Abstract
To reveal the possibly existed flow phenomena that buried in a two-dimensional symmetric triangle wake, one-dimensional orthogonal wavelet transform and POD are combined to decompose the fluctuating velocity field into different wavelet components and modes. The features of reconstructed flow fields are analyzed in terms of fluctuating energy, time frequency distribution, space correlation and Reynolds shear stress. It is found that the first two wavelet components and POD modes can give representations to the most energetic large-scale structures, contributing about 77 and 73 % to the total fluctuating energy, respectively. Comparing with the first two wavelet components, the first two POD modes are more appropriate to represent the Karman-like vortical structures. The time–frequency and length scale characteristics of wavelet components suggest that frequency behavior can reflect the spatial-related length scale and the wavelet transform can be used to extract turbulent structures of different scales. Similar to the energy distribution, the most significant contributions to the Reynolds shear stresses comes from the large-scale structures that composed of first two wavelet components and POD modes, accounting for 88 and 80 % of the measured maximum Reynolds shear stress, respectively. Due to different classification criterion of wavelet and POD analyses, the combining use of these two methods tends to be more effective for analyzing multi-scale turbulent structures.
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Addison PS, Murray KB, Watson JN (2001) Wavelet transform analysis of open channel wake flows. J Eng Mech 127(1):58–70
Alam MD, Zhou Y (2008) Strouhal numbers, forces and flow structures around two tandem cylinders of different diameters. J Fluids Struct 24:505–526
Cazemier W, Verstappen RWCP, Veldman AEP (1998) Proper orthogonal decomposition and low dimensional models for driven cavity flows. Phys Fluids 10(7):1685–1699
Cruz AS, David L, Pécheux J, Texier A (2005) Characterization by proper-orthogonal-decomposition of the passive controlled wake flow downstream of a half cylinder. Exp Fluids 39(4):730–742
Davis RW, Moore EF, Purtell LP (1983) A numerical–experimental study of confined flow around rectangular cylinders. Phys Fluids 27:46–59
Delville J, Ukeiley L, Cordier L, Bonnet JP, Glauser M (1999) Examination of large-scale structures in a turbulent plane mixing layer. Part 1. proper orthogonal decomposition. J Fluid Mech 391:91–122
Durgesh V, Naughton JW, Whitmore SA (2013) Experimental Investigation of base drag reduction via boundary layer modification. AIAA J 51(2):416–425
Farge M, Pellegrino G, Schneider K (2001) Coherent vortex extraction in 3D turbulent flows using orthogonal wavelets. Phys Rev Lett 87:054501
Graftieaux L, Michard M, Grosjean N (2001) Combining PIV, POD and vortex identification algorithms for the sturdy of unsteady turbulent swirling flows. Measur Sci Technol 12:1422–1429
Hussain AKMF, Hayakawa M (1987) Education of large-scale organized structures in a turbulent plane wake. J Fluid Mech 108:193–229
Indrusiak MLS, Moller SV (2011) Wavelet analysis of unsteady flows: application on the determination of the Strouhal number of the transient wake behind a single cylinder. Exp Thermal Fluid Sci 35:319–327
Lee HH, Miau JJ (2012) An investigation on karman-type vortex shedding from a finite square cylinder. J Mech 28:299–308
Lin JC, Vorobieff P, Rockwell D (1996) Space-time imaging of a turbulent near-wake by high-image-density particle image cinematography. Phys Fluids 8:555–564
Lumley JL (1967) The structure of inhomogeneous turbulence. In: Yaglom AM, Tatarski VI (eds) Atmospheric turbulence and wave propagation. Nauka, Moscow, pp 166–178
Mallat S (1989) A theory for multi resolution signal decomposition: the wavelet representation. IEEE Trans PAMI 11:674–693
Noack B, Afanasiev K, Morzynski M, Tadmor G, Thiele F (2003) A hierarchy of low-dimensional models for the transient and post transient cylinder wake. J Fluid Mech 497:335–363
Rinoshika A, Zhou Y (2005a) Orthogonal wavelet multi-resolution analysis of a turbulent cylinder wake. J Fluid Mech 524:229–248
Rinoshika A, Zhou Y (2005b) Effects of initial conditions on a wavelet-decomposed turbulent near-wake. Phys Rev E 71(046303):1–8
Sirovich L (1987) Turbulence and the dynamics of coherent structures, Part I Coherent structures. Q Appl Math 45:561–571
Wang Y, Yu B, Wu X (2012) POD and wavelet analyses on the flow structures of a polymer drag-reducing flow based on DNS data. Int J Heat Mass Transf 55(17):4849–4861
Wei T, Smith CR (1986) Secondary vortices in the wake of circular cylinders. J Fluid Mech 169:513–533
Weier T, Cierpka C, Gerbeth G (2008) Coherent structure eduction from PIV data of an Electro magnetically forced separated flow. J Fluids Struct 24:1339–1348
West GS, Apelt CJ (1982) The effects of tunnel blockage and aspect ratio on the mean flow past a circular cylinder with Reynolds numbers between 104 and 105. J Fluid Mech 114:361–377
Williamson CHK (1996) Vortex dynamics in the cylinder wake. Annu Rev Fluid Mech 28:477–539
Zdravkovich MM (1997) Flow around circular cylinders, vol 1. Oxford University Press, Oxford, Fundamentals
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Zheng, Y., Fujimoto, S. & Rinoshika, A. Combining wavelet transform and POD to analyze wake flow. J Vis 19, 193–210 (2016). https://doi.org/10.1007/s12650-015-0318-6
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DOI: https://doi.org/10.1007/s12650-015-0318-6