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Volumn 190, Issue 1-2, 2004, Pages 93-114

Resonant triad dynamics in weakly damped Faraday waves with two-frequency forcing

Author keywords

Faraday waves; Pattern formation; Resonant triads; Symmetry breaking

Indexed keywords

CRYSTAL SYMMETRY; DAMPING; HAMILTONIANS; NATURAL FREQUENCIES; NUMERICAL METHODS; OSCILLATIONS; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; PROBLEM SOLVING; STANDING WAVE METERS; SUPERLATTICES;

EID: 1142280190     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2003.09.044     Document Type: Article
Times cited : (23)

References (43)
  • 1
    • 0000449879 scopus 로고
    • On the forms and states of fluids on vibrating elastic surfaces
    • Faraday M., On the forms and states of fluids on vibrating elastic surfaces. Phil. Trans. Roy. Soc. Lond. 121:1831;319-340.
    • (1831) Phil. Trans. Roy. Soc. Lond. , vol.121 , pp. 319-340
    • Faraday, M.1
  • 2
    • 0000505903 scopus 로고    scopus 로고
    • Nonlinear pattern formation of Faraday waves
    • Binks D., van de Water W., Nonlinear pattern formation of Faraday waves. Phys. Rev. Lett. 78:1997;4043-4046.
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 4043-4046
    • Binks, D.1    Van de Water, W.2
  • 3
    • 41349110146 scopus 로고    scopus 로고
    • Pattern formation in two-frequency forced parametric waves
    • Arbell H., Fineberg J., Pattern formation in two-frequency forced parametric waves. Phys. Rev. E. 65:2002;036224.
    • (2002) Phys. Rev. E , vol.65 , pp. 036224
    • Arbell, H.1    Fineberg, J.2
  • 4
    • 0028534344 scopus 로고
    • Patterns and quasi-patterns in the Faraday experiment
    • Edwards W.S., Fauve S., Patterns and quasi-patterns in the Faraday experiment. J. Fluid Mech. 278:1994;123-148.
    • (1994) J. Fluid Mech. , vol.278 , pp. 123-148
    • Edwards, W.S.1    Fauve, S.2
  • 5
    • 0001523342 scopus 로고    scopus 로고
    • Spatial and temporal dynamics of two interacting modes in parametrically driven surface waves
    • Arbell H., Fineberg J., Spatial and temporal dynamics of two interacting modes in parametrically driven surface waves. Phys. Rev. Lett. 81:1998;4384-4387.
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 4384-4387
    • Arbell, H.1    Fineberg, J.2
  • 6
    • 11544349015 scopus 로고    scopus 로고
    • Superlattice patterns in surface waves
    • Kudrolli A., Pier B., Gollub J.P., Superlattice patterns in surface waves. Physica D. 123:1998;99-111.
    • (1998) Physica D , vol.123 , pp. 99-111
    • Kudrolli, A.1    Pier, B.2    Gollub, J.P.3
  • 7
    • 0000486150 scopus 로고
    • The stability of a plane free surface of a liquid in vertical periodic motion
    • Benjamin T.B., Ursell F., The stability of a plane free surface of a liquid in vertical periodic motion. Proc. Roy. Soc. Lond. A. 225:1954;505-515.
    • (1954) Proc. Roy. Soc. Lond. A , vol.225 , pp. 505-515
    • Benjamin, T.B.1    Ursell, F.2
  • 8
    • 0000089628 scopus 로고    scopus 로고
    • Two-mode rhomboidal states in driven surface waves
    • Arbell H., Fineberg J., Two-mode rhomboidal states in driven surface waves. Phys. Rev. Lett. 84:2000;654-657.
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 654-657
    • Arbell, H.1    Fineberg, J.2
  • 9
    • 0037135917 scopus 로고    scopus 로고
    • Broken symmetries and pattern formation in two-frequency forced Faraday waves
    • Porter J., Silber M., Broken symmetries and pattern formation in two-frequency forced Faraday waves. Phys. Rev. Lett. 89:2002;084501.
    • (2002) Phys. Rev. Lett. , vol.89 , pp. 084501
    • Porter, J.1    Silber, M.2
  • 10
    • 0037112203 scopus 로고    scopus 로고
    • Resonances and supperlattice pattern stabilization in two-frequency forced Faraday waves
    • Topaz C.M., Silber M., Resonances and supperlattice pattern stabilization in two-frequency forced Faraday waves. Physica D. 172:2002;1-29.
    • (2002) Physica D , vol.172 , pp. 1-29
    • Topaz, C.M.1    Silber, M.2
  • 11
    • 0000598158 scopus 로고    scopus 로고
    • Parametrically excited surface waves: Two-frequency forcing, normal form symmetries and pattern formation
    • Silber M., Skeldon A.C., Parametrically excited surface waves: two-frequency forcing, normal form symmetries and pattern formation. Phys. Rev. E. 59:1999;5446-5456.
    • (1999) Phys. Rev. E , vol.59 , pp. 5446-5456
    • Silber, M.1    Skeldon, A.C.2
  • 12
    • 0000345824 scopus 로고
    • Periodic triangular patterns in the Faraday experiment
    • Müller H.W., Periodic triangular patterns in the Faraday experiment. Phys. Rev. Lett. 71:1993;3287-3290.
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 3287-3290
    • Müller, H.W.1
  • 13
    • 17544396208 scopus 로고    scopus 로고
    • Crossover from a square to a hexagonal pattern in Faraday surface waves
    • Wagner C., Müller H.W., Knorr K., Crossover from a square to a hexagonal pattern in Faraday surface waves. Phys. Rev. E. 62:2000;R33-R36.
    • (2000) Phys. Rev. E , vol.62
    • Wagner, C.1    Müller, H.W.2    Knorr, K.3
  • 14
    • 0031126953 scopus 로고    scopus 로고
    • Pattern formation in weakly damped parametric surface waves
    • Zhang W., Viñals J., Pattern formation in weakly damped parametric surface waves. J. Fluid Mech. 336:1997;301-330.
    • (1997) J. Fluid Mech. , vol.336 , pp. 301-330
    • Zhang, W.1    Viñals, J.2
  • 15
    • 0008970449 scopus 로고    scopus 로고
    • Pattern formation in weakly damped parametric surface waves driven by two frequency components
    • Zhang W., Viñals J., Pattern formation in weakly damped parametric surface waves driven by two frequency components. J. Fluid Mech. 341:1997;225-244.
    • (1997) J. Fluid Mech. , vol.341 , pp. 225-244
    • Zhang, W.1    Viñals, J.2
  • 16
    • 0038999966 scopus 로고    scopus 로고
    • Two-frequency forced Faraday waves: Weakly damped modes and pattern selection
    • Silber M., Topaz C.M., Skeldon A.C., Two-frequency forced Faraday waves: weakly damped modes and pattern selection. Physica D. 143:2000;205-225.
    • (2000) Physica D , vol.143 , pp. 205-225
    • Silber, M.1    Topaz, C.M.2    Skeldon, A.C.3
  • 17
    • 0026141889 scopus 로고
    • Square patterns and secondary instabilities in driven capillary waves
    • Milner S.T., Square patterns and secondary instabilities in driven capillary waves. J. Fluid Mech. 225:1991;81-100.
    • (1991) J. Fluid Mech. , vol.225 , pp. 81-100
    • Milner, S.T.1
  • 19
    • 0003078274 scopus 로고
    • Symmetry and symmetry-breaking bifurcations in fluid mechanics
    • Crawford J.D., Knobloch E., Symmetry and symmetry-breaking bifurcations in fluid mechanics. Annu. Rev. Fluid Mech. 23:1991;341-387.
    • (1991) Annu. Rev. Fluid Mech. , vol.23 , pp. 341-387
    • Crawford, J.D.1    Knobloch, E.2
  • 21
    • 0000471236 scopus 로고
    • Temporal forcing of small-amplitude waves in anisotropic systems
    • Riecke H., Silber M., Kramer L., Temporal forcing of small-amplitude waves in anisotropic systems. Phys. Rev. E. 49:1994;4100-4113.
    • (1994) Phys. Rev. E , vol.49 , pp. 4100-4113
    • Riecke, H.1    Silber, M.2    Kramer, L.3
  • 22
    • 0000015763 scopus 로고
    • Hopf bifurcation with the symmetry of the square
    • Swift J.W., Hopf bifurcation with the symmetry of the square. Nonlinearity. 1:1988;333-377.
    • (1988) Nonlinearity , vol.1 , pp. 333-377
    • Swift, J.W.1
  • 24
    • 0000040998 scopus 로고
    • Introduction to bifurcation-theory
    • Crawford J.D., Introduction to bifurcation-theory. Rev. Mod. Phys. 63:1991;991-1037.
    • (1991) Rev. Mod. Phys. , vol.63 , pp. 991-1037
    • Crawford, J.D.1
  • 25
    • 0028668835 scopus 로고
    • Parametric instability of the interface between two fluids
    • Kumar K., Tuckerman L.S., Parametric instability of the interface between two fluids. J. Fluid Mech. 279:1994;49-68.
    • (1994) J. Fluid Mech. , vol.279 , pp. 49-68
    • Kumar, K.1    Tuckerman, L.S.2
  • 26
    • 34250447917 scopus 로고
    • Stability of periodic waves of finite amplitude on the surface of deep fluid
    • Zakharov V.E., Stability of periodic waves of finite amplitude on the surface of deep fluid. J. Appl. Mech. Tech. Phys. 2:1968;190-194.
    • (1968) J. Appl. Mech. Tech. Phys. , vol.2 , pp. 190-194
    • Zakharov, V.E.1
  • 27
    • 84974144443 scopus 로고
    • On Hamilton's principle for surface waves
    • Miles J.W., On Hamilton's principle for surface waves. J. Fluid Mech. 83:1977;153-158.
    • (1977) J. Fluid Mech. , vol.83 , pp. 153-158
    • Miles, J.W.1
  • 28
    • 34250417406 scopus 로고
    • On the Hamiltonian theory of surface waves
    • Broer L.J.F., On the Hamiltonian theory of surface waves. Appl. Sci. Res. 29:1974;430-446.
    • (1974) Appl. Sci. Res. , vol.29 , pp. 430-446
    • Broer, L.J.F.1
  • 29
    • 0031270647 scopus 로고    scopus 로고
    • Perturbation theory of parametrically driven capillary waves at low viscosity
    • Lyngshansen P., Alstrom P., Perturbation theory of parametrically driven capillary waves at low viscosity. J. Fluid Mech. 351:1997;301-344.
    • (1997) J. Fluid Mech. , vol.351 , pp. 301-344
    • Lyngshansen, P.1    Alstrom, P.2
  • 30
    • 0026808121 scopus 로고
    • An explicit Hamiltonian formulation of surface waves in water of finite depth
    • Radder A.C., An explicit Hamiltonian formulation of surface waves in water of finite depth. J. Fluid Mech. 237:1992;435-455.
    • (1992) J. Fluid Mech. , vol.237 , pp. 435-455
    • Radder, A.C.1
  • 31
    • 0021189038 scopus 로고
    • Nonlinear Faraday resonance
    • Miles J.W., Nonlinear Faraday resonance. J. Fluid Mech. 146:1984;285-302.
    • (1984) J. Fluid Mech. , vol.146 , pp. 285-302
    • Miles, J.W.1
  • 32
    • 0028485350 scopus 로고
    • On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves
    • Krasitskii V.P., On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves. J. Fluid Mech. 272:1994;1-20.
    • (1994) J. Fluid Mech. , vol.272 , pp. 1-20
    • Krasitskii, V.P.1
  • 33
    • 0000958580 scopus 로고
    • The 1:2 resonance with O(2) symmetry and its applications in hydrodynamics
    • Chossat P., Dias F., The 1:2 resonance with O(2) symmetry and its applications in hydrodynamics. J. Nonlinear Sci. 5:1995;105-129.
    • (1995) J. Nonlinear Sci. , vol.5 , pp. 105-129
    • Chossat, P.1    Dias, F.2
  • 34
    • 0000775231 scopus 로고    scopus 로고
    • The bifurcation of heteroclinic cycles in systems of hydrodynamical type
    • Chossat P., The bifurcation of heteroclinic cycles in systems of hydrodynamical type. Dynam. Cont. Dis. Ser. A. 8:2001;575-590.
    • (2001) Dynam. Cont. Dis. Ser. A , vol.8 , pp. 575-590
    • Chossat, P.1
  • 35
    • 0001073293 scopus 로고
    • Strong spatial resonance and traveling waves in Benard convection
    • Jones C.A., Proctor M.R.E., Strong spatial resonance and traveling waves in Benard convection. Phys. Lett. A. 121:1987;224-228.
    • (1987) Phys. Lett. A , vol.121 , pp. 224-228
    • Jones, C.A.1    Proctor, M.R.E.2
  • 36
    • 0038868531 scopus 로고
    • Resonant triad interactions in symmetric systems
    • Guckenheimer J., Mahalov A., Resonant triad interactions in symmetric systems. Physica D. 54:1992;267-310.
    • (1992) Physica D , vol.54 , pp. 267-310
    • Guckenheimer, J.1    Mahalov, A.2
  • 37
    • 45549113061 scopus 로고
    • Heteroclinic cycles and modulated traveling waves in systems with O(2) symmetry
    • Armbruster D., Guckenheimer J., Holmes P., Heteroclinic cycles and modulated traveling waves in systems with O(2) symmetry. Physica D. 29:1988;257-282.
    • (1988) Physica D , vol.29 , pp. 257-282
    • Armbruster, D.1    Guckenheimer, J.2    Holmes, P.3
  • 38
    • 84954683140 scopus 로고
    • Steady-state mode interactions in the presence of O(2)-symmetry
    • Dangelmayr G., Steady-state mode interactions in the presence of O(2)-symmetry. Dynam. Stabil. Syst. 1:1986;159-185.
    • (1986) Dynam. Stabil. Syst. , vol.1 , pp. 159-185
    • Dangelmayr, G.1
  • 39
    • 84971848073 scopus 로고
    • The interaction of two spatially resonant patterns in thermal convection. Part 1. Exact 1:2 resonance
    • Proctor M.R.E., Jones C.A., The interaction of two spatially resonant patterns in thermal convection. Part 1. Exact 1:2 resonance. J. Fluid Mech. 188:1988;301-335.
    • (1988) J. Fluid Mech. , vol.188 , pp. 301-335
    • Proctor, M.R.E.1    Jones, C.A.2
  • 40
    • 0035890542 scopus 로고    scopus 로고
    • New type of complex dynamics in the 1:2 spatial resonance
    • Porter J., Knobloch E., New type of complex dynamics in the 1:2 spatial resonance. Physica D. 159:2001;125-154.
    • (2001) Physica D , vol.159 , pp. 125-154
    • Porter, J.1    Knobloch, E.2
  • 42
    • 0001091450 scopus 로고    scopus 로고
    • Damping of nearly inviscid water waves
    • Martel C., Knobloch E., Damping of nearly inviscid water waves. Phys. Rev. E. 56:1997;5544-5548.
    • (1997) Phys. Rev. E , vol.56 , pp. 5544-5548
    • Martel, C.1    Knobloch, E.2


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