CaltechAUTHORS
  A Caltech Library Service

Stability of finite-amplitude interfacial waves. Part 3. The effect of basic current shear for one-dimensional instabilities

Pullin, D. I. and Grimshaw, R. H. J. (1986) Stability of finite-amplitude interfacial waves. Part 3. The effect of basic current shear for one-dimensional instabilities. Journal of Fluid Mechanics, 172 . pp. 277-306. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20181120-153100421

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:20181120-153100421

Abstract

We consider the linearized stability of interfacial progressive waves in a two-layer inviscid fluid, for the case when there is a basic current shear in either, or both, of the fluids. For this configuration the basic wave has been calculated by Pullin & Grimshaw (1983b). Our results here are mainly restricted to two-space-dimensional instabilities (i.e. one-dimensional in the propagation space), and are obtained both analytically and numerically. The analytical results are for the long-wavelength modulational instability of small-amplitude waves. The numerical results are restricted to the case when the lower fluid is infinitely deep, and for the Boussinesq approximation. They are obtained by solving the linearized stability problem with truncated Fourier series, and solving the resulting eigenvalue problem for the growth rate. For small values of the basic current shear, and for small or moderate basic wave amplitude, the instabilities are determined by a set of low-order resonances; for larger basic wave amplitude, these are dominated by the onset of a local wave-induced Kelvin–Helmholtz instability. For larger values of the basic current shear, this interpretation is modified owing to the appearance of a number of new effects.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/s002211208600174xDOIArticle
Additional Information:© 1986 Cambridge University Press. (Received 4 June 1985 and in revised form 13 February 1986) The contribution of D. I. Pullin to the present work was supported by the Australian Research Grants Scheme under Grant no. F8315031 R.
Funders:
Funding AgencyGrant Number
Australian Research Grants CommitteeF 8315031 R
Record Number:CaltechAUTHORS:20181120-153100421
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181120-153100421
Official Citation:Pullin, D., & Grimshaw, R. (1986). Stability of finite-amplitude interfacial waves. Part 3. The effect of basic current shear for one-dimensional instabilities. Journal of Fluid Mechanics, 172, 277-306. doi:10.1017/S002211208600174X
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91102
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:21 Nov 2018 15:47
Last Modified:21 Nov 2018 15:47

Repository Staff Only: item control page