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Turbulence in the Tachocline

Turbulence in the Tachocline. Mark Miesch HAO/NCAR. Tachocline Regimes. Howe et al 2000. Upper Tachocline Penetrative convection Lower Tachocline Stably-Stratified Shear Layer. Turbulence + Rotation. Turbulent Convection = Plumes!. Vorticity, Helicity Vortex interactions

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Turbulence in the Tachocline

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  1. Turbulence in the Tachocline Mark Miesch HAO/NCAR

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

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

  4. Turbulent Alignment Plumes are tilted toward the rotation axis

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

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

  7. Upper Convection Zone

  8. Overshoot Region

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

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

  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 Rhines Scale NL interactions Conserve Energy and Enstrophy

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

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

  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 Fr2 << Ro << 1 Nonlinear interactions conserve Energy and potential enstrophy Paradise Lost! QG theory doesn’t really apply for global-scale motions in spherical shells Alas! Metais et al 1996

  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) Ri = 0.2 • Horizontal Shear • Diffusive transport • Vertical Shear • Non-diffusive transport when the stratification is strong Ri = 2.0 Jacobitz 2004

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

  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?

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