Internal Wave Breathers in the Slightly Stratified Fluid

Talipova, Tatiana; Kurkina, Oxana; Kurkin, Andrey; Didenkulova, Ekaterina; Pelinovsky, Efim

doi:10.1007/s12217-019-09738-2

Cited by 10 publications

(6 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These waves also have no limiting maximum amplitude (in absolute value) but they do have a minimum amplitude of −2α/α 1 . In addition to this second branch of solitary waves, the Gardner equation has a completely new type of solution called a breather (Talipova et al 2020). This new type of wave has the form of a propagating localized pulsating wave packet.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Breather interactions in a three-layer fluid

Nakayama

Lamb²

2023

J. Fluid Mech.

View full text Add to dashboard Cite

In a three-layer system with equal upper and lower layer thicknesses that are sufficiently thin and with the same density difference across each interface, breathers have been shown to exist using fully nonlinear governing equations. These breathers are well modelled by theoretical solutions of the mKdV equation, provided the interfaces between the layers do not cross a critical depth. The soliton-like characteristics of fully nonlinear breathers, in particular how two breathers interact, have yet to be explored. Using numerical simulations, this study addresses this shortcoming by studying fully nonlinear overtaking collisions of two breathers in a three-layer symmetric stratification. We apply the fully nonlinear and strongly dispersive FDI-3s internal wave equations, based on a variational principle, in a three-layer system. When the amplitude is small, the analytic breathers fit the wave shapes of the overtaking collision breathers. We find that the larger the upper and lower layer thicknesses are, provided they are below the critical thickness, the more the breathers behave like solitons. We show that an overtaking collision of two breathers is close to elastic.

show abstract

Section: Introductionmentioning

confidence: 99%

“…In addition to this second branch of solitary waves, the Gardner equation has a completely new type of solution called a breather (Talipova et al. 2020). This new type of wave has the form of a propagating localized pulsating wave packet.…”

Section: Introductionmentioning

confidence: 99%

Breather interactions in a three-layer fluid

Nakayama

Lamb²

2023

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…Although rogue waves on the sea surface have been studied intensively, surprisingly, large motions in the interior of the oceans associated with internal waves have not been thoroughly considered. The Gardner equation, basically an extended Korteweg-de Vries with both quadratic and cubic nonlinearities, has been applied as an analytical model in long wave regimes for transient, large amplitude displacements [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Triads and Rogue Events for Internal Waves in Stratified Fluids with a Constant Buoyancy Frequency

Pan¹,

Yin²,

Chow³

2021

JMSE

View full text Add to dashboard Cite

Internal waves in a stratified fluid with a constant buoyancy frequency were studied, with special attention given to rogue modes, extreme waves, dynamical evolution, and Fermi–Pasta–Ulam–Tsingou type recurrence phenomena. Rogue waves for triads in a general physical setting have recently been derived analytically, but the implications in a fluid mechanics context have not yet been fully assessed. Numerical simulations were conducted for cases of coupled triads where the common member is a daughter wave mode. In sharp contrast with previous studies, rogue modes instead of plane waves were used as the initial condition. Furthermore, spatial dependence was incorporated. Rogue or extreme waves in one set of triads provided a possible mechanism for significant energy transfer among modes of the internal wave spectrum, in addition to the other known theories, e.g., weak turbulence. Remarkably, Fermi–Pasta–Ulam–Tsingou recurrence types of growth and decay cycles arose, similarly to those observed for surface gravity wave groups governed by the cubic nonlinear Schrödinger equation. These mechanisms will enhance our understanding of transport processes in oceans.

show abstract

“…Their propagation to the coastal zone can be modeled using the evolution equations of the Korteweg-de Vries hierarchy, such as the combined Korteweg-de Vries equation and the Gardner-Ostrovsky equation [Cai et al, 2002;Grimshaw et al, 2004;Holloway et al, 1999], in which the dispersive and the Earth's rotation speed corrections are small compared to the linear speed of wave propagation. Nonlinear Euler equations are now widely used for modeling of internal waves [Lamb and Warn-Varnas, 2015;Vlasenko and Stashchuk, 2015]. Terms related to the rotation lead to increasing of computer resources.…”

Section: Introductionmentioning

confidence: 99%

Comparative analysis of the first baroclinic Rossby radius in the Baltic, Black, Okhotsk, and Mediterranean seas

Kurkin¹,

Kurkina²,

Rybin³

et al. 2020

Russ. J. Earth Sci.

View full text Add to dashboard Cite

Variability of the first baroclinic Rossby radius of deformation, 𝐿 𝑅 , in the Baltic, Black, Okhotsk, and Mediterranean seas is investigated. The first baroclinic Rossby radius is the ratio of the speed of propagation of long linear internal waves of the lowest mode and the Coriolis parameter. The data from the GDEM V.3.0 climatology for the considered regions are used for calculating internal wave dynamic parameters including wave speed. The seasonal and spatial variability of the baroclinic Rossby radius is discussed in detail. Its magnitudes in the open basins do not exceed 10 km in the Baltic Sea, 20 km in the Black Sea, 18 km in the deep part of the Okhotsk Sea, and 15-18 km in the Mediterranean Sea. Its values decrease 2-5 times in the shelf zones of the seas. Seasonal differences of the baroclinic Rossby radius are studied. The knowledge of the baroclinic Rossby radius makes possible estimating the influence of the Earth's rotation on the internal wave propagation.

show abstract

Internal Wave Breathers in the Slightly Stratified Fluid

Cited by 10 publications

References 35 publications

Breather interactions in a three-layer fluid

Breather interactions in a three-layer fluid

Triads and Rogue Events for Internal Waves in Stratified Fluids with a Constant Buoyancy Frequency

Comparative analysis of the first baroclinic Rossby radius in the Baltic, Black, Okhotsk, and Mediterranean seas

Contact Info

Product

Resources

About