Analytical approximation and numerical simulations for periodic travelling water waves

Konstantinos Kalimeris
2017 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
We present recent analytical and numerical results for two-dimensional periodic travelling water waves with constant vorticity. The analytical approach is based on novel asymptotic expansions. We obtain numerical results in two different ways: the first is based on the solution of a constrained optimization problem, and the second is realized as a numerical continuation algorithm. Both methods are applied on some examples of non-constant vorticity.
doi:10.1098/rsta.2017.0093 pmid:29229793 fatcat:lxsfixdqpvbhrklfclyr7uhvp4