Skip to main content
    • Aa
    • Aa

A streamwise constant model of turbulence in plane Couette flow

  • D. F. GAYME (a1), B. J. McKEON (a1), A. PAPACHRISTODOULOU (a2), B. BAMIEH (a3) and J. C. DOYLE (a1)...

Streamwise and quasi-streamwise elongated structures have been shown to play a significant role in turbulent shear flows. We model the mean behaviour of fully turbulent plane Couette flow using a streamwise constant projection of the Navier–Stokes equations. This results in a two-dimensional three-velocity-component (2D/3C) model. We first use a steady-state version of the model to demonstrate that its nonlinear coupling provides the mathematical mechanism that shapes the turbulent velocity profile. Simulations of the 2D/3C model under small-amplitude Gaussian forcing of the cross-stream components are compared to direct numerical simulation (DNS) data. The results indicate that a streamwise constant projection of the Navier–Stokes equations captures salient features of fully turbulent plane Couette flow at low Reynolds numbers. A systems-theoretic approach is used to demonstrate the presence of large input–output amplification through the forced 2D/3C model. It is this amplification coupled with the appropriate nonlinearity that enables the 2D/3C model to generate turbulent behaviour under the small-amplitude forcing employed in this study.

Corresponding author
Email address for correspondence:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

S. C. Reddy & P. J. Ioannou 2000 Energy transfer analysis of turbulent plane Couette flow. In Laminar–Turbulent Transition IUTAM 99 (ed. W. S. Saric & H. F. Fasel ), pp. 211216. Springer Verlag, Berlin.

N. Tillmark & P. H. Alfredsson 1998 Large scale structure in turbulent plane Couette flow. In Advances in Turbulence VII (ed. U. Frish ), pp. 5962. Kluwer.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 32 *
Loading metrics...

Abstract views

Total abstract views: 122 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 29th May 2017. This data will be updated every 24 hours.