Traveling hydroelastic waves in constant vorticity flows with stagnation points

Martin, Calin and Parau, Emilian (2025) Traveling hydroelastic waves in constant vorticity flows with stagnation points. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences. ISSN 1364-5021 (In Press)

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Abstract

We present a bifurcation approach which delivers two-dimensional traveling 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 modeled 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.

Item Type:	Article
Uncontrolled Keywords:	hydroelastic waves,dirichlet–neumann map,hilbert transforms,stagnation points,cosserat theory
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Fluids & Structures
Depositing User:	LivePure Connector
Date Deposited:	23 Dec 2025 14:30
Last Modified:	23 Dec 2025 14:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/101497
DOI:	issn:1364-5021

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