Global bifurcation for steady finite-depth capillary-gravity waves with constant vorticity

Abstract

This paper is concerned with two-dimensional, steady, periodic water waves propagating at the free surface of water in a flow of constant vorticity over an impermeable flat bed. The motion of these waves is assumed to be governed both by surface tension and gravitational forces. A new reformulation of this problem is given, which is valid without restriction on the geometry or amplitude of the wave profiles and possesses a structure amenable to global bifurcation. The existence of global curves and continua of solutions bifurcating at certain parameter values from flat, laminar flows is then established through the application of real-analytic global bifurcation in the spirit of Dancer and the degree-theoretic global bifurcation theorem of Rabinowitz, respectively.