Oscillations of the large-scale circulation in experimental liquid metal convection at aspect ratios 1.4–3

Abstract

We investigate the scaling properties of the primary flow modes and their sensitivity to aspect ratio in a liquid gallium (Prandtl number $Pr = 0.02$ ) convection system through combined laboratory experiments and numerical simulations. We survey cylindrical aspect ratios $1.4 \le \varGamma \le 3$ and Rayleigh numbers $10^{4} \lesssim Ra \lesssim 10^{6}$ . In this range the flow is dominated by a large-scale circulation (LSC) subject to low-frequency oscillations. In line with previous studies, we show robust scaling of the Reynolds number $Re$ with $Ra$ and we confirm that the LSC flow is dominated by a jump-rope vortex (JRV) mode whose signature frequency is present in velocity and temperature measurements. We further show that both $Re$ and JRV frequency scaling trends are relatively insensitive to container geometry. The temperature and velocity spectra consistently show peaks at the JRV frequency, its harmonic and a secondary mode. The relative strength of these peaks changes and the presence of the secondary peak depend highly on aspect ratio, indicating that, despite having a minimal effect on typical velocities and frequencies, the aspect ratio has a significant effect on the underlying dynamics. Applying a bandpass filter at the secondary frequency to velocity measurements reveals that a clockwise twist in the upper half of the fluid layer coincides with a counterclockwise twist in the bottom half, indicating a torsional mode. For aspect ratio $\varGamma = 3$ , the unified LSC structure breaks down into multiple rolls in both simulation and experiment.

Oscillatory large-scale circulation in liquid-metal thermal convection and its structural unit

“…Two length scales were used for the dissipative time scale: the height of the domain , and the overall path length of the LSC, following Cheng et al. (2022), is approximated coarsely as , , where , , and for , 2.5, 3 and 5, respectively. Note that in the latter case, , since for the container, the flow pattern consists of two JRV building blocks, repeated in both horizontal directions, as shown above.…”

“…2022; Cheng et al. 2022). The precession, sloshing and torsional (ST) dynamics of the LSC, which dominates at , is replaced by a mode that can be described as a jump rope vortex (JRV).…”

“…However, no JRV was detected in a cylinder (Cheng et al. 2022).

Figure 1.Phase-averaged streamlines in RBC for , , as obtained in direct numerical simulations for different aspect ratios ( a ) , ( b ) , ( c ) , ( d ) (box) for square cuboid domains (new simulations) and ( e ) (cylinder), adapted from Vogt et al.

…”

“…2010; Assaf, Angheluta & Goldenfeld 2011; Stevens, Clercx & Lohse 2011; Wagner, Shishkina & Wagner 2012; Sakievich, Peet & Adrian 2020; Cheng et al. 2022). The sloshing mode is associated with the motion of the LSC plane in the radial direction, while the precession and torsion modes are related to the azimuthal motion of the LSC plane (Horn, Schmid & Aurnou 2021; Cheng et al.…”

“…The sloshing mode is associated with the motion of the LSC plane in the radial direction, while the precession and torsion modes are related to the azimuthal motion of the LSC plane (Horn, Schmid & Aurnou 2021; Cheng et al. 2022). In the precession mode, the entire LSC plane drifts in the azimuthal direction, while in the torsion mode, the azimuthal motion of the LSC plane in the upper half of the container is generally in the direction opposite to the motion of the LSC plane in the lower half of the container.…”