Skip to main content

Remarks on the Control of Turbulent Flows

  • Conference paper
Flow Control

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 68))

Abstract

Our aim in the article is to address some theoretical and computational questions related to the control of viscous incompressible flows governed by the Navier-Stokes equations or related equations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. F. Abergel, R. Temam, On some control problems in fluid mechanics, Theoret. Comput. Fluid Dynamics 1 (1990), 303–325.

    Article  MATH  Google Scholar 

  2. F. Abergel, R. Temam, Optimal control of turbulent flows, (in) [15].

    Google Scholar 

  3. T. Bewley, H. Choi, P. Moin, R. Temam, Control of channel flows, (in preparation).

    Google Scholar 

  4. J.A. Burns, S. Kang, A stabilization problem for Burgers’ equation with unbounded control and observation, Intern. Series of Num. Math. 100 Birkhauser Verlag, Basel 1991, 51–72.

    Google Scholar 

  5. J.A. Burns, S. Kang, A control problem for Burgers’ equation with bounded input (output), Nonlinear Dynamics 2 (1991), 235–262.

    Article  Google Scholar 

  6. D.H. Chambers, R.J. Adrians, P. Moin, D.S. Stewart, H.J. Sung, Karhunen-Loeve expansion of Burgers’ model of turbulence, Phys. Fluids 31 (1988), 2573.

    Article  Google Scholar 

  7. H. Choi, R. Temam, P. Moin, J. Kim, Feedback control for unsteady flow and its application to the stochastic Burgers equations, J. Fluid Mech. (to appear) (1993).

    Google Scholar 

  8. G. Da Prato, A. Debussche, R. Temam, Stochastic Burgers’ equations (to appear).

    Google Scholar 

  9. G. Da Prato, J. Zabczyk, Stochastic equations in infinite dimension, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge 1992.

    Google Scholar 

  10. I. Ekeland, R. Temam, Convex Analysis and Variational Problems, North Holland, Amsterdam 1976.

    MATH  Google Scholar 

  11. M.D. Gunzburger, L. Hou, T.P. Svobodny, Analysis and finite element approximations of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls, Math. Model. Num. Anal. M2AN 25 (1991), 711.

    MathSciNet  MATH  Google Scholar 

  12. M.D. Gunzburger, L. Hou, T.P. Svobodny, Boundary velocity control of incompressible flow with an application to viscous drag reduction, SIAM J. Control Optim. 30 (1992), 167.

    Article  MathSciNet  MATH  Google Scholar 

  13. J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non-linéaires, Dunod, Paris, 1968.

    Google Scholar 

  14. J.L. Lions, Controle Optimal des Systèmes Gouvernés par des Équations aux Dérivées Partielles, Dunod, Paris 1969. (English translation) Springer-Verlag, New York.

    Google Scholar 

  15. S. Sritharan, Optimal control of viscous flows. Frontiers in Applied Mathematics Series, SIAM, Philadelphia (to appear) 1993.

    Google Scholar 

  16. R. Temam, Navier-Stokes Equations, North Holland Pub. Comp., Amsterdam 1977.

    MATH  Google Scholar 

  17. R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Sciences Series 68 Springer-Verlag, New York 1988.

    MATH  Google Scholar 

  18. R. Temam, Navier-Stokes equations theory and approximation, Handbook of Numerical Analysis, P.G. Ciarlet, J.L. Lions, (eds.) North Holland, Amsterdam (to appear).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag New York, Inc.

About this paper

Cite this paper

Temam, R. (1995). Remarks on the Control of Turbulent Flows. In: Gunzburger, M.D. (eds) Flow Control. The IMA Volumes in Mathematics and its Applications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2526-3_16

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2526-3_16

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7569-5

  • Online ISBN: 978-1-4612-2526-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics