Abstract
The nonlinear inst ability of Faraday waves may be examined either by decomposition into standing-wave modes, as in Craik (1994, 1998), Craik & Armitage (1995b) and Decent & Craik (1999); or by means of counter-propagating wave envelopes, as in recent work of Martel, Knoblo ch & Vega (2000). The differences and equivalences of these approaches are explored, and some results reinterpret ed.
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References
Craik, A.D.D. 1994 The stability of some three-dimensional and time-dependent flows. In Nonlinear Instability of Nonparallel Flows (eds. S.P. Lin & W. Phillips) pp. 382–396. (Proc. IUTAM Symp., Potsdam, NY. July 1993) Springer.
Craik, A.D.D. & Armitage, J. 1995a Faraday excitation, hysteresis and wave instability in a narrow rectangular wave tank. Fluid Dyn. Res., 15, pp. 129–143.
Craik, A.D.D. & Armitage, J. 1995b ‘Hysteresis and interaction of standing waves with Faraday excitation’. In Asymptotic Modelling in Fluid Mechanics (eds. P.-A. Bois, E. Derait, R. Gatignol, A. Rigolot) pp.117–128 (Proc. Colloque en l’honneur de J.P. Guiraud, Paris 1994) Springer.
Craik, A.D.D. 1998 ‘Nonlinear interaction of standing waves with Faraday excitation’. In Nonlinear Instability, Chaos and Turbulence You, (eds. L. Debnath & D.N. Riahi) Ch. 4, 91–127. Computational Mechanics Publ. WIT Press, UK.
Decent, S.P. & Craik, A.D.D. 1995 Hysteresis in Faraday resonance. J. Fluid Mech., 293, pp. 237–268.
Decent, S.P. & Craik, A.D.D. 1997 On limit cycles arising from the parametric excitation of standing waves. Wave Motion 25, 275–294.
Decent, S.P. & Craik, A.D.D. 1999 Sideband instability and modulations of Faraday waves. Wave Motion 30, 43–55.
Douady, S., Fauve, S. & Thual, O. 1989 Oscillatory phase modulation of parametrically forced surface waves. Europhys. Lett., 10(4), pp. 309–315.
Knobloch, E. & De Luca, J. 1990 Amplitude equations for travelling wave convection. Nonlinearity 3, 975–980.
Martel, C., Knobloch, E. & Vega, J.M. 2000 Dynamics of counterpropagating waves in parametrically forced systems. Physica D 137, 94–123.
Martel, C. & Vega, J.M. 1996 Finite size effects near the onset of the oscillatory instability. Nonlinearity 9, 1129–1171.
Martel, C. & Vega, J.M. 1998 Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability. Nonlinearity 11, 105–142.
Miles, J.W. & Henderson, D. 1990 Parametrically forced surface waves. Ann. Rev. Fluid Mech., 22, pp. 143–165.
Miles, J.W. 1993 On Faraday waves. J. Fluid Mech. 248, 671–683. [Corrigendum: J. Fluid Mech. 269, 372 (1994)].
Milner, S.T. 1991 Square patterns and secondary instabilities in driven capillary waves. J. Fluid Mech. 225, 81–100.
Pierce, R.D. & Knobloch, E. 1994 On the modulational stability of travelling and standing waves. Phys. Fluids 6, 1177–1190.
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Craik, A.D.D. (2001). Instability of Two-Dimensional Standing Faraday Waves. In: King, A.C., Shikhmurzaev, Y.D. (eds) IUTAM Symposium on Free Surface Flows. Fluid Mechanics and Its Applications, vol 62. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0796-2_9
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DOI: https://doi.org/10.1007/978-94-010-0796-2_9
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