Submesoscale for dummies: a journey in the world of frontal kilometer scale

turbulence

X. Capet J. McWilliams, J. Molemaker, A. Shchepetkin (UCLA)

P. Klein, B.L.Hua (LPO/Ifremer)A. Paiva (UFRJ), E. Campos (USP)

Grenoble, October 6th 2008

Mesoscale activity in the ocean

SST off the east coast of the US Chlorophyll off eastern Australia

There is a natural length scale (the deformation radius) in stratified rotating fluids that will condition energy distribution and hence tracer appearance.

Tracer field and steepness of the kinetic energy spectrum below the mesoscale (1)

In classical quasi-geostrophic turbulence, -3 or steeper KE slope. Submesoscale tracer features result from stirring by the mesoscale activity (ie., dominated by nonlocal processes in the wavenumber space).

submesoscale phenomenology: fronts, filaments and meanders

There seems to be more submesoscale KE in the real ocean near the surface, as suggested by tracer patterns. Recent estimates of the surface KE spectrum based on altimetry suggest a -5/3 slope

What ROMS has to say (1) ?

Increasing KE with resolution.

Slope around -2 at highest resolution

Idealized California Current at various horizontal resolutions (12km, 6km, 3km, 1.5km, 750m). Flat bottom, straight coastline. OBC from 12km idealized USWC Atmospheric forcing spatially smooth and fixed in time (summer).

What ROMS has to say (2) ?

Slope around -2 at highest resolution

Idealized Antarctic circumpolar current at 2 km resolution (Klein et al, 2008).

What ROMS has to say (3) ?

Over shelves, mesoscale is absent.

Tracer fields and spectra reveal

variability in submesocale activitity

(on seasonal scales in solutions

forced with climatological forcing).

Realistic Argentinian shelf at 400 m resolution. OBC from 2 km resolution configuration for the Brazil/Malvinas confluence.

fall SST spring SST

Tracer field and steepness of the kinetic energy spectrum below the mesoscale (2)

In surface quasi-geostrophic turbulence, shallower surface KE slope (-5/3). There is substantial energy at submesoscale that affects the tracer appearance. The leading process in SQG is frontogenesis.

Frontogenesis: Shear Term

Thermal wind balance tends to destroy itself. It is maintained through ageostrophic secondary circulation (ASC). The ASC tends to restratify the fluid where density gradients are being intensified.

Frontogenesis: Confluence Term

Near-surface specificity: frontogenesis (1)

Near-surface specificity: frontogenesis (2)

In the interior, vertical velocities can develop as part of ASCs that can effectively check gradient intensification.

At the surface, w=0 so that ASCs cannot prevent horizontal convergence from driving frontogenesis.

Near-surface specificity: frontogenesis (3)

In QG the tracer is advected by geostrophic velocities only. Slow frontogenetic rate. Symmetry about the front axis.

In PE, ASCs contribute to tracer advection reduced convergence on the warm- -anticyclonic-ascending side, enhanced convergence on the cold-cyclonic-descending side.

Near-surface specificity: frontogenesis (4)

Near surface exhibit the signature of ASCs. At horizontal resolution O(1 km) frontal strength is mainly controlled by diffusion. The cross-front length scale is often a few grid points.

at 10m depth

submesoscale instabilities (1)

Submesoscale instabilities (2)

Frontal instability:- confined in the near-surface (the mixed layer when there is one). - wavelength in the range 5-20km- essentially baroclinic, ie, KE source for the perturbation is predominantly through wb.

- in the presence of large-scale strain, wavelength decreases and growth rate increases (McWilliams et al, 2008).

Submesoscale instabilities (3)

Most favorable conditions for frontal instability development are: - a deep mixed layer- large density gradients

Precisely, <wb> should scale like Hbl

2 < (Fox-Kemper et al, 2008)

Submesoscale modulation by the mesoscale

Submesoscale outbreak occurs at the edge of the eddies where strain is most important (and dominates over rotation).

sea level

strain ratevertical vorticity

Vertical length scale for submesoscale activity

Varies with the system stratification. ICC with marked shallow thermocline → submesoscale mostly confined to the mixed layer. ACC with deep diffuse thermocline → submesoscale effective at depth below 200m

Degree of imbalance

Solutions with meshgrid size O(1 km) are still mostly balanced.

Divergent part of the velocities are important because they are responsible for a forward flux of energy that intensifies as resolution is increased.

Role of the submesoscale (1)

- Restratification and vertical tracer flux in general- Lateral tracer flux- Energy dissipation

ICC0 ICC6

Role of the submesoscale (2)

- Restratification and vertical tracer flux in general

- Lateral tracer flux- Energy dissipation

Submesoscale turbulence mixes density laterally. Efficiency is small compared to that of mesoscale turbulence. Over shelves it is nonetheless significant.

Conclusion

Surface submesoscale energy levels in PE solutions and in the real ocean higher than predicted by classical QG. The key process that energizes submesoscale is frontogenesis but submesoscale phenomenology includes submesoscale instabilities (mixed-layer baroclinic instability, shear instability, symmetric instability, convective instability), submesoscale eddies (“spiral eddies”), SQG filament instability.

Small-scale vorticity patterns combined with wind forcing yield additional effects (Ekman ASCs, PV modification, “wind ringing”).

Remaining questions about (mechanisms responsible for frontal arrest ? KE slope convergence ? ...)

3- The analogy with Surface Quasi-Geostrophic Systems 3- The analogy with Surface Quasi-Geostrophic Systems

The whole system evolution is slaved to the evolution of the surface tracer:Frontogenesis (weak) is the main dynamical element.

SQG (and higher order surface dynamics) lead to energetic submesoscale structures.

512

1024

2048

k-5/3

Surface KE spectrum

3- The analogy with Surface Quasi-Geostrophic Systems 3- The analogy with Surface Quasi-Geostrophic Systems

At this point, the main similarity with ICC0 is the KE spectrum shape and its dependency in the vertical. The SQG+1 (Hakim et al, 2002) allows to explain the restratification effect and the skewness of vorticity and vertical velocity and also probably intensified the frontogenesis.

3- The analogy with Surface Quasi-Geostrophic Systems 3- The analogy with Surface Quasi-Geostrophic Systems

Frontal instability of a density front

We get PKm >> PKe and KmKe never the dominant term for perturbation growth (sometimes negative).

u*

v*

w

Imbalance in the vicinity of fronts

Gradient wind balance relationship:

Departure from gradient wind balance:

Submesoscale in the mixed layer: the associated direct energy cascade

How is the underlying energy budget changed (in spectral space) ?

Submesoscale in the mixed layer: the associated direct energy cascade

Submesoscale in the mixed layer: the associated direct energy cascade

3- Mechanisms: origin of negative PV ?

Buoyancy forcing: heat flux is stabilizing here1- atmospheric heat flux will be a source of positive PV 2- there can only be rearrangements inside the fluid

Friction forces: a priori when the wind blows downfront.

The end