Spatially quasi-periodic water waves of finite depth

We present a numerical study of spatially quasi-periodic gravity-capillary waves finite depth in both the initial value problem and travelling wave settings. adopt conformal mapping formulation Euler equations, where one-dimensional functions are represented by periodic on higher-dimensional torus. compute time evolution free surface presence background flow bottom boundary observe formation patterns surface. Two types computed: small-amplitude bifurcating from zero-amplitude solution larger-amplitude finite-amplitude waves. derive weakly nonlinear approximations first type investigate associated small-divisor problem. find that second exhibit striking behaviour, e.g. peaks troughs shifted non-periodically corresponding due to activation modes.