Dynamics of POD Modes in Wall Bounded Turbulent Flow

  • Giancarlo Alfonsi
  • Leonardo Primavera
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3991)


The dynamic properties of POD modes of the fluctuating velocity field developing in the wall region of turbulent channel flow are investigated. The flow of viscous incompressible fluid in a channel is simulated numerically by means of a parallel computational code based on a mixed spectral-finite difference algorithm for the numerical integration of the Navier-Stokes equations. The DNS approach (Direct Numerical Simulation of turbulence) is followed in the calculations, performed at friction Reynolds number Re τ = 180. A database representing the turbulent statistically steady state of the flow through 10 viscous time units is assembled and the Proper Orthogonal Decomposition technique (POD) is applied to the fluctuating portion of the velocity field. The dynamic properties of the most energetic POD modes are investigated showing a clear interaction between streamwise-independent modes and quasi-streamwise modes in the temporal development of the turbulent flow field.


Large Eddy Simulation Proper Orthogonal Decomposition Proper Orthogonal Decomposition Mode Turbulent Channel Flow Turbulent Flow Field 
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  1. Kolmogorov, A.N.: The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 30, 301 (1941)Google Scholar
  2. Pumir, A., Shraiman, B.I.: Persistent small scale anisotropy in homogeneous shear flows. Phys. Rev. Lett. 75, 3114 (1996)CrossRefGoogle Scholar
  3. Garg, S., Warhaft, Z.: On the small scale structure of simple shear flow. Phys. Fluids 10, 662 (1998)CrossRefGoogle Scholar
  4. Shen X. & Warhaft Z.: The anisotropy of the small scale structure in high Reynolds number (Rλ ≈ 1000 ) turbulent shear flow. Phys. Fluids 12 (2000) 2976 CrossRefGoogle Scholar
  5. Podvin, B., Lumley, J.L.: A low-dimensional approach for the minimal flow unit. J. Fluid Mech. 362, 121 (1998)MATHCrossRefMathSciNetGoogle Scholar
  6. Omurtag, A., Sirovich, L.: On low-dimensional modeling of channel turbulence. Theor. Comp. Fluid Dyn. 13, 115 (1999)MATHCrossRefGoogle Scholar
  7. Alfonsi, G., Passoni, G., Pancaldo, L., Zampaglione, D.: A spectral-finite difference solution of the Navier-Stokes equations in three dimensions. Int. J. Num. Meth. Fluids 28, 129 (1998)MATHCrossRefMathSciNetGoogle Scholar
  8. Passoni, G., Alfonsi, G., Tula, G., Cardu, U.: A wavenumber parallel computational code for the numerical integration of the Navier-Stokes equations. Parall. Comp. 25, 593 (1999)MATHCrossRefMathSciNetGoogle Scholar
  9. Passoni, G., Cremonesi, P., Alfonsi, G.: Analysis and implementation of a parallelization strategy on a Navier-Stokes solver for shear flow simulations. Parall. Comp. 27, 1665 (2001)MATHCrossRefMathSciNetGoogle Scholar
  10. Passoni, G., Alfonsi, G., Galbiati, M.: Analysis of hybrid algorithms for the Navier-Stokes equations with respect to hydrodynamic stability theory. Int. J. Num. Meth. Fluids 38, 1069 (2002)MATHCrossRefMathSciNetGoogle Scholar
  11. Dean, R.B.: Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. J. Fluids Eng. 100, 215 (1978)CrossRefGoogle Scholar
  12. Berkooz, G., Holmes, P., Lumley, J.L.: The Proper Orthogonal Decomposition in the analysis of turbulent flows. Ann. Rev. Fluid Mech. 25, 539 (1993)CrossRefMathSciNetGoogle Scholar
  13. Sirovich, L.: Turbulence and the dynamics of coherent structures. Part I: coherent structures. Part II: symmetries and transformations. Part III: dynamics and scaling. Quart. Appl. Math. 45, 561 (1987)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Giancarlo Alfonsi
    • 1
  • Leonardo Primavera
    • 2
  1. 1.Dipartimento di Difesa del SuoloUniversità della CalabriaRende (Cosenza)Italy
  2. 2.Dipartimento di FisicaUniversità della CalabriaRende (Cosenza)Italy

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