1. Turbulence in the Tachocline Mark Miesch HAO/NCAR

2. Upper Tachocline Penetrative convection Lower Tachocline Stably-Stratified Shear Layer Howe et al 2000 Tachocline Regimes Turbulence + Rotation

3. Turbulent Convection = Plumes! Julien et al 1996 Vorticity, Helicity Vortex interactions Entrainment Penetration

4. Turbulent Alignment Plumes are tilted toward the rotation axis

5. Plumes in Global-Scale Convection Temperature, Mid CZ Miesch, Brun & Toomre Radial Velocity, Upper CZ

6. Turbulent Alignment in a Spherical Shell Converging flow, Cyclonic Vorticity Negative Helicity (N) Diverging flow Anticyclonic Vorticity Positive Helicity (N) Tilted Plumes induce Equatorward Circulation, Poleward Angular Momentum Transport At high and mid-latitudes in the overshoot region

7. Upper Convection Zone

8. Overshoot Region

9. Meridional Circulation 72-day average Large fluctuations, but equatorward on average in the lower convection zone

10. Angular Momentum Transport Convection Zone Overshoot Region And Radiative Interior

11. Rotation Profile Fast poles: Overshoot too deep?

12. Turbulence in the Upper Tachocline: Summary Convective Plumes Asymmetric (downflows) Intermittent Turbulent alignment Horizontal divergence Anticyclonic vorticity Equatorward circulation Poleward angular momentum transport Gilman, Morrow & DeLuca 1989

13. Turbulence in the Lower Tachocline Drivers  Penetrative Convection (+ breaking waves)  Instabilities Rotation  Vertical coherence (vortex columns) Stratification  Horizontal layering (pancakes) Shear  Alters nonlinear interactions  Gravity wave filtering Quasi-2D?

14. 2D, Rotating Turbulence Vallis & Maltrud 1993 NL interactions Conserve Energy and Enstrophy Rhines Scale

15. 2D Turbulence on a Rotating Sphere Huang & Robinson 1998 Jets! Asymmetric halting of inverse cascade yields persistent, banded zonal flows

16. PV Homogenization in retrograde jets Huang & Robinson 1998 Retrograde jets Mix PV Retrograde jets preferred at high latitudes

17. Does this really happen in 3D? It does in 2.5D! Shallow water and two-layer systems exhibit similar phenomena Decaying or High-wavenumber forcing Peltier & Stuhne 2000

18. Paradise Regained! (if you’re particularly fond of inverse cascades) QG Limit Fr 2 << Ro << 1 Nonlinear interactions conserve Energy and potential enstrophy Metais et al 1996 Paradise Lost! QG theory doesn’t really apply for global-scale motions in spherical shells Alas!

19. 3D Stratified Turbulence Decomposition  vortex, gravity wave Interaction with background shear  Diffusive?  Turbulence is driven by shear  Homogeneous, isotropic, small-scale forcing Scale separation, local mixing  Non-Diffusive?  Waves (non-local)

20. Decaying Turbulence with Vertical Shear Non-Diffusive Transport! Galmiche et al 2002

21. Shear-Driven Turbulence (non-rotating) Jacobitz 2004 Ri = 0.2 Ri = 2.0 Horizontal Shear  Diffusive transport Vertical Shear  Non-diffusive transport when the stratification is strong

22. Randomly-Forced Turbulence Little indication for an inverse cascade or zonal bands 3D, Rotating, Stratified

23. Interaction with Shear Diffusive latitudinal transport non-diffusive vertical transport

24. Conclusion Upper tachocline  Convective plumes  Equatorward circulation  Poleward angular momentum transport Lower tachocline  Banded zonal flows?  Diffusive transport in horizontal?  Non-Diffusive transport in vertical? Radiative Interior  Long-range, non-diffusive wave transport  Rigidity imposed by fossil field?  Turbulence?