| Abstract: |
| In this talk we discuss two-dimensional periodic travelling hydroelastic waves on water of infinite depth. We track a bifurcation branch that connects small amplitude periodic waves to a large amplitude state in which the wave is motionless at rest and the fluid is static. The stability of the periodic waves on this branch is computed using a surface-variable formulation, computing growth rates numerically via Floquet theory. The stability spectrum including both superharmonic and subharmonic perturbations will be presented. For superharmonic perturbations the onset of instability via a Tanaka-type collision of eigenvalues at zero is identified. We shed light on the structure of the spectrum as wave amplitude increases and reveal a highly intricate structure. |
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