Author:
Blyth M. G.,Părău E. I.,Wang Z.
Abstract
AbstractTwo-dimensional periodic travelling hydroelastic waves on water of infinite depth are investigated. A bifurcation branch is tracked that delineates a family of such solutions connecting small amplitude periodic waves to the large amplitude static state for which the wave is at rest and there is no fluid motion. The stability of these periodic waves is then examined using a surface-variable formulation in which a linearised eigenproblem is stated on the basis of Floquet theory and solved numerically. The eigenspectrum is discussed encompassing both superharmonic and subharmonic perturbations. In the former case, the onset of instability via a Tanaka-type collision of eigenvalues at zero is identified. The structure of the eigenvalue spectrum is elucidated as the travelling-wave branch is followed revealing a highly intricate structure.
Publisher
Springer Science and Business Media LLC
Reference33 articles.
1. Korobkin, A., Părău, E.I., Vanden-Broeck, J.-M.: The mathematical challenges and modelling of hydroelasticity. Philos Trans A Math Phys Eng Sci 369, 2803–2812 (2011)
2. Părău, E., Dias, F.: Nonlinear effects in the response of a floating ice plate to a moving load. J. Fluid Mech. 460, 281–305 (2002)
3. Toland, J.F.: Steady periodic hydroelastic waves. Arch. Rat. Mech. Anal. 189, 325–362 (2008)
4. Milewski, P.A., Vanden-Broeck, J.-M., Wang, Z.: Hydroelastic solitary waves in deep water. J. Fluid Mech. 679, 628–640 (2011)
5. Guyenne, P., Părău, E.I.: Computations of fully nonlinear hydroelastic solitary waves on deep water. J. Fluid Mech. 713, 307–329 (2012)