Abstract
A weakly nonlinear fully dispersive model equation is derived which describes the propagation of waves in a thin elastic body overlying an incompressible inviscid fluid. The equation is nonlocal in the linear part, and is similar to the socalled Whitham equation which was proposed as a model for the description of wave motion at the free surface of an inviscid fluid. Steady solutions of the fully nonlinear hydroelastic Euler equations are approximated numerically, and compared to numerical approximations to steady solutions of the fully dispersive but weakly nonlinear model equation. The bifurcation curves for these two different models are compared, and it is found that the weakly nonlinear model gives accurate predictions for waves of small to moderate amplitude. For larger amplitude waves, the two models still agree on key qualitative features such as the bifurcation points, secondary bifurcations, and the number of oscillations in a given fundamental wave period.
Original language  English 

Pages (fromto)  202210 
Number of pages  9 
Journal  Applied Ocean Research 
Volume  89 
Early online date  28 May 2019 
DOIs  
Publication status  Published  Aug 2019 
Profiles

Emilian Parau
 School of Mathematics  Professor of Applied Mathematics & Head of School
 Fluid and Solid Mechanics  Member
Person: Research Group Member, Academic, Teaching & Research