Mathematics – Analysis of PDEs
Scientific paper
2008-11-29
Mathematics
Analysis of PDEs
23 pages, 3 figures
Scientific paper
The paper deals with a problem of interaction between hydrodynamics and mechanics of nonlinear elastic bodies. 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, following Antman's elasticity theory, and the fluid beneath is supposed to be in steady 2D irrotational motion under gravity. Assuming that gravity and the density of the undeformed membrane are prescribed, the free parameters of the problem are the speed of the wave and drift velocity of the membrane. The analysis relies upon a conformal formulation of the hydro-elastic problem developed in previous papers; the basic tool for the study of the bifurcation picture is the implicit function theorem, under some non-resonance assumptions. The most interesting part of the final result is the existence of a symmetry-breaking 'third sheet' of solutions, which bifurcates from primary sheets, and is a hydro-elastic analogue of the phenomenon known as 'Wilton ripples' in the surface tension case.
Baldi Pietro
Toland John F.
No associations
LandOfFree
Bifurcation and Secondary Bifurcation of Heavy Periodic Hydroelastic Travelling Waves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Bifurcation and Secondary Bifurcation of Heavy Periodic Hydroelastic Travelling Waves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bifurcation and Secondary Bifurcation of Heavy Periodic Hydroelastic Travelling Waves will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-139801