The spatial derivative of temperature in a turbulent flow and Taylor’s hypothesis

Abstract

Statistics of the streamwise derivative of temperature fluctuations on the centerline and at one streamwise station in the self-preserving region of a turbulent plane jet have been obtained by two techniques. In one, the derivative is approximated by the difference between the signals from two cold wires separated in the streamwise direction. In the other, the streamwise derivative is inferred from the temporal derivative and different convection velocities. Instantaneous values, root-mean-square values, skewness, and flatness factors are in reasonable agreement for a sufficiently large range of separations regardless of whether the mean velocity (Taylor’s hypothesis) or the instantaneous velocity are used as the convection velocity. Corrections for turbulence intensity, that are often applied to Taylor’s hypothesis, do not seem warranted. The difference between spectra of the temperature difference and temporal derivative spectra cannot be resolved by identifying the convection velocity with a frequency-dependent phase velocity of the temperature fluctuation.