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. doi:10.1017/s0022112085003494. https://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 | ||||||
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Additional Information: | © 1985 Cambridge University Press. (Received 2 April 1984 and in revised form 7 November 1984) | ||||||
DOI: | 10.1017/s0022112085003494 | ||||||
Record Number: | CaltechAUTHORS:20181120-153100310 | ||||||
Persistent URL: | https://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: | 16 Nov 2021 03:38 |
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