title: Wave-current interaction as a spatial dynamical system: analogies with rainbow and black hole physics.
abstract: We study the hydrodynamic phenomenon of waves blocking by a countercurrent with the tools of dynamical systems theory. We show that, for a uniform background velocity and within the small wavelength approximation, the stopping of gravity waves is described by a stationary saddle-node bifurcation due to the spatial resonance of an incident wave with the converted "blueshifted" wave. We explain why the classical regularization effect of interferences avoids the height singularity in complete analogy with the intensity of light close to the principal arc of a rainbow. The application to the behavior of light near a gravitational horizon is discussed.
authors.affiliation: Université de Nice-Sophia Antipolis, UMR CNRS-UNS 6621, 06108 Nice Cedex 02, France.
authors.forename: Jean-Charles
authors.initials: JC
authors.lastname: Nardin
authors.forename: Germain
authors.initials: G
authors.lastname: Rousseaux
authors.forename: Pierre
authors.initials: P
authors.lastname: Coullet