University of Tasmania
Browse

File(s) not publicly available

On the generation of mean flows by the interaction of Görtler vortices and Tollmien-Schlichting waves in curved channel flows

journal contribution
posted on 2023-05-18, 18:36 authored by Andrew BassomAndrew Bassom, Hall, P
There are many fluid flows where the onset of transition can be caused by different instability mechanisms which compete in the nonlinear regime. Here the interaction of a centrifugal instability mechanism with the viscous mechanism which causes Tollmien-Schlichting waves is discussed. The interaction between these modes can be strong enough to drive the mean state; here the interaction is investigated in the context of curved channel flows so as to avoid difficulties associated with boundary layer growth. Essentially it is found that the mean state adjusts itself so that any modes present are neutrally stable even at finite amplitude. In the first instance the mean state driven by a vortex of short wavelength in the absence of a Tollmien-Schlichting wave is considered. It is shown that for a given channel curvature and vortex wavelength there is an upper limit to the mass flow rate which the channel can support as the pressure gradient is increased. When Tollmien-Schlichting waves are present then the nonlinear differential equation to determine the mean state is modified. At sufficiently high Tollmien-Schlichting amplitudes it is found that the vortex flows are destroyed, but there is a range of amplitudes where a fully nonlinear mixed vortex-wave state exists and indeed drives a mean state having little similarity with the flow which occurs without the instability modes. The vortex and Tollmien-Schlichting wave structure in the nonlinear regime has viscous wall layers and internal shear layers; the thickness of the internal layers is found to be a function of the Tollmien-Schlichting wave amplitude.

History

Publication title

Studies in Applied Mathematics

Volume

81

Pagination

185-219

ISSN

0022-2526

Department/School

School of Natural Sciences

Publisher

Blackwell Publishers

Place of publication

350 Main Street, Ste 6, Malden, USA, Ma, 02148

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

Usage metrics

    University Of Tasmania

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC