Non-symmetric gravity and capillary-gravity travelling waves

capwavesThere has been some discussion about non-symmetric travelling waves.  The primary travelling water wave, of gravity type or capillary-gravity type, bifurcating from the trivial solution, is symmetric.  However, starting with the work of Zufiria (1997), it was recognized that non-symmetric waves could arise through a symmetry-breaking bifurcation.  The calculation of non-symmetric waves in Zufiria (1997) is for pure gravity waves.  More recently, Aider & Debiane (2004) extended this work to the case of gravity-capillary waves.  They calculated non-symmetric steady periodic gravity-capillary waves on deep water.  They are found as bifurcations from symmetric waves. In Aider & Debiane (2006), the theory is extended to finite depth, showing that non-symmetric waves bifurcate in shallow water as well. Shimizu & Shoji (2012) report on numerical computation of non-symmetric capillary-gravity waves on water of infinite depth.  They not only demonstrate the existence of non-symmetric waves with six peaks, but also clarify the mechanism of their appearance/disappearance.  Furthermore they obtained a new type of non-symmetric wave.

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