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Trichtchenko, Olga, Milewski, Paul, Parau, Emilian 
ORCID: https://orcid.org/0000-0001-5134-2068 and Vanden-Broeck, Jean-Marc
(2019)
Stability of periodic traveling flexural‐gravity waves in two dimensions.
Studies in Applied Mathematics, 142 (1).
pp. 65-90.
ISSN 1467-9590
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Abstract
In this work, we solve the Euler’s equations for periodic waves travelling under a sheet of ice using a reformulation introduced in [1]. These waves are referred to as flexural-gravity waves. We compare and contrast two models for the effect of the ice: a linear model and a nonlinear model. The benefit of this reformulation is that it facilitates the asymptotic analysis. We use it to derive the nonlinear Schrödinger equation that describes the modulational instability of periodic travelling waves. We compare this asymptotic result with the numerical computation of stability using the Fourier-Floquet-Hill method to show they agree qualitatively. We show that different models have different stability regimes for large values of the flexural rigidity parameter. Numerical computations are also used to analyse high frequency instabilities in addition to the modulational instability. In the regions examined, these are shown to be the same regardless of the model representing ice.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | asymptotic analysis,nonlinear waves,numerical methods,stability of solutions,waves under ice,applied mathematics ,/dk/atira/pure/subjectarea/asjc/2600/2604 |
| Faculty \ School: | Faculty of Science > School of Mathematics (former - to 2024) |
| UEA Research Groups: | Faculty of Science > Research Groups > Fluid and Solid Mechanics (former - to 2024) Faculty of Science > Research Groups > Fluids & Structures |
| Related URLs: | |
| Depositing User: | LivePure Connector |
| Date Deposited: | 31 Aug 2018 14:32 |
| Last Modified: | 07 Nov 2024 12:40 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/68177 |
| DOI: | 10.1111/sapm.12233 |
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