Corrections for velocity and temperature derivatives in turbulent flows

Abstract

Spectral corrections, which are based on local isotropy, are presented for all the spatial derivatives of velocity and temperature fluctuations which feature in the average dissipations of turbulent energy and temperature. The corrections, which compensate for the spectral attenuation due to the separation between sensors, depend only weakly on the choice of the three-dimensional energy (or temperature) spectrum and therefore on the turbulence Reynolds number. Corrections are also obtained for the variances of velocity and temperature derivatives. The diagonal velocity derivatives require smaller corrections than either the off-diagonal velocity derivatives or the temperature derivatives. Corrections of comparable magnitude are required for the average dissipations of turbulent energy and temperature.