A mild-slope formulation based on Weyl rule of association with application to coastal wave modelling

Akrish, G.; Smit, Pieter; Zijlema, Marcel; Reniers, A.J.H.M.

doi:10.1016/j.wavemoti.2023.103189

A mild-slope formulation based on Weyl rule of association with application to coastal wave modelling

Title

A mild-slope formulation based on Weyl rule of association with application to coastal wave modelling

Author

Akrish, G. (TU Delft Environmental Fluid Mechanics)
Smit, Pieter (Sofar Ocean Technologies)
Zijlema, Marcel (TU Delft Environmental Fluid Mechanics)
Reniers, A.J.H.M. (TU Delft Environmental Fluid Mechanics)

Date

2023

Abstract

Weyl rule of association, proposed by Hermann Weyl for quantum mechanics applications (Weyl, 1931), can be used to associate between the dispersion relation of water waves and a non-local pseudo-differential operator. The central result of this study is that this operator correctly approximates the Dirichlet-to-Neumann operator derived for linear waves over a slowly varying bathymetry. This opens the door to a formal use of Weyl's operational calculus, and consequently, allowing straightforward derivations and generalizations of water waves’ models over mild slopes. Specifically, within the framework of linear wave theory, the formulation based on Weyl rule of association provides a generalized mild-slope model which does not impose a limit on the spectral width. Most significantly, the mild-slope formulation based on Weyl rule of association allows to derive a general linear kinetic equation for which the widely used energy balance equation (the central equation of forecasting models such as SWAN and WAVEWATCH) serves as a special case. This result not only provides a formal link between the deterministic description (i.e., Euler equations) and the stochastic description (i.e., the energy balance equation), but also establishes the theoretical foundations for the statistical description of bathymetry-induced wave interferences. Such a statistical description is especially important over coastal waters, where through the interaction with the bathymetry, waves are rapidly scattered and tend to form focal zones and associated interference patterns.

Subject

A mild-slope formulation
Phase-averaged models
Spectral modelling of coastal waves
Statistical wave interferences
The energy balance equation
Weyl rule of association

To reference this document use:

http://resolver.tudelft.nl/uuid:df138b42-996d-4c9f-b181-bd4112dfb291

DOI

https://doi.org/10.1016/j.wavemoti.2023.103189

ISSN

0165-2125

Source

Wave Motion, 122

Part of collection

Institutional Repository