PROBABILITIES FOR TEMPERATURE DIFFERENCES IN RAYLEIGH-BENARD CONVECTION

This paper reports the behavior of the probability density functions (PDF's) of temperature differences, between different times, but measured at the same point, which is at the center of a helium-gas cell. One objective of this work is to study how these PDF's evolve as the separation time increases. Data from seven Rayleigh numbers (Ra), which range from 10(9) to 10(15) and are above what is called the soft-to-hard turbulence transition, are studied. These PDF's are symmetric and non-Gaussian, and are fitted approximately by a stretched-exponential form e-c\x\beta. As the separation time tau increases, the parameter beta starts from 0.51 +/- 0.05 (for the smallest separation), remains approximately constant for tau less-than-or-equal-to tau-1, then increases, and finally at tau = tau-2, it saturates to 1.7 +/- 0.01 (1.6 +/- 0.1 for the two largest Ra studied). For Ra < 7.3 x 10(10), beta increases as tau-0.27 +/- 0.03, while for Ra greater-than-or-equal-to 7.3 x 10(10), the increase has to be described by two powers: for lower tau, beta first increases slower as tau-0.15 +/- 0.03, then for tau greater-than-or-equal-to tau-b, it increases as tau-0.27 +/- 0.02. Attempts are made to understand the origin of these time scales and to relate them to time scales previously identified in the problem.