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Title: Spatial bifurcations of interfacial waves when the phase and group velocities are nearly equal
Authors: Bridges, Thomas J. 
Dias, Frederic 
Christodoulides, Paul 
Major Field of Science: Engineering and Technology
Field Category: Electrical Engineering - Electronic Engineering - Information Engineering
Keywords: Interfacial waves
Issue Date: 25-Jul-1995
Source: Journal of Fluid Mechanics, 1995, vol. 295, pp. 121-158
Volume: 295
Start page: 121
End page: 158
Journal: Journal of Fluid Mechanics 
Abstract: Steady waves at the interface between two immiscible and inviscid fluids of differing density are studied. The governing equations are reformulated as a spatial Hamiltonian system leading to new variational principles for uniform states and travelling waves. Analytical methods based on the properties of the Hamiltonian structure and numerical methods are used to find new branches of steady nonlinear interfacial waves in the eighbourhood of the singularity c = cg. While the water-wave problem (upper fluid density negligible) near this singularity has received considerable attention the results for interfacial waves present some new features. The branches of travelling waves when plotted in ($\tilde{F}, \bar{S}$)-space, where $\tilde{F}$ and $\bar{S}$ are related to the energy flux and flow force respectively, show new bifurcations in the context of hydrodynamic waves even at very low amplitudes. The secondary bifurcations are explained by a spatial analogue of the superharmonic instability. An interesting analogy is also found between the spatial bifurcations of travelling waves and the Kelvin–Helmholtz instability. The new branches of waves occur at physically realizable values of the parameters and therefore could have implications for interfacial waves in applications.
ISSN: 1469-7645
DOI: 10.1017/S0022112095001911
Rights: © Cambridge University Press
Type: Article
Affiliation: Université de Nice–Sophia Antipolis 
Affiliation : University of Surrey 
Université de Nice–Sophia Antipolis 
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