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The influence of symmetric and inertial instabilities on the evolution of oceanic fronts

Conference
Wienkers, Aaron F. & Taylor, J. R.
American Physical Society: Division of Fluid Dynamics, Chicago, IL / Virtual
Publication year: 2020

Abstract

Isolated fronts with large lateral density gradients in geostrophic and hydrostatic balance are common in the upper ocean. Such strong fronts may be the result of baroclinic frontogenesis or of sharp freshwater interfaces as are found in the northern Gulf of Mexico near the Mississippi-Atchafalaya river plume. These fronts may be unstable to symmetric or inertial instabilities which further enhance small-scale mixing and encourage vertical transport between the surface and the abyss. Here, we consider the problem of an initially balanced front of finite width and which is bounded by flat no-stress horizontal surfaces. We examine how the evolution and equilibration depends on the front strength and aspect ratio using nonlinear numerical simulations, and develop a model to predict the profile and effective width of the final equilibrated state in the absence of external forcing. While fronts with 𝑅𝑜>2.6 collapse to a self-similar profile dependent only on the deformation radius, we find that for small enough 𝑅𝑜<1, frontlets form as the front equilibrates. These frontlets increase both the kinetic and potential energy of the final balanced state, but are also found to interact with the boundaries if the front exhibits inertial oscillations.

Equilibration of symmetric instability and inertial oscillations at a finite-width submesoscale front

Conference
Wienkers, Aaron F., Thomas L., & Taylor, J. R.
American Geophysical Union: Ocean Sciences, San Diego, CA
Publication year: 2020

Abstract

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. The growing linear SI modes eventually break down through a secondary shear instability, leading to three-dimensional 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 problem of an initially balanced front with a horizontal buoyancy gradient of finite width and bounded by flat no-stress horizontal surfaces. We study the evolution to equilibration of this symmetrically-unstable front using a linear stability analysis and three-dimensional nonlinear numerical simulations. We find drastically different behaviour emerging at late times depending on the strength and width of the front. While weak fronts develop frontlets and excite subinertial oscillations, stronger fronts produce bore-like gravity currents that propagate along the top and bottom boundaries. Although the instantaneous turbulent dissipation rate can be much larger in these strong fronts, the turbulence is intermittent and peaks during periods of weak stratification. We explain the energetics as the front evolves towards the final adjusted state in terms of the dimensionless front strength and aspect ratio.

Transport and evolution of symmetric instability in an unstratified layer

Conference
Wienkers, Aaron F., Thomas L., & Taylor, J. R.
American Meteorological Society: Atmospheric and Oceanic Fluid Dynamics, Portland, ME
Publication year: 2019

Abstract

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 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. SI has linear eigenmodes which are capable of transporting buoyancy and geostrophic momentum. The unstable SI modes eventually break down through a secondary shear instability, leading to three-dimensional turbulence which further modifies the geostrophic momentum. An initially balanced front that is unstable to SI will evolve due to the momentum and buoyancy transport associated with SI and 3D turbulence.
Here, we consider an idealised problem with a front of finite width bounded by flat no-stress horizontal surfaces. The front is initially in thermal wind balance but there is no initial vertical stratification and the flow is unstable to SI. We study the evolution of the unstable front using a linear stability analysis and nonlinear numerical simulations. We find that the aspect ratio of the front and the ratio of the maximum horizontal buoyancy gradient to the Coriolis frequency are important parameters and influence the evolution of the front. Interesting behaviour emerges, particularly for fronts with large Rossby numbers. For example, fronts with relatively large horizontal density gradients develop bore-like gravity currents that propagate along the top and bottom boundaries. We then describe the final adjusted state in terms of the dimensionless parameters of the system.

The late-time evolution of an isolated symmetrically unstable front

Conference
Wienkers, Aaron F. & Taylor, J. R.
UK Fluids Conference, Cambridge, UK
Publication year: 2019

Abstract

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. SI has linear eigenmodes which are capable of transporting buoyancy and geostrophic momentum. The unstable SI modes eventually break down through a secondary shear instability, leading to three-dimensional turbulence which further modifies the geostrophic momentum. An initially balanced front that is unstable to SI will evolve due to the momentum and buoyancy transport associated with SI and 3D turbulence.

Here, we consider an idealised problem with a front of finite width bounded by flat no-stress horizontal surfaces. The front is initially in thermal wind balance but there is no initial vertical stratification and the flow is unstable to SI. We study the evolution of the unstable front using a linear stability analysis and nonlinear numerical simulations. We find that the aspect ratio of the front and the ratio of the maximum horizontal buoyancy gradient to the Coriolis frequency are important parameters and influence the evolution of the front. Interesting behaviour emerges, particularly for fronts with large Rossby numbers. For example, fronts with relatively large horizontal density gradients develop bore-like gravity currents that propagate along the top and bottom boundaries. We then describe the energetics evolving towards the final adjusted state in terms of the dimensionless parameters of the system and understand these results in the context of the primary and secondary linear instability.

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

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

Abstract

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

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

Abstract

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

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

Abstract

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.