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1. Rotating convective turbulence in moderate to high Prandtl number fluids

   https://doi.org/10.1080/03091929.2023.2280874  

   Abbate, Jewel A.; Aurnou, Jonathan M. (December 2023, Geophysical & Astrophysical Fluid Dynamics)

   Andrew Soward (Ed.)

   Rotating convective turbulence is ubiquitously found across geo- physical settings, such as surface and subsurface oceans, plane- tary atmospheres, molten metal planetary cores, magma chambers, magma oceans, and basal magma oceans. Depending on the thermal and material properties of the system, buoyant convection can be driven thermally or compositionally, where a Prandtl number (Pr = ν/κi) defines the characteristic diffusion properties of the system, with κi = κT representing thermal diffusion and κi = κC representing chemical diffusion. These numbers vary widely for geophysical sys- tems; for example, the liquid iron undergoing thermal-compositional convection in Earth’s core is defined by PrT ≈ 0.1 and PrC ≈ 100, while a thermally-driven liquid silicate magma ocean is defined by PrT ≈ 100. Currently, most numerical and laboratory data for rotat- ing convective turbulent flows exists at Pr = O(1); high Pr rotating convection relevant to compositionally-driven core flow and other systems is less commonly studied. Here, we address this deficit by carrying out a broad suite of rotating convection experiments made over a range of Pr values, employing water and three different sil- icone oils as our working fluids (Pr = 6, 41, 206, and 993). Using measurements of flow velocities (Reynolds, Re) and heat transfer effi- ciency (Nusselt, Nu), a baroclinic torque balance is found to describe the turbulence regardless of Prandtl number so long as Re is suf- ficiently large (Re 10). Estimated turbulent scales are found to remain close to onset scales in all experiments, a result that may extrapolate to planetary settings. Lastly, we use our data to build Pr-dependent predictive nondimensional and dimensional scaling relations for rotating convective velocities that can be applied across a broad range of geophysical fluid dynamical settings. 

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

   Aurnou, J.M. (July 2020, Physical review research)

   null (Ed.)

   In this study, we investigate and develop scaling laws as a function of external non-dimensional control parameters for heat and momentum transport for non-rotating, slowly rotating and rapidly rotating turbulent convection systems, with the end goal of forging connections and bridging the various gaps between these regimes. Two perspectives are considered, one where turbulent convection is viewed from the standpoint of an applied temperature drop across the domain and the other with a viewpoint in terms of an applied heat flux. While a straightforward transformation exist between the two perspectives indicating equivalence, it is found the former provides a clear set of connections that bridge between the three regimes. Our generic convection scalings, based upon an Inertial-Archimedean balance, produce the classic diffusion-free scalings for the non-rotating limit (NRL) and the slowly rotating limit (SRL). This is characterized by a free-falling fluid parcel on the global scale possessing a thermal anomaly on par with the temperature drop across the domain. In the rapidly rotating limit (RRL), the generic convection scalings are based on a Coriolis-Inertial-Archimedean (CIA) balance, along with a local fluctuating-mean advective temperature balance. This produces a scenario in which anisotropic fluid parcels attain a thermal wind velocity and where the thermal anomalies are greatly attenuated compared to the total temperature drop. We find that turbulent scalings may be deduced simply by consideration of the generic non-dimensional transport parameters --- local Reynolds $$Re_\ell = U \ell /\nu$$; local P\'eclet $$Pe_\ell = U \ell /\kappa$$; and Nusselt number $$Nu = U \vartheta/(\kappa \Delta T/H)$$ --- through the selection of physically relevant estimates for length $$\ell$$, velocity $$U$$ and temperature scales $$\vartheta$$ in each regime. Emergent from the scaling analyses is a unified continuum based on a single external control parameter, the convective Rossby number\JMA{,} $$\RoC = \sqrt{g \alpha \Delta T / 4 \Omega^2 H}$$, that strikingly appears in each regime by consideration of the local, convection-scale Rossby number $$\Rol=U/(2\Omega \ell)$$. Thus we show that $$\RoC$$ scales with the local Rossby number $$\Rol$$ in both the slowly rotating and the rapidly rotating regimes, explaining the ubiquity of $$\RoC$$ in rotating convection studies. We show in non-, slowly, and rapidly rotating systems that the convective heat transport, parameterized via $$Pe_\ell$$, scales with the total heat transport parameterized via the Nusselt number $Nu$. Within the rapidly-rotating limit, momentum transport arguments generate a scaling for the system-scale Rossby number, $$Ro_H$$, that, recast in terms of the total heat flux through the system, is shown to be synonymous with the classical flux-based `CIA' scaling, $$Ro_{CIA}$$. These, in turn, are then shown to asymptote to $$Ro_H \sim Ro_{CIA} \sim \RoC^2$$, demonstrating that these momentum transport scalings are identical in the limit of rapidly rotating turbulent heat transfer. 

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3. Oscillatory thermal–inertial flows in liquid metal rotating convection

   Vogt, T. (April 2021, Journal of fluid mechanics)

   Verzicco, R. (Ed.)

   We present the first detailed thermal and velocity field characterization of convection in a rotating cylindrical tank of liquid gallium, which has thermophysical properties similar to those of planetary core fluids. Our laboratory experiments, and a closely associated direct numerical simulation, are all carried out in the regime prior to the onset of steady convective modes. This allows us to study the oscillatory convective modes, sidewall modes and broadband turbulent flow that develop in liquid metals before the advent of steady columnar modes. Our thermo-velocimetric measurements show that strongly inertial, thermal wind flows develop, with velocities reaching those of non-rotating cases. Oscillatory bulk convection and wall modes coexist across a wide range of our experiments, along with strong zonal flows that peak in the Stewartson layer, but that extend deep into the fluid bulk in the higher supercriticality cases. The flows contain significant time-mean helicity that is anti-symmetric across the midplane, demonstrating that oscillatory liquid metal convection contains the kinematic components to sustain system-scale dynamo generation. 

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4. Latitudinal regionalization of rotating spherical shell convection

   https://doi.org/10.1017/jfm.2022.1010  

   Gastine, Thomas; Aurnou, Jonathan M. (January 2023, Journal of Fluid Mechanics)

   Convection occurs ubiquitously on and in rotating geophysical and astrophysical bodies. Prior spherical shell studies have shown that the convection dynamics in polar regions can differ significantly from the lower latitude, equatorial dynamics. Yet most spherical shell convective scaling laws use globally-averaged quantities that erase latitudinal differences in the physics. Here we quantify those latitudinal differences by analysing spherical shell simulations in terms of their regionalized convective heat-transfer properties. This is done by measuring local Nusselt numbers in two specific, latitudinally separate, portions of the shell, the polar and the equatorial regions, $$Nu_p$$ and $$Nu_e$$ , respectively. In rotating spherical shells, convection first sets in outside the tangent cylinder such that equatorial heat transfer dominates at small and moderate supercriticalities. We show that the buoyancy forcing, parameterized by the Rayleigh number $Ra$ , must exceed the critical equatorial forcing by a factor of $${\approx }20$$ to trigger polar convection within the tangent cylinder. Once triggered, $$Nu_p$$ increases with $Ra$ much faster than does $$Nu_e$$ . The equatorial and polar heat fluxes then tend to become comparable at sufficiently high $Ra$ . Comparisons between the polar convection data and Cartesian numerical simulations reveal quantitative agreement between the two geometries in terms of heat transfer and averaged bulk temperature gradient. This agreement indicates that rotating spherical shell convection dynamics is accessible both through spherical simulations and via reduced investigatory pathways, be they theoretical, numerical or experimental. 

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5. A Novel Experimental Study on Density‐Driven Instability and Convective Dissolution in Porous Media

   https://doi.org/10.1029/2021GL095619  

   Guo, Ruichang; Sun, Hanxing; Zhao, Qingqi; Li, Zihao; Liu, Yang; Chen, Cheng (November 2021, Geophysical Research Letters)

   Abstract Geological carbon dioxide (CO₂) sequestration (GCS) in deep saline aquifers is a promising solution to mitigate the impact of anthropogenic CO₂emissions on global climate change. CO₂dissolved in formation water increases the solution density and can lead to miscible density‐driven downward convection, which significantly accelerates the dissolution trapping of injected CO₂. Experimental studies on miscible density‐driven convection have been limited. In the laboratory, we found an empirical linear correlation between reflected green light intensity and solute concentration, which enabledin situmeasurements of solute concentrations in the spatial and temporal domains and consequently the mass flux across the top boundary of the porous medium. Using the novel experimental techniques, we determined the critical Rayleigh‐Darcy number and critical time scales for the onset of density‐driven instability and convective dissolution. This is the first study to determine these critical system parameters using laboratory experiments. 

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