Turbulent Convection at Aspect Ratio Four

Abstract

We report analysis of temperature fluctuations in turbulent thermal convection in a cylindrical container of aspect ratio 4. Temperature fluctuations are measured at the opposite ends of a cell diameter 4 cm inboard of the sidewall and at the cell centre in the central horizontal plane of the apparatus, for Rayleigh numbers (Ra) ranging from 1.043×109 to 6.5×1011. For these Ra, experimental conditions obey Boussinesq approximation. Autocorrelation and cross correlation have been used to analyze the data. The period of about 33 s found by autocorrelation for Ra = 1.043×109, indicates the advection of plumes by a large‐scale coherent wind, tilted along the diagonal, which encompasses the entire container. In good agreement with autocorrelation, cross‐correlation between sidewall signals in the central horizontal, but at opposite ends of a cell diameter, show a strong long‐time correlation indicative of a well ordered and robust mean wind. While no clear correlation exists between the sidewall fluctuations and those at the centre which corroborates the lack of any strong mean wind at the centre. Cross correlation of parts (5 minutes each) of the same signals, instead of the whole, has shown that about 20% of the time there is correlation between side and center sensors. The velocity of mean wind for this Ra has been calculated to be about 3.19 cm/s. Possible mean wind trajectory has also been drawn. For Ra = 6.5×1011 there is no correlation between any set of temperature signals, indicating that the mean wind is no longer coherent over the entire container.