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Abstract This study presents the linear theory of thermohaline‐shear instability, which is realized in oceanic flows that are dynamically and diffusively stable. The framework is based on the unbounded Couette model, which makes it possible to decouple the destabilizing effects of spatially uniform shear from instabilities caused by the presence of inflection points in velocity profiles. The basic state is assumed to be time dependent, which reflects the role of internal waves in controlling fine‐scale shear. Linear stability analysis suggests that conditions for thermohaline‐shear instability are met in most ocean regions where temperature and salinity concurrently increase downward. We conclude that thermohaline‐shear instability represents a plausible mechanism for the initiation of active diffusive convection, which, in turn, is essential for the formation of thermohaline staircases and maintenance of double‐diffusive interleaving.
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Modelling coexisting GSF and shear instabilities in rotating stars
ABSTRACT Zahn’s widely used model for turbulent mixing induced by rotational shear has recently been validated (with some caveats) in non-rotating shear flows. It is not clear, however, whether his model remains valid in the presence of rotation, even though this was its original purpose. Furthermore, new instabilities arise in rotating fluids, such as the Goldreich–Schubert–Fricke (GSF) instability. Which instability dominates when more than one can be excited, and how they influence each other, were open questions that this paper answers. To do so, we use direct numerical simulations of diffusive stratified shear flows in a rotating triply periodic Cartesian domain located at the equator of a star. We find that either the GSF instability or the shear instability tends to take over the other in controlling the system, suggesting that stellar evolution models only need to have a mixing prescription for each individual instability, together with a criterion to determine which one dominates. However, we also find that it is not always easy to predict which instability ‘wins’ for given input parameters, because the diffusive shear instability is subcritical, and only takes place if there is a finite-amplitude turbulence ‘primer’ to seed it. Interestingly, we find that the GSF instability can in some cases play the role of this primer, thereby providing a pathway to excite the subcritical shear instability. This can also drive relaxation oscillations, which may be observable. We conclude by proposing a new model for mixing in the equatorial regions of stellar radiative zones due to differential rotation.
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- Award ID(s):
- 1814327
- PAR ID:
- 10289878
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 506
- Issue:
- 4
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- 4914 to 4932
- Format(s):
- Medium: X
- 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/10.1093/mnras/stab1927
