On functional equations leading to exact solutions for standing internal waves

F. Beckebanze, Grant Keady

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    © 2015 Elsevier B.V. The Dirichlet problem for the wave equation is a classical example of a problem which is ill-posed. Nevertheless, it has been used to model internal waves oscillating harmonically in time, in various situations, standing internal waves amongst them. We consider internal waves in two-dimensional domains bounded above by the plane z= 0 and below by z= -d(x) for depth functions d. This paper draws attention to the Abel and Schröder functional equations which arise in this problem and use them as a convenient way of organising analytical solutions. Exact internal wave solutions are constructed for a selected number of simple depth functions d.
    Original languageEnglish
    Pages (from-to)181-195
    JournalWave Motion
    Volume60
    DOIs
    Publication statusPublished - 2016

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