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.
more » « less Award ID(s):
 1716560
 NSFPAR ID:
 10500297
 Publisher / Repository:
 Royal Society Publishing
 Date Published:
 Journal Name:
 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
 Volume:
 479
 Issue:
 2272
 ISSN:
 13645021
 Page Range / eLocation ID:
 20230019:128
 Subject(s) / Keyword(s):
 ["gravitycapillary waves, bottom topography, conformal map, bifurcation"]
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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