1 / 41

‘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

etana
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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)

More Related