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Taylor's hypothesis and the probability density functions of temporal velocity and temperature derivatives in a turbulent flow

Published online by Cambridge University Press:  19 April 2006

R. A. Antonia ,
N. Phan-Thien  and
A. J. Chambers
R. A. Antonia
Affiliation:
Department of Mechanical Engineering, University of Newcastle, New South Wales, 2308, Australia
N. Phan-Thien
Affiliation:
Department of Mechanical Engineering, University of Newcastle, New South Wales, 2308, Australia
A. J. Chambers
Affiliation:
Department of Mechanical Engineering, University of Newcastle, New South Wales, 2308, Australia
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Abstract

Equations for the instantaneous velocity and temperature fluctuations in a turbulent flow are used to assess the effect of a fluctuating convection velocity on Taylor's hypothesis when certain simplifying assumptions are made. The probability density function of the velocity or temperature derivative is calculated, with an assumed Gaussian probability density function of the spatial derivative, for two cases of the fluctuating convection velocity. In the first case, the convection velocity is the instantaneous longitudinal velocity, assumed to be Gaussian. In the second, the magnitude of the convection velocity is equal to that of the total velocity vector whose components are Gaussian. The calculated probability density function shows a significant departure, in both cases, from the Gaussian distribution for relatively large amplitudes of the derivative, at only moderate values of the turbulence intensity level. The fluctuating convection velocity affects normalized moments of measured velocity and temperature derivatives in the atmospheric surface layer. The effect increases with increasing order of the moment and is more significant for odd-order moments than even-order moments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 100 , Issue 1 , 11 September 1980 , pp. 193 - 208
Copyright
© 1980 Cambridge University Press

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