Abstract
This paper describes the solution to the problem of scattering of plane incident waves on water of constant depth by a bottom mounted circular cylinder, extending partially through the depth, which has an internal structure comprised of closely-spaced thin vertical barriers between which fluid is allowed to flow. The problem is solved under full depth dependent linearised water wave theory using an effective medium equation to describe the fluid motion in cylinder and effective boundary conditions to match that flow to the fluid region outside the cylinder. The interest in this problem lies in the development of novel solution methods for fully three dimensional water wave interaction with bathymetric plate arrays. Results computed using this theory are compared with a shallow water approximation based on the recent work of Marangos & Porter (2021) and with accurate computations of an exact representation of the geometry using discrete set of plates. Other results highlight the resonant directional lensing effects of this type of cylindrical plate array device.
| Original language | English |
|---|---|
| Article number | 20210824 |
| Number of pages | 21 |
| Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 478 |
| Issue number | 2258 |
| DOIs | |
| Publication status | Published - 23 Feb 2022 |
Bibliographical note
Funding Information:R.P. acknowledges support of the EPSRC through grant no. EP/V04740X/1. S.Z. gratefully acknowledges the State Key Laboratory of Coastal and Offshore Engineering (Dalian University of Technology) for supporting part of this work through the Open Research Fund Program (grant no. LP1928).
Publisher Copyright:
© 2022 The Authors.
Keywords
- plate arrays
- vertical cylinders
- water waves