English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Hamiltonian coupled-mode theory (HCMT), recently derived by Athanassoulisand Papoutsellis [1], provides an efficient new approach for solving fullynonlinear water-wave problems over arbitrary bathymetry. In HCMT, heavy use ismade of the roots of a local, water-wave dispersion relation with varyingparameter, which have to be calculated at every horizontal position and everytime instant. Thus, fast and accurate calculation of these roots, valid for allpossible values of the varying parameter, are of fundamental importance. Inthis paper, new, semi-explicit and highly accurate root-finding formulae arederived, especially for the roots corresponding to evanescent modes. Thederivation is based on the successive application of a Picard-type iterationand the Householder's root finding method. Explicit approximate formulae ofvery good accuracy are obtained, which are adequate to support HCMT for manytypes of applications. In most demanding cases, e.g. very steep, deep-waterwaves, machine-accurate determination of the required roots is achieved by nomore than three iterations, using the explicit forms as initial values.Exploiting this root-finding procedure in the HCMT, results in an efficient,numerical solver able to treat fully nonlinear water waves over arbitrarybathymetry. Applications to demanding nonlinear problems demonstrate theefficiency and the robustness of the present approach.

Semi-explicit solutions to the water-wave dispersion relation and their role in the nonlinear Hamiltonian coupled-mode theory