Stability of periodic traveling flexural‐gravity waves in two dimensions

Trichtchenko, Olga, Milewski, Paul, Parau, Emilian 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
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 31 Aug 2018 14:32
Last Modified: 27 May 2020 23:58
URI: https://ueaeprints.uea.ac.uk/id/eprint/68177
DOI: 10.1111/sapm.12233

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