- Access by Xinjiang University
Stability of steady cross waves: Theory and experiment
Phys. Rev. A 37, 1663 – Published 1 March, 1988
DOI: https://doi.org/10.1103/PhysRevA.37.1663
Abstract
A bifurcation analysis is performed in the neighborhood of neutral stability for cross waves as a function of forcing, detuning, and viscous damping. A transition is seen from a subcritical to a supercritical bifurcation at a critical value of the detuning. The predicted hysteretic behavior is observed experimentally. A similarity scaling in the inviscid limit is also predicted. The experimentally observed bifurcation curves agree with this scaling.
References (13)
- A. F. Jones, J. Fluid Mech. 138, 53 (1984).
- J. W. Miles, J. Fluid Mech. 151, 391 (1985).
- A. J. Bernoff, L. P. Kwok, and S. Lichter (unpublished).
- J. Miles and J. Becker (unpublished).
- B. J. S. Barnard and W. G. Pritchard, J. Fluid Mech. 55, (Pt. 2), 245 (1972).
- S. Lichter and L. Shemer, Phys. Fluids 29, 3971 (1986).
- L. Shemer and S. Lichter Phys. Fluids 30, 3427 (1987).
- S. Lichter and W. B. Underhill, Phys. Rev. A 35, 5282 (1987).
- S. Lichter and J. Chen, J. Fluid Mech. 183, 451 (1987).
- H. Haken, Synergetics, 2nd ed. (Springer-Verlag, New York, 1978).
- P. Coullet and E. A. Spiegel, SIAM J. Appl. Math. 43, 776 (1983).
- S. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
- A. J. Bernoff, Ph.D. thesis, University of Cambridge, 1986.