On the existence of two-dimensional irrotational water waves over finite depth with uniform current

ABSTRACT

The existence of large amplitude two-dimensional water waves with wave speed c, propagating on the surface of an irrotational flow over a flat bed with underlying uniform current, is investigated by means of a bifurcation approach. Two branches of travelling wave solutions exist for a parameter or 1, respectively (where is the flow velocity at the wave crest). The existence of the global bifurcating branch of solution for has not been reported in the literature and can exist in the presence of uniform underlying current, while the other branch of solution for can exist without any underlying current as has been shown by previously.

Keywords:

• Water waves
• uniform current
• finite depth
• free surface flows
• bifurcation

AMS Subject Classifications:

• 35Q35
• 35J15

Notes

No potential conflict of interest was reported by the author.