ON PASSIVE SCALAR DERIVATIVE STATISTICS IN GRID TURBULENCE

The probability density function, and related statistics, of scalar (temperature) derivative fluctuations in decaying grid turbulence with an imposed cross-stream, passive linear temperature profile, is studied for a turbulence Reynolds number range, Re(l), varying from 50 to 1200, (corresponding to a Taylor Reynolds number range 30 < R(lambda) < 130). It is shown that the temperature derivative skewness in the direction of the mean gradient, S(thetay) has a value of 1.8 +/- 0.2 (twice the value observed in shear flows), and has no significant variation with Reynolds number. The ratio of the temperature derivative standard deviation along the gradient to that normal to it is approximately 1.2 +/- 0.1 also, with no variation with Re. The kurtosis of the derivatives increases approximately as Re(l)0.2. The results show that the rare, intense temperature deviations that produce the skewed scalar derivative, increase in frequency, but their area fraction (of the total field) becomes smaller as the Reynolds number increases. Thus, since S(thetay) remains constant, they become sharper and more intense, occurring deeper in the tails of the probability density function. Measurements in a thermal mixing layer, which has a nonlinear mean temperature profile, are also presented, and these show a similar value of S(thetay) to the linear profile case. The experiments broadly confirm the two-dimensional numerical simulations of Holzer and Siggia [Phys. Fluids (in press)], as well as other recent simulations, although there are some differences.