title: Self-similar wave produced by local perturbation of the Kelvin-Helmholtz shear-layer instability.
abstract: We show that the Kelvin-Helmholtz instability excited by a localized perturbation yields a self-similar wave. The instability of the mixing layer was first conceived by Helmholtz as the inevitable growth of any localized irregularity into a spiral, but the search and uncovering of the resulting self-similar evolution was hindered by the technical success of Kelvin's wavelike perturbation theory. The identification of a self-similar solution is useful since its specific structure is witness of a subtle nonlinear equilibrium among the forces involved. By simulating numerically the Navier-Stokes equations, we analyze the properties of the wave: growth rate, propagation speed and the dependency of its shape upon the density ratio of the two phases of the mixing layer.
authors.affiliation: Institut Jean le Rond D'Alembert, UMR 7190, Université Pierre et Marie Curie, Paris, France. jerome.hoepffner@upmc.fr
authors.forename: Jérôme
authors.initials: J
authors.lastname: Hoepffner
authors.forename: Ralf
authors.initials: R
authors.lastname: Blumenthal
authors.forename: Stéphane
authors.initials: S
authors.lastname: Zaleski