DOI

We consider the propagation of surface water waves in a straight planar channel perturbed at the bottom by several thin curved tunnels and wells. We propose a method to construct non reflecting underwater topographies of this type at an arbitrary prescribed wave number. To proceed, we compute asymptotic expansions of the diffraction solutions with respect to the small parameter of the geometry taking into account the existence of boundary layer phenomena. We establish error estimates to validate the expansions using advances techniques of weighted spaces with detached asymptotics. In the process, we show the absence of trapped surface waves for perturbations small enough. This analysis furnishes asymptotic formulas for the scattering matrix and we use them to determine underwater topographies which are non-reflecting. Theoretical and numerical examples are given.

Язык оригиналаанглийский
Страницы (с-по)81-122
Число страниц42
ЖурналAsymptotic Analysis
Том118
Номер выпуска1-2
DOI
СостояниеОпубликовано - 1 янв 2020

    Предметные области Scopus

  • Математика (все)

ID: 60873187