Numerical and experimental investigation of structure-function scaling in turbulent Rayleigh-Bénard convection

Abstract

Direct numerical simulation and stereoscopic particle image velocimetry of turbulent convection are used to gather spatial data for the calculation of structure functions. We wish to add to the ongoing discussion in the literature whether temperature acts as an active or passive scalar in turbulent convection, with consequences for structure-function scaling. The simulation results show direct confirmation of the scalings derived by Bolgiano and Obukhov for turbulence with an active scalar for both velocity and temperature statistics. The active-scalar range shifts to larger scales when the forcing parameter ͑Rayleigh number͒ is increased. Furthermore, a close inspection of local turbulent length scales ͑Kolmogorov and Bolgiano lengths͒ confirms conjectures from earlier studies that the oft-used global averages are not suited for the interpretation of structure functions. In the experiment, a characterization of the domain-filling large-scale circulation of confined convection is carried out for comparison with other studies. The measured velocity fields are also used to calculate velocity structure functions, further confirming the Bolgiano-Obukhov scalings when interpreted with the local turbulent length scales found in the simulations. An extended self-similarity analysis shows that the relative scalings are different for the Kolmogorov and Bolgiano-Obukhov regimes.

Scaling behavior in turbulent Rayleigh-Bénard convection revealed by conditional structure functions

“…Numerical simulations, at Ra = 3.5 × 10 7 and Pr about 1, showed that [18] the height-dependent Bolgiano scale, constructed using the energy and thermal dissipation rates averaged over a cross section at different heights, is comparable to the height H at the center and decreases to 0.2H very close to the top and bottom boundaries. Similarly, more recent numerical simulations [19] show that the local Bolgiano scale, constructed using the local energy and thermal dissipation rates measured at each position, is comparable to H except very close to the top and bottom plates of a cylindrical convection cell where it is smaller than 0.1H for Ra = 1 × 10 9 and Pr = 6.4. The K41 and OC scalings (plus intermittency corrections) have indeed been observed experimentally in the central region [20], but until now, the BO scaling expected to hold near the top and bottom plates has not been observed in experiments.…”

“…However, the scaling behavior, whatever its nature, would hold only in a certain range of r or the corresponding range of τ , which implies that Eqs. (19) and ( …”

“…The K41 and OC scalings (plus intermittency corrections) have indeed been observed experimentally in the central region [20], but until now, the BO scaling expected to hold near the top and bottom plates has not been observed in experiments. On the contrary, there is an experimental report [19] that the vertical velocity structure functions near the top plate obey yet a different scaling behavior predicted to hold in shear flows [21]. As a result, the validity of the BO phenomenology for turbulent RB convection has again been called into question [22].…”

Physical and scale-by-scale analysis of Rayleigh–Bénard convection

“…In the large-scale range, turbulent fluctuations are produced through buoyancy mechanisms and a Bolgiano-Obukhov subrange is expected to take place as suggested by Ching et al (2013). In an intermediate range of scales, the energy content of the large scales flows down towards smaller ones through an inviscid cascade process reproducing the classical Kolmogorov inertial subrange as reported by experiments (Kunnen et al 2008;Ching et al 2013) and numerical simulations (Calzavarini, Toschi & Tripiccione 2002;Kunnen et al 2008;Kaczorowski & Xia 2013). Finally, in the viscosity-dominated range at small scales, turbulent energy is dissipated.…”

Enhanced Vertical Inhomogeneity in Turbulent Rotating Convection

“…Our convection cell is the same as in [20], except for its placement on a rotating table for this investigation. We repeat the most important characteristics here.…”