arXiv subjects

Olga Avramenko

Publications and source records attributed to Olga Avramenko.

4 recordsLinked to original sources

arXiv2026

Parameter mapping and physical reconstruction of Akhmediev breathers at the interface of two fluid half-spaces

A methodology combining parameter mapping and physical reconstruction of Akhmediev breathers at the interface between two fluid half-spaces is developed on the basis of the Nayfeh model. Parameter maps are constructed to characterize the breather modulation period, the modulational instability growth rate, and the relative contribution of the bound second harmonic to the reconstructed interfacial profile. Their combined analysis provides a physically meaningful classification of breather regimes beyond the conventional focusing condition of the nonlinear Schr\"odinger equation. Reconstruction of the physical interfacial profile establishes a quantitative relation between nonlinear wave deformation and the contribution of the bound second harmonic, making it possible to identify the range of applicability of the weakly nonlinear approximation. Representative regimes from different modulational instability regions are analyzed to demonstrate the influence of resonance and focusing boundaries on breather characteristics and interfacial wave profiles. The proposed approach provides a direct link between the mathematical description of Akhmediev breathers and their physical interpretation and can be extended to other localized solutions of the nonlinear Schr\"odinger equation and to a broad class of stratified hydrodynamic systems.

physics.flu-dyn↗

arXiv2025

Benjamin-Feir Instability of Interfacial Gravity-Capillary Waves in a Two-Layer Fluid. Part II. Surface-Tension Effects

This second part of the study develops a geometric and asymptotic description of how surface tension governs the modulational stability of interfacial waves in a two-layer fluid. Extending the analytical framework of Part~I, surface tension is treated as a freely adjustable parameter, enabling one to trace how nonlinear and dispersive properties evolve across a broad range of depth ratios and density contrasts. Using the nonlinear Schr\"odinger reduction together with long-wave asymptotics, the mechanisms shaping the boundaries between stable and unstable regimes are identified and their dependence on surface tension is quantified. The long-wave structure is governed by two density values that determine the bases of the loop and the corridor on the stability diagrams. Their ordering switches only when the lower layer is deeper, and loop-type structures arise exclusively in this regime. A second organising parameter is the classical Bond threshold, at which the dispersive and nonlinear singularities coincide. When surface tension exceeds this value and the upper layer is sufficiently deep, resonant and dispersive effects generate a capillary cut that replaces the corridor and characterises strongly capillary, upper-layer-dominated configurations. To unify these observations, full three-dimensional critical surfaces separating different types of nonlinear and dispersive behaviour are computed. The loop, corridor, and cut arise as planar sections of these surfaces, and their transitions follow from the deformation of the intersection between the resonant and dispersive sheets. Two depth ratios correspond to geometric degeneracies: equal layer depths, where the intersection reduces to a straight line, and the golden-ratio configuration, where the critical surface becomes horizontally tangent at the Bond threshold.

physics.flu-dyn↗

arXiv2025

Benjamin-Feir Instability of Interfacial Gravity-Capillary Waves in a Two-Layer Fluid. Part I

This study presents a detailed investigation of the modulational stability of interfacial wave packets in a two-layer inviscid incompressible fluid with finite layer thicknesses and interfacial surface tension. The stability analysis is carried out for a broad range of density ratios and geometric configurations, enabling the construction of stability diagrams in the (\rho,k) -plane, where \rho is the density ratio and k is the carrier wavenumber. The Benjamin-Feir index is used as the stability criterion, and its interplay with the curvature of the dispersion relation is examined to determine the onset of modulational instability. The topology of the stability diagrams reveals several characteristic structures: a localized loop of stability within an instability zone, a global upper stability domain, an elongated corridor bounded by resonance and dispersion curves, and a degenerate cut structure arising in strongly asymmetric configurations. Each of these structures is associated with a distinct physical mechanism involving the balance between focusing/defocusing nonlinearity and anomalous/normal dispersion. Systematic variation of layer thicknesses allows us to track the formation, deformation, and disappearance of these regions, as well as their merging or segmentation due to resonance effects. Limiting cases of semi-infinite layers are analyzed to connect the results with known configurations, including the `half-space--layer', `layer--half-space', and `half-space--half-space' systems. The influence of symmetry and asymmetry in layer geometry is examined in detail, showing how it governs the arrangement and connectivity of stable and unstable regions in parameter space.

physics.flu-dyn↗

arXiv2024

Benjamin-Feir instability of wave packets at interface of liquid half-space and layer

The propagation of internal waves in a hydrodynamic system comprising a solid bottom and an upper half-space is investigated. The study is conducted within the framework of a nonlinear low-dimensional model incorporating surface tension on an interface using the method of multi-scale expansions. The evolution equation of the envelope of the wave packet takes the form of the Schrodinger equation. Conditions for the Benjamin-Feir stability of the solution of the evolution equation are identified for various physical and geometrical characteristics of the system. An estimation of the parameter range in which the instability occurs is performed. Significant influence on the modulational stability of the geometrical characteristics of the system and surface tension is observed in each system for relatively small liquid layer thicknesses and waves with a wavelength comparable to the layer thickness

physics.flu-dyn↗