1. The interplay between baroclinic instability, geostrophic turbulence and Rossby waves in the ocean John Marshall, MIT 1. Theoretical framework 2. Discuss altimetric observations 3. Insights from GFD experiments of ocean turbulence on an aqua-planet David Ferreira, Majid Mohammadian, MIT Ross Tulloch, Shafer Smith, Courant, NYU Tulloch, Marshall and Smith, JGR, 2009 1 2 3

3. Interplay of eddies and waves 1

4. Let’s do this on the sphere Equator 1.3 million point vortices Trajectories

5. Estimate observed ‘eddy’ speed relative to wave speed wavesturbulence Tulloch, Marshall and Smith, JGR, 2009

6. 1 st baroclinic mode structure Rms eddy speed from Maximenko surface drifters

7. Generalized ‘Rhines (1975)’ effect baroclinic instability ubiquitous on deformation scale upscale energy transfer if there is a matching of space and timescales then excitation of waves by turbulence can occur turbulenceWaves Idea has been applied to giant planets by Theiss, 2006 and Smith, 2006 barotropic model elaborated by Vallis and Maltrud, 1993 Working hypothesis: k

8. Resting ocean See, Chelton and collaborators e.g. Chelton and Schlax (1996) First baroclinic Rossby wave speed Killworth and Blundell (2003, 2005) Revisit Interpretation of altimetic observations 2

9. Linear theory Local quasi-geostrophic assumption … but allow for background shear and stratification Linearize about climatological state Boundary conditions Linear eigenvalue problem

10. Resting ocean Project on to normal modes

11. long wave limit Captures imprint of ACC Putting in mean currents and stratification

12. Pacific Global ‘fitted’ wave speed ‘fitted’ wave length

13. Eden estimates of eddy scale ‘fitted’ scale 1 st deformation radius Summary of spatial scales c.f. Karsten Eden, 2007: JGR

14. C24 3 GFD experiments of ocean turbulence on an aqua-planet (‘Double Drake’)

15. Ongoing work – not been digested………. C510 Forced by steady winds

16. Observed phase propagation

17. 25S 35S Vertical structure of eddies

18. QGPV gradient QGPV gradients ‘Steering level’ of propagating signals

19. Effective diffusivity of eddies Steering levels of most unstable waves from linear analysis

20. Mean zonal flow surface where & steering level Eddy-driven zonal jets

21. Zonal currents at depth of 900m

22. Tracer transport at 900m cf Frank Bryan, Pavel Berloff …

23. Depth Latitude Tropics Mid-latitudes

24. Intersection at 40 Zonal jets Back to point vortices

25. Eddy scales

26. Conclusions baroclinic instability ubiquitous on deformation scale upscale energy transfer if there is a matching of space and timescales then excitation of waves by turbulence can occur A key parameter is waves turbulence Eddy scales like in turbulent regime In wave regime 1 2 3 5 Mixing is enhanced at steering levels (close to PV gradient reversals) which are deep in eastward jets and shallow in westward jets: broadly consistent with Charney/Phillips baroclinic instability considerations. 4 where is the Eady growth rate, is a good idea But…

27. Effective diffusivity in eddying models constrained by data (ECCO) 100m axis of ACC contours colors