Proper orthogonal decomposition of the flow in geometries containing a narrow gap

  • Elia Merzari
  • H. Ninokata
  • A. Mahmood
  • M. Rohde
Original Article


Geometries containing a narrow gap are characterized by strong quasi-periodical flow oscillations in the narrow gap region. The above mentioned phenomena are of inherently unstable nature and, even if no conclusive theoretical study on the subject has been published, the evidence shown to this point suggests that the oscillations are connected to interactions between eddy structures of turbulent flows on opposite sides of the gap. These coherent structures travel in the direction of homogeneous turbulence, in a fashion that strongly recalls a vortex street. Analogous behaviours have been observed for arrays of arbitrarily shaped channels, within certain range of the geometric parameters. A modelling for these phenomena is at least problematic to achieve since they are turbulence driven. This work aims to address the use of Proper Orthogonal Decomposition (POD) to reduce the Navier–Stokes equations to a set of ordinary differential equations and better understand the dynamics underlying these oscillations. Both experimental and numerical data are used to carry out the POD.


Eccentric channel POD Low-dimensional models 

List of symbols


Normalized wall distance


Cartesian coordinates (vector notation)

x, y, z

Cartesian coordinates


Velocity vector


Cartesian velocity components


Cartesian velocity component in direction x


Cartesian velocity component in direction y


Cartesian velocity component in direction z


Bulk velocity

\({\langle f \rangle}\)

Ensemble averaging operator on function f


Fluctuation over the ensemble average \({f=f-\langle f \rangle}\)




Kinematic viscosity


Filter width, mesh size


Friction velocity


Wavelength of the coherent structures


Hydraulic diameter


Bulk Reynolds number Re = D h w bulk/ν


Inner to outer diameter


Eccentricity e = d/D h


Distance between the cylinder axis for the eccentric channel








Quantum number


Length of the domain in the streamwise direction


Coefficients of the POD modes


Strain tensor


SGS stress tensor


Number of snapshots


Number of modes used in the ODE set


Number of oscillatory modes contained in the ODE set

Mathematics Subject Classification (2000)

76D99 76D05 76D06 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Elia Merzari
    • 1
  • H. Ninokata
    • 1
  • A. Mahmood
    • 2
  • M. Rohde
    • 2
  1. 1.Research Laboratory for Nuclear ReactorsTokyo Institute of TechnologyMeguro-ku, TokyoJapan
  2. 2.PNR-R3, Delft University of TechnologyDelftThe Netherlands

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