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The bifurcation of interfacial capillary-gravity waves under O(2) symmetry

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  • The evolution of an interface between two fluids of different densities is considered. The particular case under examination is when the motion is due to an interaction between the Mth and Nth harmonics of the fundamental mode. By means of a hodograph transformation the problem is cast as an operator equation between two suitable function spaces. Classical techniques are used to reduce the problem to a finite system of algebraic equations. Solutions are found which exhibit a rich variety of behaviour including primary, secondary and multiple bifurcation.
    Mathematics Subject Classification: Primary: 37G40, 76B15; Secondary: 34G56.


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