Skip to main content
Log in

Perturbation Growth Rate in Turbulent Couette Flow

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The evolution of small perturbations in turbulent Couette flow is investigated numerically at the Reynolds numbers Reτ from 35 to 125. Steady-state turbulent flows calculated on the basis of solving the Navier-Stokes equations are used as the basic flow to study the process of development of the perturbations against their background. The values of the senior Lyapunov exponent λ1 which characterizes the maximum growth rate of small perturbations in the stochastic systems are determined. It is found that the exponent, being normalized by the near-wall scales, is equal to λ1 ~ 0.02. This is in agreement with the results of the previous investigations of turbulent flows in the circular pipe and plane channel. It is shown that the λ1, whose value is smaller by three times and which was obtained earlier in calculating the Lyapunov spectrum in Couette flow at Reτ = 35 in the so-called “minimum channel”, can be explained by insufficient dimension of the computational domain but not by smallness of the Reynolds number.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T.S. Parker and L. O. Chua, Practical Numerical Algorithms for Chaotic Systems (Springer–Verlag,New York, 1989).

    Book  MATH  Google Scholar 

  2. F. Ginelli, P. Poggi, A. Turchi, H. Chaté, R. Livi, and A. Politi, “Characterizing Dynamics with Covariant Lyapunov Vectors,” Phys. Rev. Lett. 99, 130601 (2007).

    Article  ADS  Google Scholar 

  3. N. Nikitin, “On the Rate of Spatial Predictability in Near–Wall Turbulence,” J. Fluid Mech. 614, 495–507 (2008).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. N. V. Nikitin, “Disturbsance GrowthRate inTurbulentWall Flows,” Fluid Dynamics 44 (5), 652–657 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  5. K.M. Butler and B. F. Farrell, “Optimal Perturbations and Streak Spacing inWall–Bounded Turbulent Shear Flows,” Phys. Fluids A 5, 774–777 (1993).

    Article  ADS  Google Scholar 

  6. N. Nikitin, “Spatial Periodicity of Spatially Evolving Turbulent Flow Caused by Inflow Boundary Condition,” Physics of Fluids 19 (9), 091703–4 (2007).

    Article  ADS  MATH  Google Scholar 

  7. L. Keefe, P. Moin, and J. Kim, “The Dimension of Attractors Underlying Periodic Turbulent Poiseuille Flow,” J. FluidMech. 242, 1–29 (1992).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. M. Inubushi, S–i Takehiro, and M. Yamada, “Regeneration Cycle and the Covariant Lyapunov Vectors in a MinimalWall Turbulence,” Phys. Rev. E 92, 023022 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  9. K. Hamilton, J. Kim, and F. Waleffe, “Regeneration Mechanisms of Near–Wall Turbulence Structures,” J. FluidMech. 287, 317–348 (1995).

    Article  ADS  MATH  Google Scholar 

  10. N. Nikitin, “Finite–Difference Method for Incompressible Navier–Stokes Equations in Arbitrary Orthogonal Curvilinear Coordinates,” J. Comput. Phys. 217, 759–781 (2006).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. V. Avsarkisov, S. Hoyas, M. Oberlack, and J. P. Garcia–Galache, “Turbulent Plane Couette Flow at Moderately High Reynolds Number,” J. FluidMech. 751, R1–1–R1–10 (2014).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. V. Nikitin.

Additional information

Original Russian Text © N.V. Nikitin, D.E. Pivovarov, 2018, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2018, No. 6, pp. 3–8.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nikitin, N.V., Pivovarov, D.E. Perturbation Growth Rate in Turbulent Couette Flow. Fluid Dyn 53, 723–728 (2018). https://doi.org/10.1134/S0015462818060204

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462818060204

Key words

Navigation