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A multi-resolution census algorithm for calculating vortex statistics in turbulent flows. (English) Zbl 1273.62294

Summary: The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence by applying statistical models directly to the simulated vorticity field. Rather than to extract the coherent portion of the image from the background variation, as in the classical signal-plus-noise model, we present a model for individual vortices using the non-decimated discrete wavelet transform. A template image, which is supplied by the user, provides the features to be extracted from the vorticity field. By transforming the vortex template into the wavelet domain, specific characteristics that are present in the template, such as size and symmetry, are broken down into components that are associated with spatial frequencies. Multivariate multiple linear regression is used to fit the vortex template to the vorticity field in the wavelet domain. Since all levels of the template decomposition may be used to model each level in the field decomposition, the resulting model need not be identical to the template. Application to a vortex census algorithm that records quantities of interest (such as size, peak amplitude and circulation) as the vorticity field evolves is given. The multiresolution census algorithm extracts coherent structures of all shapes and sizes in simulated vorticity fields and can reproduce known physical scaling laws when processing a set of vorticity fields that evolve over time.

MSC:

62P35 Applications of statistics to physics
62J05 Linear regression; mixed models
76F99 Turbulence
65C20 Probabilistic models, generic numerical methods in probability and statistics

Software:

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References:

[1] DOI: 10.1063/1.1290391 · Zbl 1184.76069 · doi:10.1063/1.1290391
[2] DOI: 10.1103/PhysRevLett.66.2735 · doi:10.1103/PhysRevLett.66.2735
[3] DOI: 10.1016/0169-5983(92)90024-Q · doi:10.1016/0169-5983(92)90024-Q
[4] DOI: 10.1109/5.488705 · doi:10.1109/5.488705
[5] DOI: 10.1103/PhysRevLett.87.054501 · doi:10.1103/PhysRevLett.87.054501
[6] Farge M., Z. Angew. Math. Mech. 81 (3) pp S465– (2001) · doi:10.1002/zamm.20010811512
[7] Farge M., Progress in Wavelet Analysis and Applications pp 477– (1993)
[8] Ferziger J. H., Simulation and Modelling of Turbulent Flows (1996)
[9] DOI: 10.2307/2287576 · doi:10.2307/2287576
[10] Frisch U., Turbulence (1995)
[11] DOI: 10.1098/rsta.1999.0447 · Zbl 0976.68527 · doi:10.1098/rsta.1999.0447
[12] DOI: 10.1006/acha.2000.0343 · doi:10.1006/acha.2000.0343
[13] DOI: 10.1088/0034-4885/43/5/001 · doi:10.1088/0034-4885/43/5/001
[14] Lesieur M., Turbulence in Fluids (1997) · Zbl 0876.76002 · doi:10.1007/978-94-010-9018-6
[15] Luo J., J. Atmos. Ocean. Technol. 19 pp 381– (2001) · doi:10.1175/1520-0426-19.3.381
[16] Mallat S., A Wavelet Tour of Signal Processing (1998) · Zbl 1125.94306
[17] DOI: 10.1017/S0022112084001750 · Zbl 0561.76059 · doi:10.1017/S0022112084001750
[18] DOI: 10.1017/S0022112090002981 · doi:10.1017/S0022112090002981
[19] DOI: 10.1063/1.166010 · doi:10.1063/1.166010
[20] DOI: 10.1146/annurev.fluid.30.1.539 · Zbl 1398.76073 · doi:10.1146/annurev.fluid.30.1.539
[21] DOI: 10.1063/1.869318 · doi:10.1063/1.869318
[22] DOI: 10.1109/TIP.2002.1014998 · Zbl 1288.94011 · doi:10.1109/TIP.2002.1014998
[23] C. Storlie, C. Davis, T. Hoar, T. C. M. Lee, D. Nychka, J. Weiss, and B. Whitcher (2004 ) Identifying and tracking turbulence structures . InProc. 38th Asilomar Conf. Signals, Systems, and Computers,Pacific Grove, pp. 1700 -1704 . Piscataway: Institute of Electrical and Electronics Engineers Signal Processing Society.
[24] Vetterli M., Wavelets and Subband Coding (1995)
[25] DOI: 10.1063/1.858647 · Zbl 0776.76042 · doi:10.1063/1.858647
[26] Whitcher B., Recent Advances and Trends in Nonparametric Statistics pp 497– (2003)
[27] Wickerhauser M. V., Multiscale Wavelet Methods for Partial Differential Equations pp 473– (1997)
[28] Wickerhauser M. V., Wavelets: Theory, Algorithms, and Applications pp 509– (1994) · doi:10.1016/B978-0-08-052084-1.50028-4
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