Spectral Analysis

Lesson

Introduction
Some definitions
Power spectral density (PSD)
Scaling analysis
Identification of some processes
Exercises
To go further
Conclusion

Spectral scaling exponent β

Inspired by Richardson's energy cascade, A.N.Kolmogorov and Obukhov 1941^[1] made claim to the famous 5/3 law in the case of homogeneous isotropic turbulence.

(a) : Schematic view of wind-tunnel set-up for generating isotropic turbulence, (b) : Kolmogorov's energy spectrum in the S1 wind tunnel ONERA | Information^[2]

(a) : Schematic view of wind-tunnel set-up for generating isotropic turbulence, (b) : Kolmogorov's energy spectrum in the S1 wind tunnel ONERA | Information^[2]

Kolmogorov, A. N, [1941]
Kolmogorov, A. N. (1941). The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. In Dokl. Akad. Nauk SSSR (Vol. 30, No. 4, pp. 301-305).
Sagaut, P., & Cambon, C. (2008). Homogeneous turbulence dynamics (Vol. 10). Cambridge: Cambridge University Press.

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