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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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The Effect of Rotation on Double Diffusive Convection: Perspectives from Linear Stability Analysis
Abstract Diffusive convection can occur when two constituents of a stratified fluid have opposing effects on its stratification and different molecular diffusivities. This form of convection arises for the particular temperature and salinity stratification in the Arctic Ocean and is relevant to heat fluxes. Previous studies have suggested that planetary rotation may influence diffusive–convective heat fluxes, although the precise physical mechanisms and regime of rotational influence are not well understood. A linear stability analysis of a temperature and salinity interface bounded by two mixed layers is performed here to understand the stability properties of a diffusive–convective system, and in particular the transition from nonrotating to rotationally controlled heat transfer. Rotation is shown to stabilize diffusive convection by increasing the critical Rayleigh number to initiate instability. In the rotationally controlled regime, a −4/3 power law is found between the critical Rayleigh number and the Ekman number, similar to the scaling for rotating thermal convection. The transition from nonrotating to rotationally controlled convection, and associated drop in heat fluxes, is predicted to occur when the thermal interfacial thickness exceeds about 4 times the Ekman layer thickness. A vorticity budget analysis indicates how baroclinic vorticity production is counteracted by the tilting of planetary vorticity by vertical shear, which accounts for the stabilization effect of rotation. Finally, direct numerical simulations yield generally good agreement with the linear stability analysis. This study, therefore, provides a theoretical framework for classifying regimes of rotationally controlled diffusive–convective heat fluxes, such as may arise in some regions of the Arctic Ocean.
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- Award ID(s):
- 1950077
- PAR ID:
- 10549580
- Publisher / Repository:
- American Meteorological Society
- Date Published:
- Journal Name:
- Journal of Physical Oceanography
- Volume:
- 51
- Issue:
- 11
- ISSN:
- 0022-3670
- Format(s):
- Medium: X Size: p. 3335-3346
- Size(s):
- p. 3335-3346
- Sponsoring Org:
- National Science Foundation
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