Geometry of tracer trajectories in rotating turbulent flows

Abstract

The geometry of passive tracer trajectories is studied in two different types of rotating turbulent flows; rotating Rayleigh-Bénard convection (RBC; experiments and direct numerical simulations) and rotating electromagnetically forced turbulence (EFT; experiments). This geometry is fully described by the curvature and torsion of trajectories and from these geometrical quantities we can subtract information on the typical flow structures at different rotation rates. Previous studies, focusing on non-rotating homogeneous isotropic turbulence (HIT), show that the probability density functions (PDFs) of curvature and torsion reveal pronounced power laws. However, the set-ups studied here involve inhomogeneous turbulence and in RBC the flow near the horizontal plates is definitely anisotropic. We want to investigate how the typical shapes of the curvature and torsion PDFs, including the pronounced scaling laws, are influenced by this level of anisotropy and inhomogeneity and how this effect changes with rotation. A first effect of rotation is observed as a shift of the curvature and torsion PDFs towards higher values in the case of RBC and towards lower values in the case of EFT. This shift is related to the length scale of typical vortical structures that decreases with rotation in RBC, but increases with rotation in EFT, explaining the opposite shifts of the curvature (and torsion) PDFs. A second remarkable observation is that in RBC the HIT scaling laws are always recovered, as long as the boundary layer (BL) is excluded. This suggests that these scaling laws are very robust and hold as long as we measure in the turbulent bulk. In the BL of the RBC cell, however, the scaling deviates from the HIT prediction for lower rotation rates. This scaling behavior is found to be consistent with the coupling between the boundary layer dynamics and the bulk flow, that changes under rotation. In particular, it is found that the active coupling of the Ekman-type boundary layer with the bulk flow suppresses anisotropy in the BL region for increasing rotation rates.

Velocity and acceleration statistics in rapidly rotating Rayleigh–Bénard convection

“…Figure 3(a,b) shows the autocorrelation of the velocity in the xy and z directions at the cell centre, respectively. The time lag is nondimensionalised by the local Kolmogorov time scales, given in Table 1 calculated from direct numerical simulations using the same parameter settings, see Alards et al (2017) and Rajaei (2017) for the details of the numerical method. Note that the Kolmogorov time scale differs depending on the position within the cylinder.…”

“…Rossby (1969); Boubnov & Golitsyn (1986); Zhong et al (1993); Liu & Ecke (1997); Sakai (1997); Vorobieff & Ecke (2002); Kunnen et al (2008); King et al (2009); Zhong & Ahlers (2010); Niemela et al (2010); Kunnen et al (2010); Weiss & Ahlers (2011 a ); Kunnen et al (2014); Ecke & Niemela (2014); Rajaei et al (2017), numerical simulations, e.g. Julien et al (1996); Kunnen et al (2006); King et al (2009); Schmitz & Tilgner (2009); Stevens et al (2010); Julien et al (2012 b ); Stellmach et al (2014); Horn & Shishkina (2015); Alards et al (2017) and theoretical analysis, e.g. Chandrasekhar (1961); Chan (1974); Constantin et al (1999); Doering & Constantin (2001); Vitanov (2003); King et al (2012).…”

Probing turbulent superstructures in Rayleigh-Bénard convection by Lagrangian trajectory clusters

“…Numerical studies were primarily focused on the turbulent dispersion of Lagrangian particle pairs [5] and tetrads [6], the entropy production rates along individual Lagrangian trajectories [7] for convection volumes with aspect ratios Γ = L/H ≤ 4 where L is a horizontal extension (side length or diameter). Characteristic turnover times and the geometry of Lagrangian trajectories were analyzed numerically in closed non-rotating [8] and in rotating cells [9,10]. Laboratory experiments of turbulent convection pioneered the use of smart particles to measure local heat fluxes [11] along individual particle tracks.…”

Directional change of tracer trajectories in rotating Rayleigh-Bénard convection

“…Instantaneous measures for this geometry are the curvature and torsion of trajectories. Such curvature and torsion measurements of tracer trajectories in rotating RBC have shown that the predictions for the scaling of curvature and torsion probability density functions (PDFs) derived for homogeneous isotropic turbulence (HIT) [12][13][14][15] are recovered, as long as measurements are performed in the turbulent bulk [16]. In the BLs, the PDFs scale differently consistent with the type of BL, which is the Prandtl-Blasius type in the regime dominated by the LSC and the Ekman type in the regime affected by vertically aligned vortices.…”

“…In RBC, trajectories are additionally expected to be affected by the large-scale coherent flow structures at larger timescales. We therefore extend the previous study on instantaneous measurements of the geometry of tracer trajectories [16] to scale-dependent measurements of this geometry by computing the directional change of tracer trajectories in (rotating) RBC up to the timescale of the large-scale coherent flow structures.…”