Large mode-2 internal solitary waves in three-layer flows

Doak, Alex; Barros, Ricardo; Milewski, Paul A.

doi:10.1017/jfm.2022.974

Cited by 5 publications

(4 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is worth mentioning that similar solutions have been previously discovered in Liapidevskii & Gavrilov (2018) experimentally and in Doak et al. (2022) numerically. Figures 17( c ) and 17( d ) show that the waves could become even more nonlinear so that the upper interface develops an overhanging profile and tends to become self-intersecting.…”

Section: Numerical Resultssupporting

confidence: 84%

“…2020; Doak et al. 2022), and indeed when the magenta branch exits the linear spectrum, the resulting solutions are true mode-2 solitary waves with no resonances (solution B in the figure). Although linear waves do not exist for speeds , nonlinear mode-1 solitary and periodic waves do, and the other branches which exit the spectrum still have resonances with nonlinear mode-1 waves.…”

Section: Numerical Resultsmentioning

confidence: 86%

“…Using a fully nonlinear theory, a detailed description of three-layer conjugate states was obtained by Lamb (2000). Fully nonlinear wave computations have been computed by previous authors, who explored both mode-1 (Rusås & Grue 2002) and mode-2 (Doak, Barros & Milewski 2022) solitary waves. Fully nonlinear mode-1 and mode-2 periodic waves have been computed (Rusås 2000; Chen & Forbes 2008).…”

Section: Introductionmentioning

confidence: 99%

“…As the wavelength is further increased, the solutions ultimately approach generalised solitary waves (Akylas & Grimshaw 1992; Rusås & Grue 2002; Doak et al. 2022).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Nonlinear travelling periodic waves for the Euler equations in three-layer flows

Guan,

Doak,

Milewski

et al. 2024

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

In this paper, we investigate periodic travelling waves in a three-layer system with the rigid-lid assumption. Solutions are recovered numerically using a boundary integral method. We consider the case where the density difference between the layers is small (i.e. a weakly stratified fluid). We consider the system both with and without the Boussinesq assumption to explore the effect the assumption has on the solution space. Periodic solutions of both mode-1 and mode-2 are found, and their bifurcation structure and limiting configurations are described in detail. Similarities are found with the two-layer case, where large-amplitude solutions are found to overhang with an internal angle of $120^{\circ }$ . However, the addition of a second interface results in a richer bifurcation space, in part due to the existence of mode-2 waves and their resonance with mode-1 waves. New limiting profiles are found.

show abstract

Section: Numerical Resultssupporting

confidence: 84%

Section: Numerical Resultsmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

“…As the wavelength is further increased, the solutions ultimately approach generalised solitary waves (Akylas & Grimshaw 1992; Rusås & Grue 2002; Doak et al. 2022).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear travelling periodic waves for the Euler equations in three-layer flows

Guan,

Doak,

Milewski

et al. 2024

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

Evolution of linear internal waves over large bottom topography in three-layer stratified fluids

Chai,

Wang

2024

J. Fluid Mech.

View full text Add to dashboard Cite

Evolutions of internal waves of different modes, particularly mode 1 and mode 2, passing over variable bathymetry are investigated based on a new numerical scheme. The problem is idealized as interfacial waves propagating on two interfaces of a three-layer density stratified fluid system with large-amplitude bottom topography. The Dirichlet-to-Neumann operators are introduced to reduce the spatial dimension by one and to adapt the three-layer system and significant topographic effects. However, for simplicity, nonlinear interactions between interfaces are neglected. Numerical techniques such as the Galerkin approximation, proven effective in previous works, are applied to save computational costs. Shoaling of linear waves on an uneven bottom is first studied to validate the proposed formulation and the corresponding numerical scheme. Then, for two-dimensional numerical experiments, mode transition phenomena excited by locally confined bottom obstacles and quickly varying topographies, including the Bragg resonance, mode-2 excitation, wave homogenization, etc., are investigated. In three-dimensional simulations, internal wave refraction by a Luneberg lens is considered, and good agreement is found in comparison with the ray theory. Finally, in the limiting case, when the top layer can be negligible (for example, a gas layer of extremely small density), the problem is reduced to a two-and-a-half-layer fluid system, where an interface and a surface are unknown free boundaries. In this situation, the surface signature of an internal wave is simulated and verified by introducing the realistic bathymetry of the Strait of Gibraltar and qualitatively compared with the satellite image.

show abstract

Strongly non-linear Boussinesq-type model of the dynamics of internal solitary waves propagating in a multilayer stratified fluid

2023

View full text Add to dashboard Cite

We propose a system of first-order balance laws that describe the propagation of internal solitary waves in a multilayer stratified shallow water with non-hydrostatic pressure in the upper and lower layers. The construction of this model is based on the use of additional variables, which make it possible to approximate the Green–Naghdi-type dispersive equations by a first-order system. In the Boussinesq approximation, the governing equations allow one to simulate the propagation of non-linear internal waves, taking into account fine density stratification, a weak velocity shear in the layers, and uneven topography. We obtain smooth steady-state soliton-like solutions of the proposed model in the form of symmetric and non-symmetric waves of mode-2 adjoining to a given multilayer constant flow. Numerical calculations of the generation and propagation of large-amplitude internal waves are carried out using both the proposed first-order system and Green–Naghdi-type equations. It is established that the solutions of these models practically coincide. The advantage of the first-order equations is the simplicity of numerical implementation and a significant reduction in the calculation time. We show that the results of numerical simulation are in good agreement with the experimental data on the evolution of mode-2 solitary waves in tanks of constant and variable height.

show abstract

Large mode-2 internal solitary waves in three-layer flows

Cited by 5 publications

References 40 publications

Nonlinear travelling periodic waves for the Euler equations in three-layer flows

Nonlinear travelling periodic waves for the Euler equations in three-layer flows

Evolution of linear internal waves over large bottom topography in three-layer stratified fluids

Strongly non-linear Boussinesq-type model of the dynamics of internal solitary waves propagating in a multilayer stratified fluid

Contact Info

Product

Resources

About