Steady Periodic Hydroelastic Waves in Polar Regions

We construct two-dimensional steady periodic hydroelastic waves with vorticity that propagate on water of finite depth under a deformable floating elastic plate which is modeled by using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff’s hypothesis. This is achieved by providing a necessary and sufficient condition for local bifurcation from the trivial branch of laminar flow solutions.