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Stability of finite-amplitude interfacial waves. Part 1. Modulational instability for small-amplitude waves

Grimshaw, R. H. J. and Pullin, D. I. (1985) Stability of finite-amplitude interfacial waves. Part 1. Modulational instability for small-amplitude waves. Journal of Fluid Mechanics, 160 . pp. 297-315. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20181120-153100310

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Abstract

In two previous papers (Pullin & Grimshaw 1983a, b) we studied the wave profile and other properties of finite-amplitude interfacial progressive waves in a two-layer fluid. In this and the following paper (Pullin & Grimshaw 1985) we discuss the stability of these waves to small perturbations. In this paper we obtain anatytical results for the long-wavelength modulational instability of small-amplitude waves. Using a multiscale expansion, we obtain a nonlinear Schrödinger equation coupled to a wave-induced mean-flow equation to describe slowly modulated waves. From these coupled equations we determine the stability of a plane progressive wave. Our results are expressed by determining the instability bands in the (p, q)-plane, where (p, q) is the modulation wavenumber, and are obtained for a range of values of basic density ratio and undisturbed layer depths.


Item Type:Article
Related URLs:
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https://doi.org/10.1017/s0022112085003494DOIArticle
Additional Information:© 1985 Cambridge University Press. (Received 2 April 1984 and in revised form 7 November 1984)
Record Number:CaltechAUTHORS:20181120-153100310
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181120-153100310
Official Citation:Grimshaw, R., & Pullin, D. (1985). Stability of finite-amplitude interfacial waves. Part 1. Modulational instability for small-amplitude waves. Journal of Fluid Mechanics, 160, 297-315. doi:10.1017/S0022112085003494
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91101
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:21 Nov 2018 15:45
Last Modified:21 Nov 2018 15:45

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