Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · nlin/0603049

Quantitative laboratory observations of internal wave reflection on ascending slopes

Louis Gostiaux·Thierry Dauxois·Henri Didelle·Joel Sommeria·Samuel Viboud
View original source ↗Read source document ↗Export metadata ↓

Abstract

Internal waves propagate obliquely through a stratified fluid with an angle that is fixed with respect to gravity. Upon reflection on a sloping bed, striking phenomena are expected to occur close to the slope. We present here laboratory observations at moderately large Reynolds number. A particle image velocimetry (PIV) technique is used to provide time resolved velocity fields in large volumes. The generation of the second and third harmonic frequencies are clearly demonstrated in the impact zone. The mechanism for nonlinear wavelength selection is also discussed. Evanescent waves with frequency larger than the Brunt-Väisälä frequency are detected and experimental results agree very well with theoretical predictions. The amplitude of the different harmonics after reflection are also obtained.

Explore related subjects

nlin.PSphysics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Louis Gostiaux, Thierry Dauxois, Henri Didelle, Joel Sommeria, Samuel Viboud. 2006-03-23. Quantitative laboratory observations of internal wave reflection on ascending slopes. https://doi.org/10.1063/1.2197528

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Hyperbolic, Trigonometric and Periodic Solutions of Local and Nonlocal Fokas-Lennels Equations

We obtain a large number of exact hyperbolic, trigonometric, and periodic solutions in terms of Jacobi elliptic functions as well as algebraic solutions with a power law tail of the integrable local Fokas-Lennels equation and integrable nonlocal Fokas-Lennels equation. Further, we consider a one-parameter family of generalized Fokas-Lenells equations and obtain a few of their exact solutions.

nlin.PS↗
arXiv2026

Adiabatic Theory Data on Strongly Chirped Dissipative Solitons of the Cubic-Quintic Nonlinear Ginzburg-Landau Equation

This data article provides the datasets, symbolic derivations, and scripts used to reproduce master diagrams, stationary-phase spectra, windowed first-order coherence functions, and quantum-noise stability maps for strongly chirped dissipative solitons of the cubic-quintic complex Ginzburg-Landau equation in normal and anomalous group-delay dispersion regimes. The repository includes node-regularized normal-dispersion spectra and energies; small-parameter expansions of the branch roots; cavity-map gain-loss update relations; Airy uniformization at the normal-dispersion spectral edge; anomalous-dispersion spectra and coherence calculations; and processed tables for plotting and stability analysis. OriginLab projects are accompanied by open-format .csv/.txt numerical tables to support reuse without proprietary plotting software. Data and code repository: https://doi.org/10.5281/zenodo.22690899.

nlin.PS↗
arXiv2026

Degenerate Turing bifurcation and the birth of localised patterns in activator-inhibitor systems

Precise conditions are provided for the existence and criticality of Turing bifurcations in a general class of activator-inhibitor reaction-diffusion equations on a one-dimensional infinite domain. The class includes generalised Schnakenberg and Brusselator models, as well as other models with cubic autocatalytic nonlinear terms. Previous numerical work suggests the existence of a bifurcation structure containing localised patterns due to the so-called homoclinic snaking mechanism. This paper provides explicit calculations to justify those results. Two distinct scalings of parameters that lead to tractable normal-form coefficients are considered in the limit that the diffusion ratio $δ\to 0$. First, under a small-parameter scaling, the Turing bifurcation is shown to be always subcritical. Second, a large-parameter scaling reveals the Turing bifurcation to be supercritical, leading, by continuity, to the existence of a codimension-two degenerate bifurcation. The sign of a 5th-order normal form coefficient is also computed, which is shown to have the correct sign for the local birth of homoclinic snaking. For the case of the Brusselator, two such codimension-two points can be found explicitly, as can the leading-order expression for the Maxwell point, in a parameter wedge about which localised patterns emerge. Numerical results are found to be consistent with the theory.

nlin.PS↗