Olga Shishkina

Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution

Results on the Prandtl–Blasius-type kinetic and thermal boundary layer (BL) thicknesses in turbulent Rayleigh–Benard (RB) convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl–Blasius BL equations, we calculate the ratio between the thermal and kinetic BL thicknesses, which depends on the Prandtl number only. It is approximated as for and as for , with . Comparison of the Prandtl–Blasius velocity BL thickness with that evaluated in the direct numerical simulations by Stevens et al (2010 J. Fluid Mech. 643 495) shows very good agreement between them. Based on the Prandtl–Blasius-type considerations, we derive a lower-bound estimate for the minimum number of computational mesh nodes required to conduct accurate numerical simulations of moderately high (BL-dominated) turbulent RB convection, in the thermal and kinetic BLs close to the bottom and top plates. It is shown that the number of required nodes within each BL depends on and and grows with the Rayleigh number not slower than . This estimate is in excellent agreement with empirical results, which were based on the convergence of the Nusselt number in numerical simulations

Analysis of thermal dissipation rates in turbulent Rayleigh-Benard convection

Direct numerical simulations (DNS) of turbulent Rayleigh–Benard convection in a wide cylindrical container (aspect ratio

Analysis of sheet-like thermal plumes in turbulent Rayleigh-Benard convection

\Gamma\,{=}\,10

Mean temperature profiles in turbulent Rayleigh–Bénard convection of water

) with a lateral wall have been performed for the first time for the Rayleigh numbers

Local heat fluxes in turbulent Rayleigh-Bénard convection

10^5

Aspect-ratio dependency of Rayleigh-Bénard convection in box-shaped containers

,

Thermal boundary layer equation for turbulent Rayleigh-Bénard convection

10^6

Rotating non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water

and

Boundary and interior layers in turbulent thermal convection in cylindrical containers

10^7

Toroidal and poloidal energy in rotating Rayleigh–Bénard convection

and Prandtl number