Laboratory Experiments Realize Diffusivity-Free Turbulence in Rotating Convection

Core Concepts

Diffusivity-free (DF) turbulent convection, a phenomenon crucial for understanding heat and momentum transfer in astrophysical and geophysical systems, can be achieved and studied in a laboratory setting using liquid metal rotating convection experiments.

Abstract

• Bibliographic Information: Abbate, J. A., Xu, Y., Vogt, T., Horn, S., Juliene, K., & Aurnou, J. M. (2024). Diffusivity-Free Turbulence in Tabletop Rotating Rayleigh-Bénard Convection Experiments. arXiv preprint arXiv:2411.11226v1.
• Research Objective: This study aims to demonstrate the existence of diffusivity-free (DF) turbulent convection in a controlled laboratory environment using rotating Rayleigh-Bénard convection (RRBC) experiments with liquid metal.
• Methodology: The researchers utilized UCLA's RoMag device, a rotating convection cell filled with liquid gallium (Pr ≈ 0.027), to conduct a series of experiments. They systematically varied the Rayleigh and Ekman numbers over a wide range to achieve both oscillatory and steady convection regimes. Measurements of heat transfer efficiency (Nusselt number, Nu), internal temperature fluctuations (θ), and vertical flow velocity (Reynolds number, Re) were acquired using thermistors and an ultrasonic Doppler velocimeter. The experimental findings were then compared to theoretical predictions for DF convection derived from asymptotically reduced planar models.
• Key Findings: The study successfully demonstrated the existence of DF turbulent convection in a laboratory setting. By isolating the oscillatory mode of convection in the liquid metal, the researchers observed scaling behavior in Nu, Re, and θ that closely matched the theoretical predictions for DF convection. Notably, the agreement was strongest in wider, high aspect ratio convection cells, suggesting a closer resemblance to the idealized infinite plane layer geometry used in theoretical models.
• Main Conclusions: This research provides experimental validation for the existence of DF turbulent convection in a laboratory setting, confirming the applicability of theoretical models to real-world systems. The findings have significant implications for understanding and predicting convective heat and momentum transfer in astrophysical and geophysical contexts, such as Earth's outer core and stellar interiors.
• Significance: This study bridges a crucial gap between theoretical predictions and experimental observations of DF turbulent convection. By achieving this phenomenon in a controlled laboratory environment, the research enables more accurate modeling and understanding of complex fluid dynamics in celestial bodies.
• Limitations and Future Research: While the study successfully demonstrated DF convection in a specific experimental setup, further research is needed to explore the influence of different Prandtl number fluids, varying aspect ratios, and methods to suppress wall modes. Investigating the potential of lower Pr fluids like liquid sodium could provide a wider range for studying oscillatory convection. Additionally, exploring techniques to minimize wall effects in taller, slender tanks could further refine the experimental validation of DF scaling laws.

Stats

Earth's outer core flow velocities are estimated to be u ≃5 × 10−4 m/s.
The Reynolds number for Earth's outer core is Re ≃10^9.
Earth's outer core has an Ekman number of E ≃10^−15.
The Prandtl number for Earth's outer core is Pr ≃0.1.
The Rayleigh number for Earth's outer core is estimated to be Ra ≃4 × 10^23.
The superadiabatic temperature differential ∆T in Earth's core is estimated to be ≃3 mK.
The temperature anomaly in Earth's core is calculated as θ ≃ 10^−6 K.
The flux Rayleigh number in Earth's core is estimated to be RaF ≃10^28.
The convective heat flux in Earth's core is predicted to be qconv ≃3 mW/m2.
The superadiabatic heat flow driving thermal convection in Earth's core is estimated as Qconv ≃0.5 TW.

Quotes

"Diffusivity-free (DF) turbulent convection is theorized to occur in the convection zones of stars and the fluid cores of planets, where it drives vortical flows, jets, and dynamo action that sustains global-scale magnetic fields."
"The fundamental barrier to achieving diffusion-free convection in RRBC lies in the physical boundaries through which heat is supplied and extracted."
"These experiments show that diffusion-free physics can exist even in relatively small, closed containers of rotating fluid."
"By verifying here that diffusivity-free convection exists in a standard desktop-scale RRBC experimental cell, it is now possible to accurately and confidently model the convective turbulence that exists in rapidly rotating planetary and stellar interiors."

Key Insights Distilled From

Diffusivity-Free Turbulence in Tabletop Rotating Rayleigh-B\'enard Convection Experiments

by Jewel A. Abb... at arxiv.org 11-19-2024

https://arxiv.org/pdf/2411.11226.pdf

Deeper Inquiries

How might the findings of this research be applied to improve our understanding of other astrophysical phenomena, such as stellar dynamos or accretion disks?

This research provides a validated framework for understanding diffusivity-free turbulence in rapidly rotating systems, which has direct implications for astrophysical phenomena like stellar dynamos and accretion disks:

Stellar Dynamos: Stars, particularly those with convective envelopes and rapid rotation, generate magnetic fields through dynamo action. This process relies heavily on the turbulent motions within the convective zone. The study's findings on scaling laws for heat and momentum transfer in the diffusivity-free regime can be incorporated into stellar dynamo models. This can lead to more accurate predictions of magnetic field strengths, geometries, and temporal variations in stars.
Accretion Disks: Accretion disks, formed by material spiraling onto a central object (like a black hole or a young star), also exhibit turbulent behavior. While the study focuses on Rayleigh-Bénard convection, the fundamental insights into inertial oscillations and their role in driving turbulence can be extended to understand the dynamics of accretion disks. This can help explain observed accretion rates, disk structures, and the formation of jets from these systems.
Furthermore, the study's success in achieving laboratory-scale realization of diffusivity-free turbulence opens avenues for future experimental investigations. By tailoring the experimental setup to mimic specific aspects of stellar interiors or accretion disks, researchers can gain a more nuanced understanding of these complex astrophysical systems.

Could the presence of magnetic fields, which are not considered in this study, significantly alter the dynamics of rotating convection and the realization of diffusivity-free turbulence?

Yes, the presence of magnetic fields can significantly alter the dynamics of rotating convection and the realization of diffusivity-free turbulence.

Magnetohydrodynamic Effects: Introducing magnetic fields into the system brings into play magnetohydrodynamic (MHD) effects. The Lorentz force, arising from the interaction of magnetic fields and electric currents, can influence fluid motion. This can lead to the suppression of certain convective instabilities, modification of heat and momentum transport, and the emergence of new wave modes (like Alfvén waves).
Magnetic Field Generation: In astrophysical objects, the convective motions themselves can generate magnetic fields, leading to a complex interplay between convection and magnetic fields. This is the basis of dynamo theory. The presence of a pre-existing magnetic field can significantly influence the dynamo process, affecting the growth or decay of the generated field.
Diffusivity-Free Regime: The realization of diffusivity-free turbulence in the presence of magnetic fields depends on the relative strengths of inertial, Coriolis, buoyancy, and magnetic forces. Strong magnetic fields can suppress small-scale turbulent motions, potentially affecting the attainment of the diffusivity-free regime.
Investigating the effects of magnetic fields on rotating convection is a complex but crucial area of research. Future studies incorporating magnetic fields into similar experimental setups or numerical simulations can provide valuable insights into the dynamics of astrophysical systems where both rotation and magnetic fields play dominant roles.

If we could create a perfectly insulated rotating convection experiment, eliminating all heat losses, how would the system behave and would it provide further insights into the fundamental physics of turbulence?

A perfectly insulated rotating convection experiment, while idealistic, offers intriguing possibilities for exploring fundamental turbulence physics:

Sustained Turbulence: Without heat losses, the system would not reach a steady state where heat input equals heat output. Instead, the continuously injected energy would cascade to smaller scales, potentially leading to a state of sustained turbulence. This allows for studying long-term turbulent behavior without reaching a thermal equilibrium.
Absence of Boundary Effects: Perfect insulation eliminates thermal gradients at the boundaries, effectively removing the influence of boundary layers on the bulk flow. This allows for isolating and studying the intrinsic dynamics of rotating convection in a more idealized setting, free from wall modes and boundary layer effects.
Energy Cascade and Dissipation: Observing how energy injected at large scales cascades down to smaller scales in the absence of boundary effects can provide insights into the energy dissipation mechanisms in turbulent flows. This can help refine turbulence models and improve our understanding of the energy budget in turbulent systems.
However, achieving perfect insulation in a real-world experiment is practically impossible. Even with advanced insulation techniques, some residual heat losses will always exist. Nevertheless, striving for higher levels of insulation in experimental setups can minimize boundary effects and provide valuable data for comparison with theoretical models and simulations.