wavefronts-and-modal-structure-of-long-surface-and-internal-ring-waves-on-a-parallel-shear-current.pdf (3.55 MB)
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Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current

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journal contribution
posted on 21.10.2021, 08:58 by Curtis Hooper, Karima KhusnutdinovaKarima Khusnutdinova, Roger Grimshaw
We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear current. The far-field modal and amplitude equations for the ring waves are presented in dimensional form. We re-derive the modal equations from the formulation for plane waves tangent to the ring wave, which opens a way to obtaining important characteristics of the ring waves (group speed, wave action conservation law) and to constructing more general ‘hybrid solutions’ consisting of a part of a ring wave and two tangent plane waves. The modal equations constitute a new spectral problem, and are analysed for a number of examples of surface ring waves in a homogeneous fluid and internal ring waves in a stratified fluid. Detailed analysis is developed for the case of a two-layered fluid with a linear shear current where we study their wavefronts and two-dimensional modal structure. Comparisons are made between the modal functions (i.e. eigenfunctions of the relevant spectral problems) for the surface waves in a homogeneous and two-layered fluids, as well as the interfacial waves described exactly and in the rigid-lid approximation. We also analyse the wavefronts of surface and interfacial waves for a large family of power-law upper-layer currents, which can be used to model wind generated currents, river inflows and exchange flows in straits. A global and local measure of the deformation of wavefronts are introduced and evaluated.

History

School

  • Mechanical, Electrical and Manufacturing Engineering
  • Science

Department

  • Mathematical Sciences

Published in

Journal of Fluid Mechanics

Volume

927

Publisher

Cambridge University Press (CUP)

Version

VoR (Version of Record)

Rights holder

© The Authors

Publisher statement

This is an Open Access Article. It is published by Cambridge University Press under the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/

Acceptance date

06/09/2021

Publication date

2021-09-29

Copyright date

2021

ISSN

0022-1120

eISSN

1469-7645

Language

en

Depositor

Dr Karima Khusnutdinova. Deposit date: 6 September 2021

Article number

A37

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