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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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Constraints on the Long-term Existence of Dilute Cores in Giant Planets
Abstract Post-Cassini ring seismology analysis suggests the existence of a stable stratification inside Saturn that extends from the center to ∼60% of its radius, in what is recognized today as Saturn’s dilute core. Similarly, gravity measurements on Jupiter suggest the existence of a dilute core of weekly constrained radial extent. These cores are likely in a double-diffusive regime, which prompts the question of their long-term stability. Indeed, previous direct numerical simulation (DNS) studies in triply periodic domains have shown that, in some regimes, double-diffusive convection tends to spontaneously form shallow convective layers, which coarsen until the region becomes fully convective. In this paper, we study the conditions for layering in double-diffusive convection using different boundary conditions, in which temperature and composition fluxes are fixed at the domain boundaries. We run a suite of DNSs varying microscopic diffusivities of the fluid and the strength of the initial stratification. We find that convective layers still form as a result of the previously discoveredγ-instability, which takes place whenever the local stratification drops below a critical threshold that only depends on the fluid diffusivities. We also find that the layers grow once formed, eventually occupying the entire domain. Our work thus recovers the results of previous studies, despite the new boundary conditions, suggesting that this behavior is universal. The existence of Saturn’s stably stratified core, today, therefore suggests that this threshold has never been reached, which places a new constraint on scenarios for the planet’s formation and evolution.
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- Award ID(s):
- 1908338
- PAR ID:
- 10537674
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Planetary Science Journal
- Volume:
- 5
- Issue:
- 8
- ISSN:
- 2632-3338
- Format(s):
- Medium: X Size: Article No. 190
- Size(s):
- Article No. 190
- Sponsoring Org:
- National Science Foundation
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