wavefronts-and-modal-structure-of-long-surface-and-internal-ring-waves-on-a-parallel-shear-current.pdf (3.55 MB)
Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current
journal contribution
posted on 2021-10-21, 08:58 authored by Curtis Hooper, Karima KhusnutdinovaKarima Khusnutdinova, Roger GrimshawWe 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 MechanicsVolume
927Publisher
Cambridge University Press (CUP)Version
- VoR (Version of Record)
Rights holder
© The AuthorsPublisher 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
2021-09-06Publication date
2021-09-29Copyright date
2021ISSN
0022-1120eISSN
1469-7645Publisher version
Language
- en
Depositor
Dr Karima Khusnutdinova. Deposit date: 6 September 2021Article number
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