Boundary layer structure in turbulent rayleigh-bénard convection in a slim box

Logarithmic boundary layers have been observed in different regions in turbulence. However, how thermal plumes correlate to the log law of temperature and how the velocity profile changes with pressure gradient are not fully understood. Here, we perform three-dimensional simulations of turbulence in a slim-box without the front and back walls with aspect ratio, width:depth:height=L:D:H=1:1/6:1width:depth:height=L:D:H=1:1/6:1 (respectively corresponding to xx, yy and zz coordinates), in the Rayleigh number Ra=[1×10^8,1×10^10]Ra=[1×10^8,1×10^10] for Prandtl number Pr=0.7Pr=0.7. To investigate the structures of the viscous and thermal boundary layers, we examine the velocity profiles in the streamwise and vertical directions (i.e. UU and WW) along with the mean temperature profile throughout the plume-impacting, plume-ejecting, and wind-shearing regions. The velocity profile is successfully quantified by a two-layer function of a stress length, e^+u=e^+0(z^+)3/2[1+(z^+/z^+sub)4]^1/4eu+=e^+0(z+)3/2[1+(z+/zsub+)4]1/4, as proposed by She et al.(J Fluid Mech, 2017), though it is neither \pb type nor logarithmic. In contrast, the temperature profile in the plume-ejecting region is logarithmic for all simulated cases, being attributed to the emission of thermal plumes. The coefficient of the temperature log-law, AA, can be described by composition of the thermal stress length ■■θ0■θ0■ and the thicknesses of thermal boundary layer z■subzsub■ and z?bufzbuf■, i.e. A■z?sub/(■■θ0z■buf3/2)A■zsub?/(■θ0■zbuf^3/2). The adverse pressure gradient responsible for turning the wind direction contributes to intensively emitting plumes and the logarithmic temperature profile at the plume-ejecting region. The Nusselt number scaling and the local heat flux in the slim box are consistent with previous results of the confined cells. Therefore, the slim-box RBC is a preferable system for investigating in-box kinetic and thermal structures of turbulent convection with the large-scale circulation in a fixed plane.