No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

Amplification and nonlinear mechanisms in plane Couette flow

Rent:

Rent this article for

USD

10.1063/1.3599701

### Abstract

We study the input-output response of a streamwise constant projection of the Navier-Stokes equations for plane Couette flow, the so-called 2D/3C model. Study of a streamwise constant model is motivated by numerical and experimental observations that suggest the prevalence and importance of streamwise and quasi-streamwise elongated structures. Periodic spanwise/wall-normal (*z*–*y*) plane stream functions are used as input to develop a forced 2D/3C streamwise velocity field that is qualitatively similar to a fully turbulentspatial field of direct numerical simulation data. The input-output response associated with the 2D/3C nonlinear coupling is used to estimate the energy optimal spanwise wavelength over a range of Reynolds numbers. The results of the input-output analysis agree with previous studies of the linearized Navier-Stokes equations. The optimal energy corresponds to minimal nonlinear coupling. On the other hand, the nature of the forced 2D/3C streamwise velocity field provides evidence that the nonlinear coupling in the 2D/3C model is responsible for creating the well known characteristic “S” shaped turbulent velocity profile. This indicates that there is an important tradeoff between energy amplification, which is primarily linear, and the seemingly nonlinear momentum transfer mechanism that produces a turbulent-like mean profile.

© 2011 American Institute of Physics

Received 18 November 2010
Accepted 17 May 2011
Published online 17 June 2011

Acknowledgments: The authors would like to thank H. Kawamura and T. Tsukahara for providing them with their DNS data. This research is partially supported by AFOSR (FA9550-08-1-0043). B.J.M. gratefully acknowledges support from NSF-CAREER Award No. 0747672 (program managers W. W. Schultz and H. H. Winter).

Article outline:

I. INTRODUCTION

II. MODELS

A. The 2D/3C model

B. The stream function model

III. FORCED SOLUTIONS

A. The velocity field

B. Mean profile

IV. INPUT-OUTPUT AMPLIFICATION

A. Energy amplification

B. Reynolds number scaling

C. Optimal spanwise spacing

D. Mean velocity profile versus optimal k_{z}

V. CONCLUSIONS AND FUTURE WORK

/content/aip/journal/pof2/23/6/10.1063/1.3599701

http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/6/10.1063/1.3599701

Article metrics loading...

/content/aip/journal/pof2/23/6/10.1063/1.3599701

2011-06-17

2014-04-18

Full text loading...

### Most read this month

Article

content/aip/journal/pof2

Journal

5

3

Commenting has been disabled for this content