Velocity fluctuations and boundary layer structure in a rough Rayleigh-Bénard cell filled with water

We report particle image velocimetry of the large-scale circulation and the viscous boundary layer in turbulent thermal convection. We use two parallelepipedic Rayleigh-Bénard cells with a top smooth plate. The first one has a rough bottom plate and the second one has a smooth one, so we compare the rough-smooth and the smooth-smooth configurations. The dimensions of the cell allow us to consider a bidimensional mean flow. Many previous heat flux measurements have shown a Nusselt-Rayleigh regime transition corresponding to an increase of the heat flux in the presence of roughness that is higher than the surface increase. Our velocity measurements show that if the mean velocity field is not clearly affected by the roughness, the velocity fluctuations rise dramatically, which is accompanied by a change of the longitudinal velocity structure functions scaling. Moreover, we show that the boundary layer becomes turbulent close to roughness, as it was observed recently in air [O. Liot et al., J. Fluid Mech. 786, 275 (2016)]. Finally, we discuss the link between the change of the boundary layer structure and the changes observed in the velocity fluctuations.

Figure 1

Sketch of the RS convection cell. The four dark circles in the plates show the locations of the PT100 temperature sensors. The close-up shows the roughness dimensions. Particle image velocimetry measurements of the viscous boundary layer are performed in the green hatched area.

Figure 2

Detail of roughness with the three different locations according to the flow direction.

Figure 3

Velocity magnitude fields in (a) the RS cell for $\text{Ra}=7.0\times {10}^{10}$ and (b) the SS cell for $\text{Ra}=6.9\times {10}^{10}$.

Figure 4

Horizontal velocity fluctuation rms field in (a) the RS cells for $\text{Ra}=7.0\times {10}^{10}$ and (b) the SS cells for $\text{Ra}=6.9\times {10}^{10}$, with counterclockwise LSC.

Figure 5

Vertical velocity fluctuations rms field in (a) the RS cells for $\text{Ra}=7.0\times {10}^{10}$ and (b) the SS cells for $\text{Ra}=6.9\times {10}^{10}$, with counterclockwise LSC.

Figure 6

Profiles of average fields of horizontal velocity rms. Profiles of the bottom region are horizontally flipped for a better comparison. Statistical uncertainties do not exceed 0.02 cm/s. For more details about calculations, see the text.

Figure 7

Comparison of the velocity fluctuations longitudinal structure functions in zones 1–4 in (a) the RS cell and (b) the SS cell. Vertical axes are compensated by ${\ell }_i^{2/3}$, where $i=x,z$. The dashed line in (a) corresponds to $S_{v_i^{\prime }}^2\left({\ell }_i\right)\propto {\ell }_i^{0.4}$. The inset shows zones where statistics are computed; see the text for the exact box dimensions.

Figure 8

Horizontal velocity normalized by the function $U^{*}$ of the normalized altitude $z^{+}$ for the three locations (described in Fig. 2). The dashed line represents Eq. (16) for $B=-3.4$. The origin of $z$ is taken at the plate in the groove or notch. Consequently, the obstacle profile starts at $h_0$. The first points of the profiles are removed because of the lack of resolution very close to the plate.