Jump rope vortex flow in liquid metal Rayleigh–Bénard convection in a cuboid container of aspect ratio

Abstract

We study the topology and the temporal dynamics of turbulent Rayleigh–Bénard convection in a liquid metal with a Prandtl number of 0.03 located inside a box with a square base area and an aspect ratio of $\varGamma = 5$ . Experiments and numerical simulations are focused on the Rayleigh number range $6.7 \times 10^{4} \leqslant Ra \leqslant 3.5 \times 10^{5}$ , where a new cellular flow regime has been reported previously (Akashi et al., Phys. Rev. Fluids, vol. 4, 2019, 033501). This flow structure shows symmetries with respect to the vertical planes crossing at the centre of the container. The dynamic behaviour is dominated by strong three-dimensional oscillations with a period length that corresponds to the turnover time. Our analysis reveals that the flow structure in the $\varGamma = 5$ box corresponds in key features to the jump rope vortex structure, which has recently been discovered in a $\varGamma = 2$ cylinder (Vogt et al., Proc. Natl Acad. Sci. USA, vol. 115, 2018, pp. 12674–12679). While in the $\varGamma = 2$ cylinder a single jump rope vortex occurs, the coexistence of four recirculating swirls is detected in this study. Their approach to the lid or the bottom of the convection box causes a temporal deceleration of both the horizontal velocity at the respective boundary and the vertical velocity in the bulk, which in turn is reflected in Nusselt number oscillations. The cellular flow regime shows remarkable similarities to properties commonly attributed to turbulent superstructures.

Experimental pub crawl from Rayleigh–Bénard to magnetostrophic convection

“…The RC wall mode frequency is fp,SW = 10, in good agreement with theory (dashed green vertical line (Zhang & Liao 2009)). The central sensor spectrum peaks at fp,0 90, near the predicted frequency for oscillatory inertial convection (dashed blue vertical line (Zhang & Liao 2009)) and in good agreement with the thermovelocimetric RC measurements of Vogt et al (2021). The S 2/3 sensor contains both longer-period thermal oscillations due to the wall modes and shorter-period content due to the inertial bulk oscillations, revealing the multi-modal nature of low-Pr RC flows.…”

“…2018; Akashi et al. 2021; Horn, Schmid & Aurnou 2021). The spectral peaks in figure 3( b ) agree within 0.7 % of the JRV overturn frequency prediction of Vogt et al.…”

Unravelling the large-scale circulation modes in turbulent Rayleigh-Bénard convection (a)

“…For larger convection tanks, multiple circulations exist. In a Γ = 5 Cartesian cell, the dynamics is also dominated by JRVs, in this case four separate vortices [31]. Pandey et al [9] defined superstructures in RBC as coherent turbulent flow structure whose horizontal length-scale is greater than the height of the fluid layer.…”

“…Direct numerical simulations (DNS) have complemented these efforts. The three most prominent LSC modes are torsional oscillations [7], sloshing [8,29], and jump rope vortices (JRVs) [30,31], all of which have frequencies of the order of the turnover frequency. The quasi-2D sloshing and torsional (ST) modes dominate in enclosures with diameter-to-height aspect ratios of Γ = D/H 1 [32], whereas 3D JRVs dominate for Γ √ 2 [30].…”

“…-In the following, we will briefly present the traditional analysis methods to detect torsional oscillations, sloshing, and JRVs for the sake of completeness and to facilitate comparison with the DMD results. Shadowgraphs [7], PIV [8], and UDV [30,31] are means of diagnosing the interior flow in experiments. However, the arguably most convenient and straightforward method for identifying signatures of the different LSC dynamics are thermal measurements acquired along the circumference, at midheight, z = H/2, and in the lower and upper part of the cylinder, especially at H/4 and 3H/4 [8,29,35,46].…”