Interaction between upper-ocean submesoscale currents and convective turbulence

The interaction between upper-ocean submesoscale fronts evolving with coherent features, such as vortex filaments and eddies, and finescale convective turbulence generated by surface cooling of varying magnitude is investigated. While convection is energized by gravitational instability, predominantly at the finescale (FS), which feeds off the potential energy that is input through cooling, the submesoscale (SMS) is energized at larger scales by the release of available potential energy stored in the front. Here, we decompose the flow into FS and SMS fields explicitly to investigate the energy pathways and the strong interaction between them. Overall, the SMS is energized due to surface cooling. The frontogenetic tendency at the submesoscale increases, which counters the enhanced horizontal diffusion by convection-induced turbulence. Downwelling/upwelling strengthens, and the peak SMS vertical buoyancy flux increases as surface cooling is increased. Furthermore, the production of FS energy by SMS velocity gradients is significant, up to half of the production by convection. Examination of potential vorticity reveals that surface cooling promotes higher levels of secondary symmetric instability, which coexists with the persistent baroclinic instability.

Diffusive effects in local instabilities of a baroclinic axisymmetric vortex

We present a local stability analysis of an idealized model of the stratified vortices that appear in geophysical settings. The base flow comprises an axisymmetric vortex with background rotation and an out-of-plane stable stratification, and a radial stratification in the thermal wind balance with the out-of-plane momentum gradient. Solving the local stability equations along fluid particle trajectories in the base flow, the dependence of short-wavelength instabilities on the Schmidt number $Sc$ (ratio between momentum and mass diffusivities) is studied, in the presence of curvature effects. In the diffusion-free limit, the well-known symmetric instability is recovered. In the viscous, double-diffusive regime, instability characteristics are shown to depend on three non-dimensional parameters (including $Sc$ ), and two different instabilities are identified: (i) a monotonic instability (same as symmetric instability at $Sc = 1$ ), and (ii) an oscillatory instability (absent at $Sc = 1$ ). Separating the base flow and perturbation characteristics, two each of base flow and perturbation parameters (apart from $Sc$ ) are identified, and the entire parameter space is explored for the aforementioned instabilities. In comparison with $Sc = 1$ , monotonic and oscillatory instabilities are shown to significantly expand the instability region in the space of base flow parameters as $Sc$ moves away from unity. Neutral stability boundaries on the plane of $Sc$ and a modified gradient Richardson number are then identified for both these instabilities. In the absence of curvature effects, our results are shown to be consistent with previous studies based on normal mode analysis, thus establishing that the local stability approach is well suited to capturing symmetric and double-diffusive instabilities. The paper concludes with a discussion of curvature effects, and the likelihood of monotonic and oscillatory instabilities in typical oceanic settings.

The influence of front strength on the development and equilibration of symmetric instability. Part 1. Growth and saturation

Submesoscale fronts with large horizontal 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. Here, we use a weakly nonlinear stability analysis to study SI in an idealised frontal zone with a uniform horizontal buoyancy gradient in thermal wind balance. We find that the structure and energetics of SI strongly depend on the front strength, defined as the ratio of the horizontal buoyancy gradient to the square of the Coriolis frequency. Vertically bounded non-hydrostatic SI modes can grow by extracting potential or kinetic energy from the balanced front and the relative importance of these energy reservoirs depends on the front strength and vertical stratification. We describe two limiting behaviours as ‘slantwise convection’ and ‘slantwise inertial instability’ where the largest energy source is the buoyancy flux and geostrophic shear production, respectively. The growing linear SI modes eventually break down through a secondary shear instability, and in the process transport considerable geostrophic momentum. The resulting breakdown of thermal wind balance generates vertically sheared inertial oscillations and we estimate the amplitude of these oscillations from the stability analysis. We finally discuss broader implications of these results in the context of current parameterisations of SI.

The influence of front strength on the development and equilibration of symmetric instability. Part 2. Nonlinear evolution

In Part 1 (Wienkers, Thomas & Taylor, J. Fluid Mech., vol. 926, 2021, A6), we described the theory for linear growth and weakly nonlinear saturation of symmetric instability (SI) in the Eady model representing a broad frontal zone. There, we found that both the fraction of the balanced thermal wind mixed down by SI and the primary source of energy are strongly dependent on the front strength, defined as the ratio of the horizontal buoyancy gradient to the square of the Coriolis frequency. Strong fronts with steep isopycnals develop a flavour of SI we call ‘slantwise inertial instability’ by extracting kinetic energy from the background flow and rapidly mixing down the thermal wind profile. In contrast, weak fronts extract more potential energy from the background density profile, which results in ‘slantwise convection.’ Here, we extend the theory from Part 1 using nonlinear numerical simulations to focus on the adjustment of the front following saturation of SI. We find that the details of adjustment and amplitude of the induced inertial oscillations depend on the front strength. While weak fronts develop narrow frontlets and excite small-amplitude vertically sheared inertial oscillations, stronger fronts generate large inertial oscillations and produce bore-like gravity currents that propagate along the top and bottom boundaries. The turbulent dissipation rate in these strong fronts is large, highly intermittent and intensifies during periods of weak stratification. We describe each of these mechanisms and energy pathways as the front evolves towards the final adjusted state, and in particular focus on the effect of varying the dimensionless front strength.

Symmetric Instability in Cross-Equatorial Western Boundary Currents

The upper limb of the Atlantic meridional overturning circulation draws waters with negative potential vorticity from the Southern Hemisphere into the Northern Hemisphere. The North Brazil Current is one of the cross-equatorial pathways in which this occurs: upon crossing the equator, fluid parcels must modify their potential vorticity to render them stable to symmetric instability and to merge smoothly with the ocean interior. In this work a linear stability analysis is performed on an idealized western boundary current, dynamically similar to the North Brazil Current, to identify features that are indicative of symmetric instability. Simple two-dimensional numerical models are used to verify the results of the stability analysis. The two-dimensional models and linear stability theory show that symmetric instability in meridional flows does not change when the nontraditional component of the Coriolis force is included, unlike in zonal flows. Idealized three-dimensional numerical models show anticyclonic barotropic eddies being spun off as the western boundary current crosses the equator. These eddies become symmetrically unstable a few degrees north of the equator, and their PV is set to zero through the action of the instability. The instability is found to have a clear fingerprint in the spatial Fourier transform of the vertical kinetic energy. An analysis of the water mass formation rates suggest that symmetric instability has a minimal effect on water mass transformation in the model calculations; however, this may be the result of unresolved dynamics, such as secondary Kelvin–Helmholtz instabilities, which are important in diabatic transformation.

Wind-Forced Submesoscale Symmetric Instability around Deep Convection in the Northwestern Mediterranean Sea

During the winter from 2009 to 2013, the mixed layer reached the seafloor at about 2500 m in the northwestern Mediterranean Sea. Intense fronts around the deep convection area were repeatedly sampled by autonomous gliders. Subduction down to 200–300 m, sometimes deeper, below the mixed layer was regularly observed testifying of important frontal vertical movements. Potential Vorticity dynamics was diagnosed using glider observations and a high resolution realistic model at 1-km resolution. During down-front wind events in winter, remarkable layers of negative PV were observed in the upper 100 m on the dense side of fronts surrounding the deep convection area and successfully reproduced by the numerical model. Under such conditions, symmetric instability can grow and overturn water along isopycnals within typically 1–5 km cross-frontal slanted cells. Two important hotpspots for the destruction of PV along the topographically-steered Northern Current undergoing frequent down-front winds have been identified in the western part of Gulf of Lion and Ligurian Sea. Fronts were there symmetrically unstable for up to 30 days per winter in the model, whereas localized instability events were found in the open sea, mostly influenced by mesoscale variability. The associated vertical circulations also had an important signature on oxygen and fluorescence, highlighting their under important role for the ventilation of intermediate layers, phytoplankton growth and carbon export.

The scale and activity of symmetric instability estimated from a global submesoscale-permitting ocean model

Symmetric instability (SI) extracts kinetic energy from fronts in the surface mixed layer (SML), potentially affecting the SML structure and dynamics. Here, a global submesoscale-permitting ocean model named MITgcm LLC4320 simulation is used to examine the Stone (1966) linear prediction of the maximum SI scale to estimate grid spacings needed to begin resolving SI. Furthermore, potential effects of SI on the usable wind-work are estimated roughly: this estimate of SI “activity” is useful for assessing if these modes should be resolved or parameterized. The maximum SI scale varies by latitude with median values of 568 m to 23 m. Strong seasonality is observed in the SI scale and activity. The median scale in winter is 188 m globally, 2.5 times of that of summer (75 m). SI is more active in winter: 15% of the time compared with 6% in summer. The strongest SI activity is found in the western Pacific, western Atlantic, and Southern Oceans. The required grid spacings for a global model to begin resolving SI eddies in the SML are 24 m (50% of regions resolved) and 7.9 m (90%) in winter, decreasing to 9.4 m (50%) and 3.6 m (90%) in summer. It is also estimated that SI may reduce usable wind-work by an upper bound of 0.83 mW m−2 globally, or 5% of the global magnitude. The sensitivity of these estimates to empirical thresholds is provided in the text.

Wind-forced submesoscale symmetric instability around deep convection in the NW Mediterranean Sea

<p>During the winter from 2009 to 2013, the mixed layer reached the seafloor at about 2500m in the NW Mediterranean. Intense fronts around the deep convection area were repeatedly sampled by autonomous gliders, mainly as part of the MOOSE observatory of the NW Mediterrnean Sea (https://www.moose-network.fr/). Subduction down to 200-300m, sometimes deeper, below the mixed layer was regularly observed testifying of important frontal vertical movements. Potential Vorticity dynamics was diagnosed using glider observations and a high resolution realistic model at 1-km resolution (SYMPHONIE model, https://sirocco.obs-mip.fr/ocean-models/s-model/).</p><p>During down-front wind events in winter, remarkable layers of negative PV were observed in the upper 100m on the dense side of fronts surrounding the deep convection area and successfully reproduced by the numerical model. Under such conditions, symmetric instability can grow and overturn water along isopycnals within typically 1-5km cross-frontal slanted cells. Two important hotpspots for the destruction of PV along the topographically-steered Northern Current undergoing frequent down-front winds have been identified in the western part of Gulf of Lion and Ligurian Sea. Fronts were there symmetrically unstable for up to 30 days per winter in the model, whereas localized instability events were found in the open-sea, mostly influenced by mesoscale variability. The associated vertical circulations also had an important signature on oxygen and fluorescence, highlighting their under important role for the ventilation of intermediate layers, phytoplankton growth and carbon export.</p>