Evolution and statistics of thermal plumes in tilted turbulent convection

Abstract

We present a systematic experimental study of thermal plumes within tilted turbulent thermal convection using the shadowgraph technique. The measurements are performed in a rectangular cell (aspect ratio Γx=1 and Γy=0.25) over a wide range of tilt angles (0⩽β⩽π/2rad) at constant Prandtl (Pr≃10) and Rayleigh (Ra≃6.80×1010) numbers. It is found that the plume width, λ, is distributed log-normally in space and the time-averaged most probable plume width, 〈λp〉, has similar scale with the thermal boundary layer thickness, λT. 〈λp〉 and λT slowly increase as tilt angle, β, increases from 0 to 1rad and they broaden rapidly as β>1rad. The average plume area density, 〈Φ〉, deduced from the image intensity, is proposed to represent the heat flux of thermal plumes. Its β dependence is consistent with that of the Nusselt number, Nu, over the tilt angle range. λp and Φ exhibit oscillation of convective flow. The oscillation intensity and period strongly depend on β, but are less affected by Ra and Pr. The plume velocity exhibits a different pattern from that of the two-dimensional convective flow measured at Pr≃6.3 and Ra≃4.42×109. The magnitude of plume velocity peak is weakly affected by the cell tilting. The position of the plume velocity peak increases linearly with increasing β.