect to their two-layer counterparts. The generator of the x-translational symmetry in the n-layer setup is also identified by the appropriate Hamiltonian formalism. The Boussinesq limit and a family of special solutions recently introduced by de Melo Viríssimo and Milewski are also discussed.

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Section: Sharply Stratified N-layered Euler Fluidsmentioning

confidence: 97%

Hamiltonian Aspects of Three-Layer Stratified Fluids

et al. 2021

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“…The coefficients A and B are rather cumbersome and therefore they are not presented here. The existence of a positive root of this equation is a necessary condition for constructing a non-trivial solution to system (20) satisfying condition (22) for ξ → −∞. In particular, the fulfilment of this condition is necessary for the construction of solitary waves.…”

Section: Travelling Wavesmentioning

confidence: 99%

“…We recall that such a non-symmetric solitary wave exists only for a specific set of governing parameters [20]. In addition, similar non-symmetric solitary waves were recently obtained and studied in [22] within the framework of a three-layer long-wave dispersive model.…”

Section: Travelling Wavesmentioning

confidence: 99%

“…In particular, non-symmetric mode-2 ISWs were obtained and verified by comparison with the laboratory experiment [20]. Recently, a strongly non-linear long-wave model for large amplitude internal waves in a three-layer flow between two rigid boundaries was considered in [22]. Emphasis was given to the solitary waves of the second baroclinic mode and their strongly non-linear characteristics that fail to be captured by weakly non-linear models.…”

Section: Introductionmentioning

confidence: 99%

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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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“…x , the u i 's are the layer-mean velocities, ρ i is the density of the i-th layer, and P (x, t) is the interfacial pressure. These results were generalized in [15,2] to the case of n > 2 layers, together with the discussion of suitable conditions leading to systems of quasi-linear equations, which we summarize hereafter for the reader's convenience.…”

Section: Sharply Stratified N-layered Euler Fluidsmentioning

confidence: 99%

Hamiltonian aspects of 3-layer stratified fluids

Camassa,

Falqui,

Ortenzi

et al. 2021

Preprint

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The theory of 3-layer density stratified ideal fluids is examined with a view towards its generalization to the n-layer case. The focus is on structural properties, especially for the case of a rigid upper lid constraint. We show that the long-wave dispersionless limit is a system of quasi-linear equations that do not admit Riemann invariants. We equip the layer-averaged one-dimensional model with a natural Hamiltonian structure, obtained with a suitable reduction process from the continuous density stratification structure of the full two-dimensional equations proposed by Benjamin. For a a laterally unbounded fluid between horizontal rigid boundaries, the paradox about the non-conservation of horizontal total momentum is revisited, and it is shown that the pressure imbalances causing it can be intensified by three-layer setups with respect to their two-layer counterparts. The generator of the x-translational symmetry in the n-layer setup is also identified by the appropriate Hamiltonian formalism. The Boussinesq limit and a family of special solutions recently introduced by de Melo Viríssimo and Milewski are also discussed.

show abstract

Strongly nonlinear effects on internal solitary waves in three-layer flows

Cited by 31 publications

References 32 publications

Hamiltonian Aspects of Three-Layer Stratified Fluids

Hamiltonian Aspects of Three-Layer Stratified Fluids

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

Hamiltonian aspects of 3-layer stratified fluids

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