The Anomalous Behavior of Oscillatory Temperature Fluctuations near the Threshold of Thermal Convection

Abstract

Experimental studies concerning the instability of thermal convection of a fluid between two parallel vertical plates kept at different temperatures have been carried out. When the Rayleigh number A exceeds some critical value A_c, traveling, wave-like temperature fluctuations of fluid are observed. The variance, angular frequency, wave number, correlation time and correlation length of the temperature fluctuations have been obtained from the measurements of distribution, auto-correlation and cross-correlation function. The variance depends on A as (A-A_c). The angular frequency is proportional to (A-A_c)^1⁄2 and the wave number is independent of A. The correlation time and correlation length increase anomalously as the Rayleigh number approches the critical value A_c and both the correlation time and correlation length depend on the Rayleigh number as (A-A_c)⁻¹.