Thermal dissipation field and its statistical properties in turbulent Rayleigh-Bénard convection

Abstract

A systematic study of the thermal dissipation field and its statistical properties is carried out in turbulent Rayleigh-Bénard convection. A local temperature gradient probe consisting of four identical thermistors is made to measure the normalized thermal dissipation rate εN(r) in two convection cells filled with water. The measurements are conducted over varying Rayleigh numbers Ra (8.9×108 ≤ Ra ≤ 9.3×109) and spatial positions r across the entire cell. It is found that εN(r) contains two contributions; one is generated by thermal plumes, present mainly in the plume-dominated bulk region, and decreases with increasing Ra. The other contribution comes from the mean temperature gradient, being concentrated in the thermal boundary layers, and increases with Ra. From the measured instantaneous thermal dissipation rate εN(r,t), we construct a locally averaged thermal dissipation rate ετ(r,t) over a time interval τ and study the τ-dependence of the moments, <ετp(r,t)>t, averaged over time t. A good scaling regime, in which <(ετi)p> goes as <(ετi)p>~τμi(p) for all values of p up to 8, is found for all three dissipation contributions ετi (r,t) (i = x, y, z). The obtained exponents μi(p) at three representative locations in the convection cell are explained by a phenomenological model, which combines the effects of both buoyancy for velocity statistics and geometric shape of the most dissipative structures in turbulent convection. The experiment thus provides a complete physical picture about the thermal dissipation field and its statistical properties in turbulent convection.

Date of Award	2009
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology