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Equilibration of symmetric instability and inertial oscillations at an idealised submesoscale front

Wienkers, Aaron F., Thomas L., & Taylor, J. R.
American Physical Society: Division of Fluid Dynamics, Seattle, WA, 2019
Publication year: 2019


Submesoscale fronts with large lateral buoyancy gradients and O(1) Rossby numbers are common in the upper ocean. These fronts are associated with large vertical transport and are hotspots for biological activity. Submesoscale fronts are susceptible to symmetric instability (SI) — a form of stratified inertial instability which can occur when the potential vorticity is of the opposite sign to the Coriolis parameter. Growing SI modes eventually break down through a secondary shear instability, leading to 3D turbulence and vertically mixing the geostrophic momentum. Once out of thermal wind balance, the front undergoes inertial oscillations which can drive further small-scale turbulence.

Here, we consider the idealised problem of a balanced front with uniform horizontal buoyancy gradient and bounded by flat no-stress horizontal surfaces. We study the equilibration of this unstable front using a linear stability analysis and 3D numerical simulations. We find drastically different behaviour emerging at late times. While weak fronts develop frontlets and excite subinertial oscillations, stronger fronts produce bore-like gravity currents. We describe the details of these energy pathways as the front evolves toward the final adjusted state in terms of the dimensionless front strength.

Nonlinear oscillations and zonal flows in turbulent eccentric astrophysical discs with vertical structure

Wienkers, Aaron F. & Ogilvie, G. I.
American Physical Society: Division of Fluid Dynamics, Denver, CO, 2017
Publication year: 2017


The classical theory of astrophysical discs (including Saturn’s rings, protoplanetary systems, and high-energy accretion discs around black holes) assumes circular orbital motion around a central mass. However, certain systems are known to contain eccentric forcing, necessitating a generaliza- tion to the shearing box model to include the oscillatory local geometry associated with this eccentricity. The hydrodynamic equations in this model are non-standard because of the use of time-dependent, non-orthogonal coordinates, and are known to lead to hydrodynamic instability involving the growth of internal waves. Here we present the results of the first ever local nonlinear simulations in an eccentric shearing box representing an elliptic disc with vertical structure. The nonlinear sat- uration of this parametric instability inherent to eccentric discs generates further self-regulating azimuthal zonal flows, and results in stable limit cycle behavior. We explore this energy pathway from the global eccentric mode into turbulence and finally the zonal flows, and discuss the viability of this instability to balance the eccentricity growth in systems exhibiting mean-motion orbital resonances such as the eccentric Lindblad resonance.

The role of interactions between waves and baroclinic critical layers in zombie vortex self-replication

Jiang, C. H., Wienkers, Aaron F., & Marcus, P. S. et al.
American Physical Society: Division of Fluid Dynamics, Pittsburgh, PA, 2013
Publication year: 2013


Inertio-gravity waves are triggered from various types of perturbations in numerical simulations of rotating, vertically-stratified and horizontal-shearing flows (Marcus et al. 2013 PRL). The interactions of these waves and baroclinic critical layers can create large vortices when the shear is sufficiently strong. An important feature of these flows is that an instability at one critical layer can excite an instability at its neighboring critical layers and spawn new generations of waves and vortices. Because the self- replication of these vortices in simulations of “dead zones” in protoplanetary disks reminds us of zombies multiplying by infecting each other, we call them “zombie vortices.” However, not all interactions between waves and critical layers produce zombie vortices. The manner in which one “infected” critical layer infects its neigh- bor is not clear. The interaction of waves and critical layers are sensitive to the local Brunt-Vaisala frequency and to the wavelengths of the waves. Here we discuss how the interactions and formation of vortices depend upon the Brunt-Vaisala frequency (including its change in value as a function of vertical position) and our progress in understanding how the instability passes from a critical layer to its neighbor.