Pair dispersion in Rayleigh-Bénard convection: effets of roughness at the boundaries

The Rayleigh-Bénard cell is a useful model system to understand the physics of turbulent thermal convection, because the

boundary conditions are well defined. However, boundaries in nature or in the industry are seldom hydrodynamically smooth. It is therefore

tempting to add roughness at the boundaries of the Rayleigh-Bénard cell, to investigate how the heat transfer and the flow

features are modified.

Several rough Rayleigh-Bénard cells have been operated in the last decade, in particular in the group of K.-Q. Xia,

and in our group in Lyon. These experiments evidence a roughness triggered regime with enhanced heat transfer

efficiency when the thickness of the thermal boundary layer matches the roughness size. The enhancement appears to

saturate at larger Rayleigh numbers, when the boundary layers are much smaller.

If the effect of roughness is clear on non dimensionnal number such as the Nusselt, the effect on flow structures and

statistics of turbulence is less known. We performed lagrangian tracking in a thin square Rayleigh Bénard cell, with rough

hot plate and smooth cold place, at different Ra number from Ra = 2.1 × 10¹⁰ to Ra = 6.3 × 10¹⁰. From the tracks,

we were able to compute the pair dispersion in different region of the flow to compare the case with or without

rough boundaries.