Directional change of tracer trajectories in rotating Rayleigh-Bénard convection

Abstract

The angle of directional change of tracer trajectories in rotating Rayleigh-Bénard convection is studied as a function of the time increment τ between two instants of time along the trajectories, both experimentally and with direct numerical simulations. Our aim is to explore the geometrical characterization of flow structures in turbulent convection in a wide range of timescales and how it is affected by background rotation. We find that probability density functions (PDFs) of the angle of directional change θ(t,τ) show similar behavior as found in homogeneous isotropic turbulence, up to the timescale of the large-scale coherent flow structures. The scaling of the averaged (over particles and time) angle of directional change Θ(τ)=〈|θ(t,τ)|〉 with τ shows a transition from the ballistic regime [Θ(τ)∼τ^{c} with c=1] for τ≲τ_{η}, with τ_{η} the Kolmogorov timescale, to a scaling with smaller exponent c for τ_{η}≲τ≲T_{L}, with T_{L} the Lagrangian integral timescale. This scaling exponent is approximately constant in the weakly rotating regime (Rossby number Ro≳2.5) and is decreasing for increasing rotation rates when Ro≲2.5. We show that this trend in the scaling exponent is related with the large-scale coherent structures in the flow; the large-scale circulation for Ro≳2.5 and vertically aligned vortices emerging from the boundary layers (BLs) near the top and bottom plates and penetrating into the bulk for Ro≲2.5. In the viscous BLs, the PDFs of θ(t,τ) and scaling properties of Θ(τ) are in general different from those measured in the bulk and depend on the type of boundary layer, in particular whether the BL is of Prandtl-Blasius type (Ro≳2.5) or of Ekman type (Ro≲2.5). When it is of Ekman type, a stronger dynamic coupling exists between the BL and the bulk of the flow, resulting in similar scaling exponents in BL and bulk.