Global bifurcation of irrotational water waves using a flow force formulation

Abstract

Using a novel formulation based on flow force, we prove the existence of a global continuum of periodic traveling wave solutions to the irrotational water wave problem in finite depth where the flow force is held fixed, instead of fixing the mass flux. We further establish the limiting behaviour of solutions in this continuum where the flow force remains fixed throughout the continuum of the solutions. The global solutions, with a fixed flow force, show the possibility that a weak stagnation point can be approached at the surface, which is a characteristic of large amplitude irrotational water waves. The formulation is suitable for applications to numerical studies on water waves.