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The Problem

Geostrophic turbulence on a b -plane: a laboratory investigation of “How the planets got their stripes…”. Oxford University (UK): Peter Read , Stephen Lewis, Hiro Yamazaki, Kuniko Yamazaki, Paul Williams, Robin Wordsworth LEGI/Grenoble: Joel Sommeria, Henri Didelle, Adam Fincham

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The Problem

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  1. Geostrophic turbulence on a b-plane: a laboratory investigation of “How the planets got their stripes…” Oxford University (UK):Peter Read, Stephen Lewis, Hiro Yamazaki, Kuniko Yamazaki, Paul Williams, Robin Wordsworth LEGI/Grenoble: Joel Sommeria, Henri Didelle, Adam Fincham Support: EC HCMR Programme (HYDRALAB)

  2. The Problem • Zonally anisotropic flows observed on the outer planets (Jupiter, Saturn, Neptune….) • Intense, barotropic(?) and very stable • ‘Zonation’ in the terrestrial oceans…? • ‘Eddy-resolving’ models • Satellite observations…? • Origin of anisotropic organisation of flow? - geostrophic turbulence on a b-plane? - deep or shallow? - what determines preferred scales - LR, Lb...? • Evidence in idealised numerical models …e.g.Chekhlov et al. 1996 and ff? • Laboratory experiments….? EGU 2005 Vienna

  3. Jovian Jets • b - uyy < 0 in easterly jets • Barotropically unstable…? • Need to take into account full PV…? Cassini ISS winds (Porco et al. 2003) EGU 2005 Vienna

  4. Zonation in the Ocean Global Ocean (Satellite Observations) Pacific Ocean (OCCAM model) (Maximenko et al. (2005) From Andrew Coward (SOC) EGU 2005 Vienna

  5. Schematic “Rhines Effect” Anisotropic (nonlocal) Zonal cascade EGU 2005 Vienna

  6. Anisotropic KE spectraGalperin & Sukoriansky (2001,2002…) • Accumulation of energy along ky axis • cKe2/3k-5/3 spectrum in almost all directions • czb2k-5 spectrum representing anisotropic inverse energy cascade along ky axis for k < kb…? [cz ~ 0.5] EGU 2005 Vienna

  7. Conditions for anisotropic geostrophic turbulence (Galperin 2005) • Anisotropic energy transfer (into zonal flow) • Stabilisation of zonal flow by b-effect • Forcing must be on scales unaffected by b-effect (v. small) • kb/kfr extends over > half decade • Sufficient for existence of an inertial range • Dissipation sufficient to suppress enstrophy subrange EGU 2005 Vienna

  8. Comparison of zonal and residual spectra in the ocean, giant planets and computer simulations (Galperin & Sukoriansky 2001-2004) EGU 2005 Vienna

  9. Experimental Requirements • Horizontal scale L > Lb ~ (U/b)1/2 • Reynolds number UL/n > 103 • Suitable forcing on a small scale (<< L) - preferably not fixed in space… • Rapid rotation (small Rossby number) ß LARGE-SCALE EXPERIMENT EGU 2005 Vienna

  10. Coriolis Laboratory (Grenoble) • Largest rotating fluids facility • 13 m dia. cylindrical tank • Up to 1 m deep • Rotation to 40s period (2W </= p/10 rad s-1) • Equipped for CIV and various measurement systems (profilers etc.) EGU 2005 Vienna

  11. Experimental configuration Free upper surface Water layer Slope ~ 5 - 6o LRext~ 5 - 7 m LRint~ 0.1 m Lb > 1 - 2 m EGU 2005 Vienna

  12. Experimental configuration EGU 2005 Vienna

  13. Convective forcing • Overhead salt-water spray system • Nozzles mounted on rotating, radial arm • Spacing/orientation designed to supply uniform buoyancy flux • Rotation, density and flow rate controlled EGU 2005 Vienna

  14. Vertical section - velocities & convection 50 cm EGU 2005 Vienna

  15. Measurement configuration EGU 2005 Vienna

  16. Visualisation of vortices & jets EGU 2005 Vienna

  17. Vertical flow structure • Vertically-averaged flow on large scales • RMS baroclinic KE fluctuations on small scales • L~1-10 cm (~LRint) << Lb EGU 2005 Vienna

  18. WA Horizontal velocities (b~0.002 m-1 s-1) EGU 2005 Vienna

  19. Zonal mean flow - (b~0.002 m-1 s-1) EGU 2005 Vienna

  20. WA Horizontal velocities (b=0.05 m-1 s-1) EGU 2005 Vienna

  21. NA Horizontal velocities (b=0.05 m-1 s-1) EGU 2005 Vienna

  22. Zonal mean flow - (b=0.05 m-1 s-1) Lb EGU 2005 Vienna

  23. Jet scale as fn of b 0.001 • Jet width decreases with increasing b • Direction alternates with radius • Time-varying meanders - transient effects? • Wind-stress residuals? 0.02 0.05 EGU 2005 Vienna

  24. Vorticity gradients: Rayleigh-Kuo/Arnol’d-Dickii criteria? • Sloping bottom case: urr ~ b even in time-mean • Instantaneous urr > b by factor > 5…. EGU 2005 Vienna

  25. KE Spectra b=0.05 m-1 s-1(slope)b=0.002 m-1 s-1(flat) EGU 2005 Vienna

  26. Eddy-zonal flow interactions:non-local spectral energy transfer? • Separately compute 1/r ∂(ru’v’)/∂r and ∂u/∂t • Correlate in time (with delay) • Strong covariance around t = 0: • KE conversion from eddies->mean flow EGU 2005 Vienna

  27. Conclusions • Successful generation (& measurement) of (~barotropic) geostrophic turbulence via salt-driven natural convection [on a very large scale!] • Clear evidence of Rhines effect, vortices & zonation • Eddy momentum fluxes - directly into zonal jets • Total and eddy KE spectra • Clear k-5/3 “inertial ranges” • Possible evidence for czb2k-5 with sloping bottom (large b only?) • …leading into k-8/3 for k > 20 m-1 for zonal flow? • Barotropic stability of zonal jets….? • Rossby critical layers & PV staircase… • Near-neutral stability in time-average flow (NOT instantaneously) • Unifies dynamics in giant planet atmospheres, oceans & lab. • Future Work: • Long-term development of jets? • Model studies….QUAGMIRE… EGU 2005 Vienna

  28. QUAsi-Geostrophic Model for Investigation of Rotating Experiments • 1,2 or more-layer QG dynamics • Cylindrical annular geometry • High resolution semi-spectral representation of fields: • Fourier harmonics in azimuth • Finite-difference in r and z • Steady and/or stochastic (small-scale) forcing EGU 2005 Vienna

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