Locally averaged thermal dissipation rate in turbulent thermal convection: A decomposition into contributions from different temperature gradient components

Using a homemade local temperature gradient probe, the instantaneous thermal dissipation rate ε_T(r,t) is obtained in an aspect-ratio-one cylindrical convection cell filled with water. From the time series measurements, a locally averaged thermal dissipation ε_T(r,t) over a time interval ) is constructed. Herein we decompose ε_T(r,t) into three contributions ε_Tⁱ(r,t) (i=x, y , z) from the temperature gradient components in the x, y, and z directions and systematically study their statistics and scaling properties. It is found that the moments of μⁱ (r,t) exhibit good scaling in ), i.e., (ε_Tⁱ)ⁱ~τ^μ)ⁱ(p), for all three components and for p up to 6. The obtained exponents μⁱ (p) at three representative locations in the convection cell are explained by a phenomenological model, which combines the effects of velocity statistics and geometric shape of the most dissipative structures in turbulent convection.