CaltechAUTHORS
  A Caltech Library Service

Stability of finite-amplitude interfacial waves. Part 2. Numerical results

Pullin, D. I. and Grimshaw, R. H. J. (1985) Stability of finite-amplitude interfacial waves. Part 2. Numerical results. Journal of Fluid Mechanics, 160 . pp. 317-336. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20181120-153100107

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20181120-153100107

Abstract

In the preceding paper (Grimshaw & Pullin 1985) we discussed the long-wavelength modulational instability of interfacial progressive waves in a two-layer fluid. In this paper we complement our analytical results by numerical results for the linearized stability of finite-amplitude waves. We restrict attention to the case when the lower layer is infinitely deep, and use the Boussinesq approximation. For this case the basic wave profile has been calculated by Pullin & Grimshaw (1983a, b). The linearized stability problem for perturbations to the basic wave is solved numerically by seeking solutions in the form of truncated Fourier series, and solving the resulting eigenvalue problem for the growth rate as a function of the perturbation wavenumber. For small or moderate basic wave amplitudes we show that the instabilities are determined by a set of low-order resonances. The lowest resonance, which contains the modulational instability, is found to be dominant for all cases considered. For higher wave amplitudes, the resonance instabilities are swamped by a local wave-induced Kelvin–Helmholtz instability.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/s0022112085003500DOIArticle
Additional Information:© 1985 Cambridge University Press. (Received 2 April 1984 and in revised form 7 November 1984)
Record Number:CaltechAUTHORS:20181120-153100107
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181120-153100107
Official Citation:Pullin, D., & Grimshaw, R. (1985). Stability of finite-amplitude interfacial waves. Part 2. Numerical results. Journal of Fluid Mechanics, 160, 317-336. doi:10.1017/S0022112085003500
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91099
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:21 Nov 2018 15:33
Last Modified:21 Nov 2018 15:33

Repository Staff Only: item control page