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Steady periodic hydroelastic waves in polar regions

Bogdan-Vasile Matioc, Emilian Parau

Abstract

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 necessary and sufficient condition for local bifurcation from the trivial branch of laminar flow solutions.

Steady periodic hydroelastic waves in polar regions

Abstract

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 necessary and sufficient condition for local bifurcation from the trivial branch of laminar flow solutions.
Paper Structure (8 sections, 12 theorems, 115 equations)

This paper contains 8 sections, 12 theorems, 115 equations.

Table of Contents

  1. Introduction
  2. Equivalent formulations of the hydroelastic waves problem
  3. The velocity formulation
  4. The height function formulation
  5. An equivalent formulation of \ref{['FOR3']}
  6. Local bifurcation analysis
  7. Laminar flow solutions for \ref{['PBF']}
  8. Bifurcation analysis for \ref{['PBF']}

Key Result

Theorem 1.1

Let $\alpha>0$, $d>0$, $p_0<0,$ and $g>0$ be fixed and choose $\beta\in(0,1)$. Assume that the vorticity function $\gamma$ belongs to ${\rm C}^\beta([p_0,0])$ and set Then we have:

Theorems & Definitions (26)

  • Theorem 1.1
  • Remark 1.2
  • Remark 1.3
  • Proposition 2.1: Equivalence of formulations
  • proof
  • Lemma 3.1
  • proof
  • Lemma 4.1
  • proof
  • Lemma 4.2
  • ...and 16 more