POD of vorticity fields: A method for spatial characterization of coherent structures

Abstract We present a method to identify large scale coherent structures, in turbulent flows, and characterize them. The method is based on the linear combination of the proper orthogonal decomposition (POD) modes of vorticity. Spanwise vorticity is derived from the two-dimensional and two-component velocity fields measured by means of particle image velocimetry (PIV) in the streamwise–wall normal plane of a fully developed turbulent boundary layer in a flume. The identification method makes use of the whole data set simultaneously, through the two-point correlation tensor, providing a statistical description of the dominant coherent motions in a turbulent boundary layer. The identified pattern resembles an elongated, quasi-streamwise, vortical structure with streamwise length equal to the water height in the flume and inclined upwards in the streamwise–wall normal plane at angle of approximately 8°.

[1]  J. Klewicki.  Self-sustaining traits of near-wall motions underlying boundary layer stress transport , 1997 .

[2]  D. Kaftori,et al.  Funnel‐shaped vortical structures in wall turbulence , 1994 .

[3]  P. S. Klebanoff,et al.  Characteristics of turbulence in a boundary layer with zero pressure gradient , 1955 .

[4]  R. Gurka,et al.  XPIV–Multi-plane stereoscopic particle image velocimetry , 2004 .

[5]  F. A. Schraub,et al.  The structure of turbulent boundary layers , 1967, Journal of Fluid Mechanics.

[6]  J. Kestin,et al.  Boundary-Layer Theory (Seventh Edition) , 1980 .

[7]  S. Balachandar,et al.  Mechanisms for generating coherent packets of hairpin vortices in channel flow , 1999, Journal of Fluid Mechanics.

[8]  J. Lumley.  Stochastic tools in turbulence , 1970 .

[9]  Mark N. Glauser,et al.  Collaborative testing of eddy structure identification methods in free turbulent shear flows , 1998 .

[10]  J. L. Zakin,et al.  Low-speed streaks in drag-reduced turbulent flow , 1997 .

[11]  A. Liberzon,et al.  Characterization of Turbulent Flow in a Flume with Surfactant , 2004 .

[12]  H. Schlichting.  Boundary Layer Theory , 1955 .

[13]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[14]  S. K. Robinson,et al.  Coherent Motions in the Turbulent Boundary Layer , 1991 .

[15]  P. Holmes,et al.  Turbulence, Coherent Structures, Dynamical Systems and Symmetry , 1996 .

[16]  Carlos Alberto Brebbia,et al.  Advances in fluid mechanics: proceedings of a conference held at Aachen, March 26-28, 1980 , 1981 .

[17]  Roi Gurka,et al.  Vorticity characterization in a turbulent boundary layer using PIV and POD analysis , 2001 .

[18]  P. Holmes,et al.  The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows , 1993 .

[19]  Markus Raffel,et al.  Particle Image Velocimetry: A Practical Guide , 2002 .

[20]  P. Moin,et al.  Turbulence statistics in fully developed channel flow at low Reynolds number , 1987, Journal of Fluid Mechanics.

[21]  M. S. Chong,et al.  PIV Measurements of a Backward Facing Step Flow , 2001 .

[22]  Fazle Hussain,et al.  Coherent structure dynamics in near-wall turbulence , 2000 .

[23]  Stanislav Gordeyev,et al.  Coherent structure in the turbulent planar jet. Part 2. Structural topology via POD eigenmode projection , 2002, Journal of Fluid Mechanics.

[24]  Iztok Tiselj,et al.  Spatial characterization of the numerically simulated vorticity fields of a flow in a flume , 2005 .

[25]  U. Rist,et al.  Proper orthogonal decomposition reconstruction of a transitional boundary layer with and without control , 2004 .

[26]  M. R. Head,et al.  New aspects of turbulent boundary-layer structure , 1981, Journal of Fluid Mechanics.

[27]  R. Adrian.  Particle-Imaging Techniques for Experimental Fluid Mechanics , 1991 .

[28]  Ronald L. Panton,et al.  Self-Sustaining Mechanisms of Wall Turbulence , 1997 .