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 ε_N(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 ε_N(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....[ Read more ]

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 ε_N(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 ε_N(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 ε_N(r,t), we construct a locally averaged thermal dissipation rate ε_τ(r,t) over a time interval τ and study the τ-dependence of the moments, <ε_τ^p(r,t)>_t, averaged over time t. A good scaling regime, in which <(ε_τⁱ)^p> goes as <(ε_τⁱ)^p>~τ^μi(p) for all values of p up to 8, is found for all three dissipation contributions ε_τⁱ (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.