Numerical investigations of two-dimensional irrotational water waves over finite depth with uniform current

Abstract

We investigate large amplitude steady water waves in the presence of underlying uniform current with $u\ne c$ using a numerical continuation method. The two branches of traveling wave solutions, whose existence has been proved recently by Basu [On the existence of two-dimensional irrotational water waves over finite depth with uniform current. Appl Anal. 2018;97(14):2523–2532.] for a parameter $\mu =c^3/q_C^3<1$ or $>1$ are computed numerically. The numerical results for the case $0<\mu <1$ have not been previously reported in the literature. The properties of the waves and flows in this solution branch are discussed as comparison to those in the case of $\mu >1$.

Keywords:

• Periodic water waves
• uniform current
• free surface flows
• irrotational flow
• bifurcation
• numerical continuation

AMS Subject Classifications (2010):

• 35Q35
• 35J15

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

L.C. was supported by the Irish Research Council (IRC) through the Government of Ireland Postdoctoral Fellowship (Project ID: GOIPD/2017/1260).