Abstract
We present a numerical study of parametrically driven surface waves in fluids of low viscosity. The equations governing fluid motion in the bulk and the appropriate boundary conditions at the free surface are approximated by a nonlocal set of equations involving surface coordinates alone, thus allowing the numerical analysis of the large aspect ratio limit (the aspect ratio being the ratio between the size of the system and the wavelength of the waves). The numerical calculation supports the predictions of a previously given multi-scale asymptotic analysis, yielding stable patterns of square symmetry above onset in the capillary dominated regime. In the case of mixed capillary-gravity waves, patterns of eight-fold symmetry are obtained, again in agreement with the predictions of the asymptotic expansion. These calculations provide indirect evidence about the stability of such patterns, analysis that is too involved to be carried out analytically.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 225-243 |
| Number of pages | 19 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 116 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - Jan 1 1998 |
| Externally published | Yes |
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Keywords
- Faraday waves
- Parametric instability
- Quasipatterns
Cite this
Numerical study of pattern formation in weakly damped parametric surface waves. / Zhang, Wenbin; Viñals, Jorge.
In: Physica D: Nonlinear Phenomena, Vol. 116, No. 1-2, 01.01.1998, p. 225-243.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Numerical study of pattern formation in weakly damped parametric surface waves
AU - Zhang, Wenbin
AU - Viñals, Jorge
PY - 1998/1/1
Y1 - 1998/1/1
N2 - We present a numerical study of parametrically driven surface waves in fluids of low viscosity. The equations governing fluid motion in the bulk and the appropriate boundary conditions at the free surface are approximated by a nonlocal set of equations involving surface coordinates alone, thus allowing the numerical analysis of the large aspect ratio limit (the aspect ratio being the ratio between the size of the system and the wavelength of the waves). The numerical calculation supports the predictions of a previously given multi-scale asymptotic analysis, yielding stable patterns of square symmetry above onset in the capillary dominated regime. In the case of mixed capillary-gravity waves, patterns of eight-fold symmetry are obtained, again in agreement with the predictions of the asymptotic expansion. These calculations provide indirect evidence about the stability of such patterns, analysis that is too involved to be carried out analytically.
AB - We present a numerical study of parametrically driven surface waves in fluids of low viscosity. The equations governing fluid motion in the bulk and the appropriate boundary conditions at the free surface are approximated by a nonlocal set of equations involving surface coordinates alone, thus allowing the numerical analysis of the large aspect ratio limit (the aspect ratio being the ratio between the size of the system and the wavelength of the waves). The numerical calculation supports the predictions of a previously given multi-scale asymptotic analysis, yielding stable patterns of square symmetry above onset in the capillary dominated regime. In the case of mixed capillary-gravity waves, patterns of eight-fold symmetry are obtained, again in agreement with the predictions of the asymptotic expansion. These calculations provide indirect evidence about the stability of such patterns, analysis that is too involved to be carried out analytically.
KW - Faraday waves
KW - Parametric instability
KW - Quasipatterns
UR - http://www.scopus.com/inward/record.url?scp=0000355977&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0000355977&partnerID=8YFLogxK
U2 - 10.1016/S0167-2789(97)00172-3
DO - 10.1016/S0167-2789(97)00172-3
M3 - Article
AN - SCOPUS:0000355977
VL - 116
SP - 225
EP - 243
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 1-2
ER -