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    Dimitriadis, Panayiotis Koutsoyiannis, Demetris and Papanicolaou, Panos 2016. Stochastic similarities between the microscale of turbulence and hydro-meteorological processes. Hydrological Sciences Journal, Vol. 61, Issue. 9, p. 1623.


    Shen, Lihua Ostoja-Starzewski, Martin and Porcu, Emilio 2015. Harmonic oscillator driven by random processes having fractal and Hurst effects. Acta Mechanica, Vol. 226, Issue. 11, p. 3653.


    Taqqu, Murad S. 2014. Wiley StatsRef: Statistics Reference Online.


    Taqqu, Murad S. 2006. Encyclopedia of Statistical Sciences.


    ZUNINO, LUCIANO PÉREZ, DARÍO G. GARAVAGLIA, MARIO and ROSSO, OSVALDO A. 2004. CHARACTERIZATION OF LASER PROPAGATION THROUGH TURBULENT MEDIA BY QUANTIFIERS BASED ON THE WAVELET TRANSFORM. Fractals, Vol. 12, Issue. 02, p. 223.


    Lienhard V, J. H. and Van Atta, C. W. 1990. The decay of turbulence in thermally stratified flow. Journal of Fluid Mechanics, Vol. 210, Issue. -1, p. 57.


    HELLAND, K.N. LII, K.S. and ROSENBLATT, M. 1979.


    Sumer, B. Mutlu and Şen, Zekâi 1979. Comment on ‘A note on the Hurst Phenomenon in turbulent flows’ by C. W. Van Atta and K. N. Helland. Water Resources Research, Vol. 15, Issue. 2, p. 498.


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The ‘Hurst phenomenon’ in grid turbulence

  • K. N. Helland (a1) and C. W. Van Atta (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112078000798
  • Published online: 01 April 2006
Abstract

Measurements of the statistical property called the ‘rescaled range’ in grid-generated turbulence exhibit a Hurst coefficient H = 0·5 for 43 < UT/M < 1850, where M/U is a characteristic time scale associated with the grid size M and mean velocity U. Theory predicts that H = 0·5 for independence of two observations separated by a time interval T, and the deviation from H = 0·5 is referred to as the ‘Hurst phenomenon’. The rescaled range obtained for grid turbulence contains an initial region UT/M < 43 of large H, approaching 1·0, corresponding approximately to the usual region of a finite non-zero autocorrelation of turbulent velocity fluctuations. For UT/M > 1850 the rescaled range breaks from H = 0·5 and rises at a significantly faster rate, H = 0·7-0·8, implying a long-term dependence or possibly non-stationarity at long times. The measured autocorrelations remain indistinguishable from zero for UT/M > 20. The break in the trend H = 0·5 is probably caused by motions on scales comparable to characteristic time scales of the wind-tunnel circulation. Rescaled-range analysis is a powerful statistical tool for determining the time scale separating the grid turbulence from the background wind-tunnel motions.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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