Travelling hydroelastic waves in constant vorticity flows with stagnation points

Abstract We present a bifurcation approach which delivers two-dimensional travelling hydroelastic water waves propagating at the free surface of a rotational ideal fluid of constant vorticity and finite depth, covered by a thin ice sheet which is modelled by using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff’s hypothesis. The approach is based on a reformulation of the water wave problem as a pseudodifferential equation for a function of one variable, giving the elevation of the free surface (allowed to have overhanging profiles). Moreover, the involved method permits the existence of stagnation points whose existence in the resulting solution flows is then proved rigorously.