Rotating thermal convection in liquid gallium: multi-modal flow, absent steady columns

Abstract

Earth’s magnetic field is generated by convective motions in its liquid metal core. In this fluid, the heat diffuses significantly more than momentum, and thus the Prandtl number$Pr$is well below unity. The thermally driven convective flow dynamics of liquid metals are very different from moderate-$Pr$fluids, such as water and those used in current dynamo simulations. In order to characterise rapidly rotating thermal convection in low-$Pr$number fluids, we have performed laboratory experiments in a cylinder of aspect ratio$\unicode[STIX]{x1D6E4}=1.94$using liquid gallium ($Pr\simeq 0.025$) as the working fluid. The Ekman number varies from$E\simeq 5\times 10^{-6}$to$5\times 10^{-5}$and the Rayleigh number varies from$Ra\simeq 2\times 10^{5}$to$1.5\times 10^{7}$. Using spectral analysis stemming from point-wise temperature measurements within the fluid and measurements of the Nusselt number$Nu$, we characterise the different styles of low-$Pr$rotating convective flow. The convection threshold is first overcome in the form of container-scale inertial oscillatory modes. At stronger forcing, sidewall-attached modes are identified for the first time in liquid metal laboratory experiments. These wall modes coexist with the bulk oscillatory modes. At$Ra$well below the values where steady rotating columnar convection occurs, the bulk flow becomes turbulent. Our results imply that rotating convective flows in liquid metals do not develop in the form of quasisteady columns, as in moderate-$Pr$fluids, but in the form of oscillatory convective motions. Thus, thermally driven flows in low-$Pr$geophysical and astrophysical fluids can differ substantively from those occurring in$Pr\simeq 1$models. Furthermore, our experimental results show that relatively low-frequency wall modes are an essential dynamical component of rapidly rotating convection in liquid metals.

Connections between nonrotating, slowly rotating, and rapidly rotating turbulent convection transport scalings

“…and convection onsets in the form of stationary modes. In lower Prandtl number fluids such that Pr 0.67, convection first develops via oscillatory modes [27,33,34] and the critical Rayleigh number in a plane layer is Ra crit 17.4 (Ek/Pr) −4/3 [35,36]. Thus, in plane-layer geometries, Ra crit depends on the rotation rate and the fluid's thermal diffusivity in low Pr fluids.…”

Jump rope vortex in liquid metal convection

“…Twenty-three experiments were conducted where the range of mean fluid temperatures varied between 35 ○C ≤Tm≤ 47 ○C and the temperature drop across the fluid layer between 0.28≤normalΔ≤19.36 K. Using the material properties for gallium (40), the Prandtl number ranges between 0.026≤Pr≤0.028 and the Rayleigh number between 7.1×104≤Ra≤5.1×106. Ultrasound Doppler velocimetry is used to measure the instantaneous velocity distribution along four different measuring lines, as shown in Fig.…”

Competition between Ekman Plumes and Vortex Condensates in Rapidly Rotating Thermal Convection

“…Here, g is gravitational acceleration, α, ν, and κ are, respectively, the kinematic viscosity, thermal diffusivity, and thermal expansion coefficient of the fluid, Δ and H the temperature difference and distance between bottom and top wall, respectively, and Ω the rotation rate. The critical Rayleigh number for onset of oscillatory convection (Pr<0.68) is Ra c ¼ 17.4ðEk= PrÞ −4=3 ; for steady convection (Pr ≥ 0.68) it is Ra c ¼ 8.7Ek −4=3 [23,24]; R ≡ Ra=Ra c measures supercriticality.…”

“…is the horizontal length scale for onset of oscillatory convection [23,24]. Resolutions up to 1408 × 1408 × 1280 points resolve the Kolmogorov length η K , the smallest active flow length scale.…”