Periodic traveling interfacial hydroelastic waves with or without mass

Well-posedness of two-dimensional hydroelastic waves with mass

We study hydroelastic waves in interfacial flow of two-dimensional irrotational fluids. Each of the fluids is taken to be of infinite extent in one vertical direction, and bounded by a free surface in the other vertical direction. Elastic effects are considered at the free surface; this can describe physical settings such as the ocean bounded above by a layer of ice. A previous study proved wel...

Periodic Traveling Water Waves with Isobaric Streamlines

It is shown that in water of finite depth, there are no periodic traveling waves with the property that the pressure in the underlying fluid flow is constant along streamlines. In the case of infinite depth, there is only one such solution, which is due to Gerstner.

Bifurcation and Secondary Bifurcation of Heavy Periodic Hydroelastic Travelling Waves

The existence question for two-dimensional symmetric steady waves travelling on the surface of a deep ocean beneath a heavy elastic membrane is analyzed as a problem in bifurcation theory. The behaviour of the two-dimensional cross-section of the membrane is modelled as a thin (unshearable), heavy, hyperelastic Cosserat rod, and the fluid beneath is supposed to be in steady two-dimensional irro...

Modelling nonlinear hydroelastic waves.

This paper uses the special Cosserat theory of hyperelastic shells satisfying Kirchoff's hypothesis and irrotational flow theory to model the interaction between a heavy thin elastic sheet and an infinite ocean beneath it. From a general discussion of three-dimensional motions, involving an Eulerian description of the flow and a Lagrangian description of the elastic sheet, a special case of two...

Periodic Traveling Waves in Diatomic Granular Chains