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1. 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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2. Effects of confinement on absolute and convective instabilities for momentum-driven countercurrent shear layers

   https://doi.org/10.1103/PhysRevFluids.6.073901  

   Yang, Jinwei ; Anderson, Matt J. ; Strykowski, Paul J. ; Srinivasan, Vinod ( July 2021 , Physical Review Fluids)
3. Topographically Generated Submesoscale Shear Instabilities Associated with Brazil Current Meanders

   https://doi.org/10.1175/JPO-D-22-0122.1  

   Luko, Caique D. ; Lazaneo, Cauê Z. ; Silveira, Ilson C. ; Pereira, Filipe ; Tandon, Amit ( July 2023 , Journal of Physical Oceanography)

   Abstract The western boundary current system off southeastern Brazil is composed of the poleward-flowing Brazil Current (BC) in the upper 300 m and the equatorward flowing Intermediate Western Boundary Current (IWBC) underneath it, forming a first-baroclinic mode structure in the mean. Between 22° and 23°S, the BC-IWBC jet develops recurrent cyclonic meanders that grow quasi-stationarily via baroclinic instability, though their triggering mechanisms are not yet well understood. Our study, thus, aims to propose a mechanism that could initiate the formation of these mesoscale eddies by adding the submesoscale component to the hydrodynamic scenario. To address this, we perform a regional 1/50° (∼2 km) resolution numerical simulation using CROCO (Coastal and Regional Ocean Community model). Our results indicate that incoming anticyclones reach the slope upstream of separation regions and generate barotropic instability that can trigger the meanders’ formation. Subsequently, this process generates submesoscale cyclones that contribute, along with baroclinic instability, to the meanders’ growth, resulting in a submesoscale-to-mesoscale inverse cascade. Last, as the mesoscale cyclones grow, they interact with the slope, generating inertially and symmetrically unstable anticyclonic submesoscale vortices and filaments. Significance Statement Off southeastern Brazil, the Brazil Current develops recurrent cyclonic meanders. Such meanders enhance the open-ocean primary productivity and are of societal importance as they are located in a region rich in oil and gas where oil-spill accidents have already happened. This study aims to explore the processes responsible for triggering the formation of these mesoscale eddies. We find that incoming anticyclones reach the slope upstream of separation regions and generate barotropic instabilities that eject submesoscale filaments and vortices and can trigger the meanders’ formation. Such results show that topographically generated submesoscale instabilities can play an important role in the dynamics of mesoscale meanders off southeastern Brazil. Moreover, this may indicate that resolving the submesoscale dynamics in operational numerical models may contribute to an increase in the predictability of the regional eddies. 

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4. Non-ideal instabilities in sinusoidal shear flows with a streamwise magnetic field

   https://doi.org/10.1017/jfm.2022.782  

   Fraser, A.E. ; Cresswell, I.G. ; Garaud, P. ( October 2022 , Journal of Fluid Mechanics)

   We investigate the linear stability of a sinusoidal shear flow with an initially uniform streamwise magnetic field in the framework of incompressible magnetohydrodynamics (MHD) with finite resistivity and viscosity. This flow is known to be unstable to the Kelvin–Helmholtz instability in the hydrodynamic case. The same is true in ideal MHD, where dissipation is neglected, provided the magnetic field strength does not exceed a critical threshold beyond which magnetic tension stabilizes the flow. Here, we demonstrate that including viscosity and resistivity introduces two new modes of instability. One of these modes, which we refer to as an Alfvénic Dubrulle–Frisch instability, exists for any non-zero magnetic field strength as long as the magnetic Prandtl number ${{{Pm}}} < 1$ . We present a reduced model for this instability that reveals its excitation mechanism to be the negative eddy viscosity of periodic shear flows described by Dubrulle & Frisch ( Phys. Rev. A, vol. 43, 1991, pp. 5355–5364). Finally, we demonstrate numerically that this mode saturates in a quasi-stationary state dominated by counter-propagating solitons. 

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5. Shear Instabilities and Stratified Turbulence in an Estuarine Fluid Mud

   https://doi.org/10.1175/JPO-D-21-0230.1  

   Tu, Junbiao ; Fan, Daidu ; Sun, Feixiang ; Kaminski, Alexis ; Smyth, William ( September 2022 , Journal of Physical Oceanography)

   Abstract This study presents field observations of fluid mud and the flow instabilities that result from the interaction between mud-induced density stratification and current shear. Data collected by shipborne and bottom-mounted instruments in a hyperturbid estuarine tidal channel reveal the details of turbulent sheared layers in the fluid mud that persist throughout the tidal cycle. Shear instabilities form during periods of intense shear and strong mud-induced stratification, particularly with gradient Richardson number smaller than or fluctuating around the critical value of 0.25. Turbulent mixing plays a significant role in the vertical entrainment of fine sediment over the tidal cycle. The vertical extent of the billows identified seen in the acoustic images is the basis for two useful parameterizations. First, the aspect ratio (billow height/wavelength) is indicative of the initial Richardson number that characterizes the shear flow from which the billows grew. Second, we describe a scaling for the turbulent dissipation rate ε that holds for both observed and simulated Kelvin–Helmholtz billows. Estimates for the present observations imply, however, that billows growing on a lutocline obey an altered scaling whose origin remains to be explained. 

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