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The connection between the heat transfer and characteristic flow velocities of planetary core-style convection remains poorly understood. To address this, we present novel laboratory models of rotating Rayleigh–Bénard convection in which heat and momentum transfer are simultaneously measured. Using water (Prandtl number, Pr≃6) and cylindrical containers of diameter-to-height aspect ratios of Γ≃3,1.5,0.75, the non-dimensional rotation period (Ekman number, E) is varied between 10−7≲E≲3×10−5 and the non-dimensional convective forcing (Rayleigh number, Ra) ranges from 107≲Ra≲1012. Our heat transfer data agree with those of previous studies and are largely controlled by boundary layer dynamics. We utilize laser Doppler velocimetry (LDV) to obtain experimental point measurements of bulk axial velocities, resulting in estimates of the non-dimensional momentum transfer (Reynolds number, Re) with values between 4×102≲Re≲5×104. Behavioral transitions in the velocity data do not exist where transitions in heat transfer behaviors occur, indicating that bulk dynamics are not controlled by the boundary layers of the system. Instead, the LDV data agree well with the diffusion-free Coriolis–Inertia–Archimedian (CIA) scaling over the range of Ra explored. Furthermore, the CIA scaling approximately co-scales with the Viscous–Archimedian–Coriolis (VAC) scaling over the parameter space studied. We explain this observation by demonstrating that the VAC and CIA relations will co-scale when the local Reynolds number in the fluid bulk is of order unity. We conclude that in our experiments and similar laboratory and numerical investigations with E≳10−7, Ra≲1012, Pr≃7, heat transfer is controlled by boundary layer physics while quasi-geostrophically turbulent dynamics relevant to core flows robustly exist in the fluid bulk.
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Rotating convective turbulence in moderate to high Prandtl number fluids
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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- Award ID(s):
- 2143939
- PAR ID:
- 10494666
- Editor(s):
- Andrew Soward
- Publisher / Repository:
- Taylor & Francis
- Date Published:
- Journal Name:
- Geophysical & Astrophysical Fluid Dynamics
- ISSN:
- 0309-1929
- Page Range / eLocation ID:
- 1 to 40
- Subject(s) / Keyword(s):
- Rotating convection convection turbulence Prandtl number core dynamics planetary core convection dynamo physics geophysical fluid dynamics
- Format(s):
- Medium: X Size: 5.7 MB Other: PDF
- Size(s):
- 5.7 MB
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1080/03091929.2023.2280874
