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‘Horizontal convection’ 3 Coriolis effects adjustment to changing bc’s, thermohaline effects

‘Horizontal convection’ 3 Coriolis effects adjustment to changing bc’s, thermohaline effects. Ross Griffiths Research School of Earth Sciences The Australian National University. Outline (#3). • Effects of rotation • Adjustment processes and timescales

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‘Horizontal convection’ 3 Coriolis effects adjustment to changing bc’s, thermohaline effects

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  1. ‘Horizontal convection’ 3Coriolis effectsadjustment to changing bc’s, thermohaline effects Ross Griffiths Research School of Earth Sciences The Australian National University

  2. Outline (#3) • Effects of rotation • Adjustment processes and timescales • full-depth or partial-depth overturning? • Effects of salt or freshwater fluxes (B.C.s and DDC)? • simplified condition for ‘shut-down’ of deep sinking?

  3. Effects of Rotation Geostrophic flow, PV dynamics, horizontal gyres, boundary currents along meridional (N-S) boundaries, baroclinic instability and eddies, convective instability in eddies (‘open ocean’ sinking?), Northern/Southern boundary sinking. Ekman transport, Ekman pumping

  4. Boundary layer scaling - geostrophic case (Bryan & Cox, 1967; Park & Bryan 2000) Ta h u, v Tc Steady state balances when h>>hE: • continuity & vertical advection-diffusion vh ~ wL ~ L/h • thermal wind (geostrophic constraint) gTh/L ~ fu u ~ v • conservation of heat FL ~ ocpTvh h/L ~ (RaE)–1/3 uL/ ~ (RaE)2/3 => Nu ~ (RaE)1/3 bl/L ~ (RaE)1/3 (indept. of viscosity)

  5. Simple GCMs (Bryan 1987, Park & Bryan 2000, Winton 1995,96) Dependence on  sometimes weaker than scaling result 2/3 owing to different B.C.s (with restoring B.C.s use internal T)

  6. Rotating annulus geometry, bottom forced 1990 Annular geometry Strong zonal flow Meridional overturning

  7. Rotating annulus geometry, bottom forced(photo from Miller & Reynolds, JFM, 1990)

  8. Rotating HC with meridional boundariesmovie shows Ω = 0.3 rad/s anticlockwise

  9. Parameters (and flow regimes)? Ocean: Ra ~ 1025, Pr ≈ 1, hT/hv ~ 10-20, Rd/L = (g’D)1/2/fL ≈ 10-3, N/f ~ 30, Ni/f ~ 3 Horizontal convection in lab: Ra ≈ 1014, Pr ≈ 4, hT/hv ~ 10-20, Rd/L = (g’D)1/2/fL ≈ 5x10-2, N/f ≈ 2, Ni/f ~ 0.02

  10. Rotating ‘horizontal convection’ Applied heating flux 140 W Ω = 0.2 rad/s Viewed after thermal equilibration - steady state 3D, unsteady flow Boundary currents and gyres B.L. convective instability Baroclinic instability 3D endwall plume interior vortex plume convection

  11. Local/mesoscale processes in deep-convection A small patch of surface buoyancy flux above a density stratification (eg. a polynya of 12km diameter). Fernando & Smith, Eur. J. Mech. 2001

  12. Rotating ‘horizontal convection’ Applied heating flux 140 W, Ω = 0.2 rad/s Viewed after thermal equilibration, at 8x speedup

  13. Rotating ‘horizontal convection’ Applied heating flux 140 W, Ω = 0.2 rad/s Viewed after thermal equilibration, at 16x speedup

  14. Temporal adjustmentsto a sensitive balance Ocean circulation: • How would a convective MOC respond to perturbations in the surface B.C.s. • would the response be different for changes at high or low latitudes? • What B.C. changes will shut-down deep overturning, and will it return to full-depth? • timescales for adjustment and equilibration? Horizontal convection: • mechanisms for adjustment to changed B.C.s? • switch to shallow convection? • can a shallow circulation persist? • timescales of response? • Role of interior diffusion? Sensitivity to type of B.C.s?

  15. The steady state Non-rotating, applied T 792h:42min + 13 min + 33 min T1=10˚C T2=34˚C Box 1.25m long x 0.2m high x 0.3m wide

  16. Adjustment to perturbed BCs Conditions: Applied F or T Rotating or non-rotating Effects of ambient temperature Perturbations: Warm up the hot plate Cool down hot plate Warm up cold plate Cool down cold plate +

  17. Warm up case Example #1: non-rotating, applied T Warm up hot plate (34˚ to 38˚C), applied cooling T1= 10˚C

  18. Warm up hot plateie. increase destablizing buoyancy(showing heated end of box)

  19. Warm up hot plate(showing whole box)

  20. Simplest model: full-depth circulation and applied heat input • Hold Tc fixed, increase heat input from F0 to Fo+∆F • plume carries base heat input to top - assume well-mixed interior • Flux imbalance: cpDLTt = ∆F - F’(t) • Boundary layer conduction: F0 + F’(t) = cp(T - Tc)L/h, h ~ 2.65LRa-1/6 => T = T0 + ∆T(1- e-t/hD), ∆T = Tf - T0 = h∆F/(cpL) or (T-Tf)/(T0-Tf) = e-t/hD D T(t) ~uniform F0+∆F h F0+F’(t) Tc L

  21. Warm up case(ie. increase destabilizing buoyancy input or decrease stablizing flux) Example #2: Constant applied heating flux (1556 Wm-2), hot lab (Tlab=31.15˚, T0=31.16˚, Tf=34.94˚C) Warm up cold plate (10˚–>15˚C) T(t) at mid-depth (above hot plate, thermistor #8) T* = (T(t) - Tf)/(T0 - Tf)

  22. Cool down case(ie. decrease de-stabilizing buoy. input or increase stablizing flux) Example #3: Cool downcold plate (from 15˚ to 10˚C), constant hot plate temperature (34˚C) Note long timescale of re-adjustment to full-depth ~ 20 hours

  23. Cool down case Example #4: Constant applied heating flux (1556 Wm-2), hot lab (Tlab=31.15˚, T0=34.94˚, Tf=31.13˚C) Cool down cold plate (15˚–>10˚C) T(t) at mid-depth above hot plate, thermistor #8 T* = (T(t) - Tf)/(T0 - Tf)

  24. timescales interior boundary layer e-folding time = hD/ 95% of change = hD/

  25. Time development - infinite Prinitial T = lowest T applied at top (ie. box starts at T = 0, colder than final equilib.T) T=1 T=0

  26. Response to changed B.C.s Implications for a convective MOC • An increased sea surface cooling at high latitudes, or decreased heat input at low latitudes ––> enhanced full-depth overturning ––> exponential adjustment (hD/ ~ 500 - 8000 yrs • A decreased surface cooling (or freshwater input), or increased heat input ––> temporary partial-depth circulation ––> return to full depth with oscillations in fountain penetration (entrainment?) ––> equilibration times may approach D2/ (~ 5000 - 50000 yrs) ––> timescale is longest for applied flux • Coriolis accelerations have little effect on equilibration times • Need to examine magnitude of changes required to shut down the deep sinking (see thermohaline effects)

  27. Thermohaline effects Questions: • interaction of thermally-driven circulation and surface freshwater fluxes at high latitudes? (opposing buoyancy fluxes) • or with brine rejection on seasonal timescales? (reinforcing thermal buoyancy flux) • steady or fluctuating behaviour? • does double-diffusive convection play significant roles? (salt-fingering at low latitude, ‘diffusive’ layering at high latitudes)

  28. Modelling a surface freshwater input Parameters: RaF = gFL4/(ocpT2  = S/T Pr = /T R = S/T A = D/L BS/BT = 2cpSQ/(FLW

  29. Thermal convection ‘Synthetic schlieren’ image / heated end x=0 L/2=60cm 20cm imposed heat flux

  30. Small salinity buoyancy fluxsteady flow

  31. Large salt buoyancy fluxflooding of forcing surface DS = 2.0% Q = 2.7x10-7 m3s-1 BS/BT = 0.5

  32. Large salt buoyancy fluxflooding of forcing surface DS = 2.0% Q = 2.7x10-7 m3s-1 BS/BT = 0.5

  33. Intermediate salt buoyancy flux oscillatory flow

  34. Small-intermediate salt fluxoscillatory flow 1 DS = 1.0% Q = 0.99x10-7 m3s-1BS/BT = 0.1

  35. Intermediate salt flux Thermistor positions

  36. Large-intermediate salt fluxintrusions above b.l. DS = 0.51% Q = 3.6x10-7 m3s-1 BS/BT = 1.04

  37. Flow regimesand ratio of buoyancy fluxes

  38. Timescales • flushing by the volume input tf ~ V/Q ~ 105 s • convective ventilation time tc ~ V/uW ~ 2000 - 5000 s • internal wave travel time along the thermocline tw ~ L/N* ~ 45 s • observed fluctuation time scales ~ tc

  39. Summary A stabilising salinity flux adds: • a mostly stable halocline (in the ‘sinking’ region) • steady, oscillatory or surface-flooding regimes • regime depends primarily on the ratio of buoyancy fluxes (BS/BT).

  40. Conclusions • ‘horizontal convection’ shows a wide range of behaviour and poses many fascinating questions that remain unexplored. • ocean MOC and THC has buoyancy as one important motive force (with wind also very important) and studies of horizontal convection can contribute to the understanding of the ocean circulation. • there is argument about the extent to which the overturning circulation relies on diffusion and the extent to which the sub-surface flow is adiabatic. • in a diffusive circulation (with energy for mixing provided by tides and winds), the flow is governed equally by both mixing rate and buoyancy supply.

  41. Further questions • scaling of T-H fluctuation times to the oceans • effects of time-varying heat and salinity fluxes • effects of marginal seas and hydraulic controls • rotation and thermohaline effects • -effects • non-Boussinesq effects (eg. nonlinear density equation)

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