Modulational stability of Taylor vortices in a curved channel

Authors

A. H. Dando, The University of Manchester
P. Hall, Imperial College London
D. T. Papageorgiou, New Jersey Institute of Technology

Document Type

Article

Publication Date

1-1-2000

Abstract

In this paper we use a multiple scales approach to derive an equation governing the modulational stability of Taylor vortices in a high Reynolds number flow through a curved channel of small gap. The evolution equation governing the two-dimensional modulation of Taylor vortices is found to be a modified Burgers equation with a new nonlinear term (AT+A²AX = ±AXX). When finite but small curvature effects are accounted for, this modified Burgers equation generalizes to AT+A²AX = ±AXX+λA. Numerical solutions of this equation show that a family of periodic traveling waves exists, with profiles becoming increasingly steeper as the length of the system is increased.

Identifier

0033645053 (Scopus)

Publication Title

SIAM Journal on Applied Mathematics

External Full Text Location

https://doi.org/10.1137/S003613999731557X

ISSN

00361399

First Page

1543

Last Page

1564

Issue

5

Volume

60

Recommended Citation

Dando, A. H.; Hall, P.; and Papageorgiou, D. T., "Modulational stability of Taylor vortices in a curved channel" (2000). Faculty Publications. 15776.
https://digitalcommons.njit.edu/fac_pubs/15776