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Fronts with large horizontal density gradients and O(1) Rossby numbers are common in the upper ocean. Such fronts develop through a variety of mechanisms including by mesoscale eddy strains, coastal upwelling, or the input of freshwater via river discharge. These fronts may be unstable to symmetric instability — a form of convective-inertial instability which occurs when the potential vorticity is of opposite sign to the Coriolis param- eter. Symmetric instability is characterised by growing slantwise convection cells aligned with isopycnals and which encourage vertical transport of important biogeochemical tracers in addition to geostrophic momentum. We previously found that this momentum transport destabilises the balanced thermal wind and can prompt geostrophic adjustment which often leaves remnant inertial oscillations (Wienkers et al., 2021a,b).

Here we consider the equilibration of an initially balanced but symmetrically unstable front and explore the parameter space of front strength and Rossby number using theory & nonlinear numerical simulations. 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, self-similar frontlets form during equilibration. These frontlets increase the energy of the equilibrated state and can interact with the near-surface currents to further enhance mixing. We finally propose a scaling model for the incurred diabatic mixing and to describe the ultimate state of the front compared to the classical (i.e. inviscid, adiabatic, & 0-PV) adjustment theory of Ou (1984).

Fronts with large lateral density gradients in geostrophic and hydrostatic balance are common in the upper ocean. Such strong fronts develop through a variety of mechanisms including frontogenesis forced by mesoscale eddies, coastal upwelling, and the input of freshwater via river discharge. These fronts may be unstable to symmetric instability (SI) — a form of stratified inertial instability which occurs when the potential vorticity is of opposite sign to the Coriolis parameter. SI encourages vertical transport of biogeochemical tracers as well as of geostrophic momentum. We previously found that this momentum transport destabilises the balanced thermal wind which further enhances small-scale turbulent mixing and often leaves remnant inertial oscillations.

Here, we consider the equilibration of an initially balanced front of finite width and which is bounded by flat no-stress horizontal surfaces. We examine how the adjustment depends on the aspect ratio and strength of the front using nonlinear numerical simulations, and develop a model to predict the resultant mixing and the energy in the final equilibrated state. 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 the kinetic and potential energy of the equilibrated state and interact with the near-surface currents if the front exhibits inertial oscillations.

Conference

American Physical Society: Division of Fluid Dynamics, Chicago, IL / Virtual

Publication year: 2020

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.

Conference

American Meteorological Society: Atmospheric and Oceanic Fluid Dynamics, Portland, ME

Publication year: 2019

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.

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.

Conference

American Physical Society: Division of Fluid Dynamics, Seattle, WA

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.

Conference

American Physical Society: Division of Fluid Dynamics, Pittsburgh, PA

Publication year: 2013