Magnetic modulation of flow reversals in liquid metal thermal convection

TL;DR

This study addresses the rarity of flow reversals in low-$Pr$ liquid-metal convection by demonstrating that a transverse magnetic field can induce reversals in a quasi-two-dimensional cell. It combines GaInSn experiments across ranges of $Ra$ and $Ha$ with a theoretical framework that accounts for magnetic-field effects to predict reversal frequencies. The results reveal two linear thresholds in $(Ra/Ha)$ that separate stable-LSC, periodic-reversal, and stochastic-reversal regimes, and they validate an extended Ni-based model predicting reversal frequencies that closely match observations. The work shows that magnetic fields can controllably modulate reversal dynamics in low-$Pr$ convection by increasing an effective viscosity and $Pr^*$, offering a practical framework for studying MHD-reversal phenomena.

Abstract

Flow reversals are rarely observed in low-Prandtl-number liquid metal convection due to the fluid's exceptionally high thermal diffusivity. Here, we demonstrate that an external transverse magnetic field can induce such reversals in a quasi-two-dimensional (Q2D) rectangular cell with an aspect ratio ($\itΓ$) of $0.2$. Our experimental observations reveal that the system initially exhibits periodic dynamics at the onset of reversals before transitioning to stochastic behavior as the ratio of Rayleigh number ($Ra$) to Hartmann number ($Ha$) increases. This transition is governed by the competition between buoyancy and Lorentz forces, with experimental data showing a linear scaling relationship between $Ra$ and $Ha$ at critical points. We develop a theoretical model that incorporates magnetic field effects in low-Prandtl-number convection to predict the reversal frequencies. These findings provide new insights into how magnetic fields can modulate flow regimes in low-Prandtl-number convection, establishing a controlled framework for investigating reversal dynamics in magnetohydrodynamic systems.

Figures (5)

• Figure 1: Probe arrangement and velocity distribution without magnetic field. (a) Arrangement of temperature and ultrasonic probes in the experimental setup. (b) Measured $Nu$ and $Re$: black squares for $Nu$, blue triangles for $Re$, with the dotted line showing the fit and the red line indicating GL theory. (c) Time evolution of velocity at $Ra = 4.54 \times 10^6$, normalized by the free-fall time $\tau_{ff} = \sqrt{H/(\alpha g \Delta T)}$, showing a clear LSC with red and blue denoting opposite flow directions.
• Figure 2: Typical flow reversal at $Ha=705.39$, $Ra=7.20\times10^6$ from experiment. (a) Spatiotemporal velocity distribution: red indicates flow in the positive $x$-direction (away from the probe), blue indicates the opposite. (b) Time series of temperature difference $\Delta T_{top} = T_1 - T_4$. (c) Instantaneous Nusselt number ($Nu$), synchronized with the velocity field; time is normalized by the free-fall time $\tau_{ff}$. The black box highlights a full reversal cycle, with dashed lines marking $\tau_r/4$, $\tau_r/2$, and $3\tau_r/4$. (d)-(g) Cartoons of flow structures at four typical moments within a cycle. Arrows represent velocity vectors derived from MPUDV, with color and size scaled by the instantaneous velocity normalized by $u_{max}$. The $x$ and $y$ axes correspond to directions defined in figure \ref{['fig:Fig_1']}(a).
• Figure 3: Heat transfer in liquid metal convection. The scaling of $Nu$ versus $Ra$ is shown. Our data are compared with previous work, as indicated in the legend. The dashed line represents fitted results for $Ha=0$. The solid data points correspond to cases where a magnetic field is applied. For clarity, the $Nu$ values for $Ha =$ 554.23, 705.39, 857.11, 1158.85 and 1461.16 have been vertically shifted by +8, +6, +4, and +2 units, respectively. These artificial vertical shifts are illustrated in the inset plot.
• Figure 4: The reversal characteristics in different regions. (a) and (b) are $\Delta T_{top}$ and its PSD for $Ra=2.86\times10^6$, $Ha=1461.16$ (white region in figure \ref{['fig:Fig_5']} (a)). (c) and (d) for $Ra=4.54\times10^6$, $Ha=554.23$ (orange region in figure \ref{['fig:Fig_5']} (a)). (e) and (f) for $Ra=2.28\times10^7$, $Ha=1158.85$ (blue region in figure \ref{['fig:Fig_5']} (a)). Red squares and green diamonds mark the start and end of reversals.
• Figure 5: The statistical characteristics of flow reversal. (a) Phase diagram with three regimes divided by $(Ra/Ha)_{c1} \simeq 5250$ and $(Ra/Ha)_{c2} \simeq 16750$: Region I (stable LSC, inverted triangles), Region II (periodic reversals, squares), Region III (stochastic reversals, upright triangles). The marker color shows normalized $Nu$. Dimensionless reversal frequency with error bars. The error bar originates from the statistics of the reversals. Regions and vertical lines match figure \ref{['fig:Fig_5']} (a).