TY - JOUR
T1 - Square patterns and quasipatterns in weakly damped Faraday waves
AU - Zhang, Wenbin
AU - Viñals, Jorge
PY - 1996
Y1 - 1996
N2 - Pattern formation in parametric surface waves is studied in the limit of weak viscous dissipation. A set of quasipotential equations (QPEs) is introduced that admits a closed representation in terms of surface variables alone. A multiscale expansion of the QPEs reveals the importance of triad resonant interactions, and the saturating effect of the driving force leading to a gradient amplitude equation. Minimization of the associated Lyapunov function yields standing wave patterns of square symmetry for capillary waves, and hexagonal patterns and a sequence of quasipatterns for mixed capillary-gravity waves. Numerical integration of the QPEs reveals a quasipattern of eightfold symmetry in the range of parameters predicted by the multiscale expansion.
AB - Pattern formation in parametric surface waves is studied in the limit of weak viscous dissipation. A set of quasipotential equations (QPEs) is introduced that admits a closed representation in terms of surface variables alone. A multiscale expansion of the QPEs reveals the importance of triad resonant interactions, and the saturating effect of the driving force leading to a gradient amplitude equation. Minimization of the associated Lyapunov function yields standing wave patterns of square symmetry for capillary waves, and hexagonal patterns and a sequence of quasipatterns for mixed capillary-gravity waves. Numerical integration of the QPEs reveals a quasipattern of eightfold symmetry in the range of parameters predicted by the multiscale expansion.
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U2 - 10.1103/PhysRevE.53.R4283
DO - 10.1103/PhysRevE.53.R4283
M3 - Article
AN - SCOPUS:0001657306
SN - 1063-651X
VL - 53
SP - R4283-R4286
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 5
ER -