The effect of cell tilting on turbulent thermal convection in a rectangular cell

In this study the influence of cell tilting on flow dynamics and heat transport is explored experimentally within a rectangular cell (aspect ratios ${\it\Gamma}_{x}=1$ and ${\it\Gamma}_{y}=0.25$). The measurements are carried out over a wide range of tilt angles ($0\leqslant {\it\beta}\leqslant {\rm\pi}/2\ \text{rad}$) at a constant Prandtl number ($\mathit{Pr}\simeq 6.3$) and Rayleigh number ($\mathit{Ra}\simeq 4.42\times 10^{9}$). The velocity measurements reveal that the large-scale circulation (LSC) is sensitive to the symmetry of the system. In the level case, the high-velocity band of the LSC concentrates at about a quarter of the cell width from the boundary. As the cell is slightly tilted (${\it\beta}\simeq 0.04\ \text{rad}$), the position of the high-velocity band quickly moves towards the boundary. With increasing ${\it\beta}$, the LSC changes gradually from oblique ellipse-like to square-like, and other more complicated patterns. Oscillations have been found in the temperature and velocity fields for almost all ${\it\beta}$, and are strongest at around ${\it\beta}\simeq 0.48\ \text{rad}$. As ${\it\beta}$ increases, the Reynolds number ($\mathit{Re}$) initially also increases, until it reaches its maximum at the transition angle ${\it\beta}=0.15\ \text{rad}$, after which it gradually decreases. The cell tilting causes a pronounced reduction of the Nusselt number ($\mathit{Nu}$). As ${\it\beta}$ increases from 0 to 0.15, 1.05 and ${\rm\pi}/2\ \text{rad}$, the reduction of $\mathit{Nu}$ is approximately 1.4 %, 5 % and 18 %, respectively. Over the ranges of $0\leqslant {\it\beta}\leqslant 0.15\ \text{rad}$, $0.15\leqslant {\it\beta}\leqslant 1.05\ \text{rad}$ and $1.05\leqslant {\it\beta}\leqslant {\rm\pi}/2\ \text{rad}$, the decay slopes are $8.57\times 10^{-2}$, $3.27\times 10^{-2}$ and $0.24\ \text{rad}^{-1}$, respectively.