Turbulence in the Tachocline Mark Miesch HAONCAR Tachocline
Turbulence in the Tachocline Mark Miesch HAO/NCAR
Tachocline Regimes Upper Tachocline Penetrative convection Lower Tachocline Stably-Stratified Shear Layer Turbulence + Rotation Howe et al 2000
Turbulent Convection = Plumes! • Vorticity, Helicity • Vortex interactions • Entrainment • Penetration Julien et al 1996
Turbulent Alignment Plumes are tilted toward the rotation axis
Plumes in Global-Scale Convection Radial Velocity, Upper CZ Temperature, Mid CZ Miesch, Brun & Toomre
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)
Upper Convection Zone
Overshoot Region
Meridional Circulation Large fluctuations, but equatorward on average in the lower convection zone 72 -day average
Angular Momentum Transport Convection Zone Overshoot Region And Radiative Interior
Rotation Profile Fast poles: Overshoot too deep?
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 & De. Luca 1989
Turbulence in the Lower Tachocline • Drivers w Penetrative Convection (+ breaking waves) w Instabilities • Rotation w Vertical coherence (vortex columns) • Stratification w Horizontal layering (pancakes) • Shear w Alters nonlinear interactions w Gravity wave filtering Quasi-2 D?
2 D, Rotating Turbulence Vallis & Maltrud 1993 Rhines Scale NL interactions Conserve Energy and Enstrophy
2 D Turbulence on a Rotating Sphere Jets! Asymmetric halting of inverse cascade yields persistent, banded zonal flows Huang & Robinson 1998
PV Homogenization in retrograde jets Retrograde jets Mix PV Retrograde jets preferred at high latitudes Huang & Robinson 1998
Peltier & Stuhne 2000 Does this really happen in 3 D? It does in 2. 5 D! Shallow water and two-layer systems exhibit similar phenomena Decaying or High-wavenumber forcing
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!
3 D Stratified Turbulence • Decomposition w vortex, gravity wave • Interaction with background shear w Diffusive? § Turbulence is driven by shear § Homogeneous, isotropic, small-scale forcing • Scale separation, local mixing w Non-Diffusive? § Waves (non-local)
Decaying Turbulence with Vertical Shear Non-Diffusive Transport! Galmiche et al 2002
Shear-Driven Turbulence (non-rotating) Ri = 0. 2 • Horizontal Shear w Diffusive transport • Vertical Shear Ri = 2. 0 w Non-diffusive transport when the stratification is strong Jacobitz 2004
Randomly-Forced Turbulence 3 D, Rotating, Stratified Little indication for an inverse cascade or zonal bands
Interaction with Shear Diffusive latitudinal transport non-diffusive vertical transport
Conclusion • Upper tachocline w Convective plumes w Equatorward circulation w Poleward angular momentum transport • Lower tachocline w Banded zonal flows? w Diffusive transport in horizontal? w Non-Diffusive transport in vertical? • Radiative Interior w Long-range, non-diffusive wave transport w Rigidity imposed by fossil field? w Turbulence?
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