Statistics of kinetic and thermal energy dissipation rates in vibrational turbulent Rayleigh-Bénard convection with rough surface

In this paper, the statistical properties of the kinetic epsilon u and thermal epsilon theta dissipation rates in two-dimensional (2D) turbulent Rayleigh-B & eacute;nard convection (RBC) are studied by using the thermal lattice Boltzmann method (LBM). A series of direct numerical simulations (DNS) are implemented in a square cell with the unit aspect ratio for the Rayleigh number Ra = 108 and Prandtl number Pr = 4.38. The roughness height h* and vary the vibration frequency omega* from 0 to 1000 are fixed in the vibrational RBC with rough plates to explore their effect on the kinetic and thermal dissipation rates. The global features indicate that the epsilon u and epsilon theta are more intense in the regions with high gradients of velocity and temperature, which is in good agreement with the previous work. The scalings of Nu similar to omega*0.55 +/- 0.1 and Re similar to 0.59 +/- 0.2 are proposed between the ensemble averaged Nusselt number Nu and Reynolds number Re. The probability density functions (PDFs) of both logarithmic kinetic dissipation rate lg epsilon u and thermal dissipation rate lg epsilon theta are not conformed to the log-normal distributions. Through the analysis of the time-averaged epsilon u and epsilon theta vertical profiles, it is further demonstrated that the local dissipation rates from the boundary layer region are still the major contribution in the vibrational RBC with rough plates.