A Streamwise Constant Model of Turbulence in Plane Couette Flow

Journal article

Streamwise and quasi-streamwise elongated structures have been shown to play a significant role in turbulent shear flows. We model the mean behavior 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 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 system 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.

Authors: Gayme, D; McKeon, B; Papachristodoulou, A; Bamieh, B; Doyle, J

• Publication status: Published
• Journal: JOURNAL OF FLUID MECHANICS
• Volume: 665
• Pages: 99-119
• Publication date: 2010-01-05
• DOI: 10.1017/S0022112010003861
• EISSN: 1469-7645
• ISSN: 0022-1120
• Language: English
• Keywords: physics.flu-dyn