Oscillatory thermal–inertial flows in liquid metal rotating convection

Vogt, Tobias; Horn, Susanne; Aurnou, J. M.

doi:10.1017/jfm.2020.976

Cited by 29 publications

(25 citation statements)

References 116 publications

(309 reference statements)

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“…These MRWs are multimodal, consisting of several modes with different azimuthal symmetries and time scales, and we demonstrate that this multimodal character can be indeed predicted from the stability analysis of the RWs. The unstable eigenfunction (Floquet mode) at the bifurcation reveals the main mode structure of the multimodal MRWs, which include wall-attached and interior modes as seen in recent numerical and experimental studies [31,34,38]. Finally, in agreement with [36], triadic resonances have been found and interpreted in terms of MRWs as done in [45] in the case of the magnetized spherical Couette flow.…”

Section: Introductionsupporting

confidence: 70%

“…When Pr is small enough, strong oscillatory flows with multimodal nature, in which the interaction of certain modes with different spatial localizations play a relevant role in the dynamics, may appear right after the onset ( [31,34]). For instance, a flow consisting of convective structures, either attached to the boundary or located in the interior, has been observed in a recent experiment [38] with liquid gallium (Pr = 0.026) inside a cylindrical vessel. In these experiments, in agreement with [31,34], steady convective columns (i.e RWs) have not been found to exist at the onset.…”

Section: Introductionmentioning

confidence: 99%

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Weak branch and multimodal convection in rapidly rotating spheres at low Prandtl number

Garcia,

Stefani,

Dormy

2021

Preprint

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The focus of this study is to investigate primary and secondary bifurcations to weakly nonlinear flows (weak branch) in convective rotating spheres in a regime where only strongly nonlinear oscillatory sub-and supercritical flows (strong branch) were previously found in [E. J. Kaplan, N. Schaeffer, J. Vidal, and P. Cardin, Phys. Rev. Lett. 119, 094501 (2017)]. The relevant regime corresponds to low Prandtl and Ekman numbers, indicating a predominance of Coriolis forces and thermal diffusion in the system. We provide the bifurcation diagrams for rotating waves (RWs) computed by means of continuation methods and the corresponding stability analysis of these periodic flows to detect secondary bifurcations giving rise to quasiperiodic modulated rotating waves (MRWs). Additional direct numerical simulations (DNS) are performed for the analysis of these quasiperiodic flows for which Poincaré sections and kinetic energy spectra are presented. The diffusion time scales are investigated as well. Our study reveals very large initial transients (more than 30 diffusion time units) for the nonlinear saturation of solutions on the weak branch, either RWs or MRWs, when DNS are employed. In addition, we demonstrate that MRWs have multimodal nature involving resonant triads. The modes can be located in the bulk of the fluid or attached to the outer sphere and exhibit multicellular structures. The different resonant modes forming the nonlinear quasiperiodic flows can be predicted with the stability analysis of RWs, close to the Hopf bifurcation point, by analyzing the leading unstable Floquet eigenmode.

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Section: Introductionsupporting

confidence: 70%

Section: Introductionmentioning

confidence: 99%

Weak branch and multimodal convection in rapidly rotating spheres at low Prandtl number

Garcia,

Stefani,

Dormy

2021

Preprint

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“…Turbulent MC is relevant for understanding many geophysical and astrophysical phenomena (e.g. Proctor & Weiss 1982; King & Aurnou 2015; Vogt, Horn & Aurnou 2021). If under planetary interior conditions (e.g.…”

Section: Discussionmentioning

confidence: 99%

Thermoelectric precession in turbulent magnetoconvection

Horn

Aurnou

2021

J. Fluid Mech.

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We present laboratory measurements of the interaction between thermoelectric currents and turbulent magnetoconvection. In a cylindrical volume of liquid gallium heated from below and cooled from above and subject to a vertical magnetic field, it is found that the large-scale circulation (LSC) can undergo a slow axial precession. Our experiments demonstrate that this LSC precession occurs only when electrically conducting boundary conditions are employed, and that the precession direction reverses when the axial magnetic field direction is flipped. A thermoelectric magnetoconvection (TEMC) model is developed that successfully predicts the zeroth-order magnetoprecession dynamics. Our TEMC magnetoprecession model hinges on thermoelectric current loops at the top and bottom boundaries, which create Lorentz forces that generate horizontal torques on the overturning large-scale circulatory flow. The thermoelectric torques in our model act to drive a precessional motion of the LSC. This model yields precession frequency predictions that are in good agreement with the experimental observations. We postulate that thermoelectric effects in convective flows, long argued to be relevant in liquid metal heat transfer and mixing processes, may also have applications in planetary interior magnetohydrodynamics.

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“…In this study, the flow velocities are measured using ultrasonic Doppler velocimetry (UDV) which is an established measurement technique for opaque fluids like liquid metals (Aubert et al 2001;Brito et al 2001;Eckert & Gerbeth 2002;Gillet et al 2007;Nataf et al 2008;Vogt, Räbiger & Eckert 2014;Vogt et al 2018a,b;Zürner et al 2019Zürner et al , 2020Yang, Vogt & Eckert 2021;Vogt, Horn & Aurnou 2021a;Vogt et al 2021b). The used UDV system is a DOP3010 (from Signal Processing SA, Lausanne) equipped with 8 MHz transducers.…”

Section: Measuring Techniquementioning

confidence: 99%

Dynamics and length scales in vertical convection of liquid metals

et al. 2021

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Using complementary experiments and direct numerical simulations, we study turbulent thermal convection of a liquid metal (Prandtl number $\textit {Pr}\approx 0.03$ ) in a box-shaped container, where two opposite square sidewalls are heated/cooled. The global response characteristics like the Nusselt number ${\textit {Nu}}$ and the Reynolds number $\textit {Re}$ collapse if the side height $L$ is used as the length scale rather than the distance $H$ between heated and cooled vertical plates. These results are obtained for various Rayleigh numbers $5\times 10^3\leq {\textit {Ra}}_H\leq 10^8$ (based on $H$ ) and the aspect ratios $L/H=1, 2, 3$ and $5$ . Furthermore, we present a novel method to extract the wind-based Reynolds number, which works particularly well with the experimental Doppler-velocimetry measurements along vertical lines, regardless of their horizontal positions. The extraction method is based on the two-dimensional autocorrelation of the time–space data of the vertical velocity.

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Oscillatory thermal–inertial flows in liquid metal rotating convection

Abstract: Abstract

Cited by 29 publications

References 116 publications

Weak branch and multimodal convection in rapidly rotating spheres at low Prandtl number

Weak branch and multimodal convection in rapidly rotating spheres at low Prandtl number

Thermoelectric precession in turbulent magnetoconvection

Dynamics and length scales in vertical convection of liquid metals

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