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1. Initiation of diffusive layering by time-dependent shear

   https://doi.org/10.1017/jfm.2018.790  

   Brown, Justin M.; Radko, Timour (January 2019, Journal of Fluid Mechanics)

   null (Ed.)

   The Arctic halocline is generally stable to the development of double-diffusive and dynamic instabilities – the two major sources of small-scale mixing in the mid-latitude oceans. Despite this, observations show the abundance of double-diffusive staircases in the Arctic Ocean, which suggests the presence of some destabilizing process facilitating the transition from smooth-gradient to layered stratification. Recent studies have shown that an instability can develop in such circumstances if weak static shear is present even when the flow is dynamically and diffusively stable. However, the impact of oscillating shear, associated with the presence of internal gravity waves, has not yet been addressed for the diffusive case. Through two-dimensional simulations of diffusive convection, we have investigated the impact of the magnitude and frequency of externally forced oscillatory shear on the thermohaline-shear instability. Simulations with stochastic shear – characterized by a continuous spectrum of frequencies from inertial to buoyancy – indicate that thermohaline layering does occur due to the presence of destabilizing modes (oscillations of near the buoyancy frequency). These simulations show that such layers appear as well-defined steps in the temperature and salinity profiles. Thus, the thermohaline-shear instability is a plausible mechanism for staircase formation in the Arctic and merits substantial future study. 

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2. The Effect of Rotation on Double Diffusive Convection: Perspectives from Linear Stability Analysis

   https://doi.org/10.1175/JPO-D-21-0060.1  

   Liang, Yu; Carpenter, Jeffrey_R; Timmermans, Mary-Louise (November 2021, Journal of Physical Oceanography)

   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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3. Modelling coexisting GSF and shear instabilities in rotating stars

   https://doi.org/10.1093/mnras/stab1927  

   Chang, Eonho; Garaud, Pascale (August 2021, Monthly Notices of the Royal Astronomical Society)

   null (Ed.)

   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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4. The 3-Helium Problem

   Balser, D.; Bania, T. (January 2020, American Astronomical Society meeting #235)

   The light element 3He is produced in copious amounts during the first three minutes after the Big Bang. The 3He abundance is then modified primarily by nucleosynthesis in stars, whereby low-mass stars (< 2 solar masses) are expected to produce 3He due to the astration of deuterium. The higher temperatues in more massive stars fuse 3He completely into 4He thus destroying 3He. Measurements of 3He are made via observations of the hyperfine transition of 3He+ at 3.46 cm. Observations of 3He+ in HII regions located throughout the Milky Way disk reveal very little variation in the 3He/H abundance ratio — the "3He Plateau", indicating that the net effect of 3He production in stars is negligible. This is in contrast to much higher 3He/H abundance ratios found in some planetary nebula (PNe). This discrepancy is known as the "3He Problem." One solution to this problem is that thermohaline mixing occurs just above the hydrogen-burning shell to process 3-Helium: 3He(3He, 2p)4He. Thermohaline mixing is a double-diffusive instability that occurs in oceans and is also called thermohaline convection. We discuss how more accurate observations of the 3He/H abundance ratio can constrain stellar evolution models that include thermohaline mixing. 

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5. A Cavity-Based Micromechanical Model for the Shear-Band Failure in Metallic Glasses Under Arbitrary Stress States

   https://doi.org/10.1115/1.4062724  

   Gao, Yanfei (December 2023, Journal of Applied Mechanics)

   Abstract Deformation and fracture of metallic glasses are often modeled by stress-based criteria which often incorporate some sorts of pressure dependence. However, detailed mechanisms that are responsible for the shear-band formation and the entire damage initiation and evolution process are complex and the origin of such a pressure dependence is obscure. Here, we argue that the shear-band formation results from the constitutive instability, so that the shear-band angle and arrangements can be easily related to the macroscopic constitutive parameters such as internal friction and dilatancy factor. This is one reason for the observed tension-compression asymmetry in metallic glasses. The free volume coalescence leads to precipitous formation of voids or cavities inside the shear bands, and the intrinsic “ductility” is therefore governed by the growth of these cavities. Based on a generalized Stokes–Hookean analogy, we can derive the critical shear-band failure strain with respect to the applied stress triaxiality, in which the cavity evolution scenarios are sharply different between tension-controlled and shear/compression-dominated conditions. This is another possible reason for the tension-compression asymmetry. It is noted that diffusive-controlled cavity growth could also be the rate-determining process, as suggested by the recent measurements of shear-band diffusivity and viscosity that turn out to satisfy the Stokes–Einstein relationship. This constitutes the third possible reason for the tension-compression asymmetry. 

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