We present a numerical study of spatially quasiperiodic gravitycapillary waves of finite depth in both the initial value problem and travelling wave settings. We adopt a quasiperiodic conformal mapping formulation of the Euler equations, where onedimensional quasiperiodic functions are represented by periodic functions on a higherdimensional torus. We compute the time evolution of free surface waves in the presence of a background flow and a quasiperiodic bottom boundary and observe the formation of quasiperiodic patterns on the free surface. Two types of quasiperiodic travelling waves are computed: smallamplitude waves bifurcating from the zeroamplitude solution and largeramplitude waves bifurcating from finiteamplitude periodic travelling waves. We derive weakly nonlinear approximations of the first type and investigate the associated smalldivisor problem. We find that waves of the second type exhibit striking nonlinear behaviour, e.g. the peaks and troughs are shifted nonperiodically from the corresponding periodic waves due to the activation of quasiperiodic modes.
 Award ID(s):
 1716560
 NSFPAR ID:
 10500298
 Publisher / Repository:
 Elsevier
 Date Published:
 Journal Name:
 Journal of Computational Physics
 Volume:
 478
 Issue:
 C
 ISSN:
 00219991
 Page Range / eLocation ID:
 111954:134
 Subject(s) / Keyword(s):
 ["Water waves, quasiperiodic solution, bifurcation detection, numerical continuation, analytic singular value decomposition, BlochFourier theory"]
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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