On the buoyancy-driven theory of the Atlantic Meridional Overturning Circulation

Transcription

1 On the buoyancy-driven theory of the Atlantic Meridional Overturning Circulation Rémi Tailleux Department of Meteorology, University of Reading AMOC Meeting, Brest, 4 May 217

2 Outline A survey of thermodynamic and mechanical effects on AMOC strength Buoyancy-Driven theory of AMOC and Theory of Available Potential Energy Importance of ocean state for estimating driving forces Conclusions

3 Strength of AMOC is determined both by thermodynamic and mechanical effects

4 AMOC strength increases with strength of buoyancy source GCM world: Swingedouw et al. (27) Laboratory Experiments

5 Bryan (JPO, 1987): Thermocline depth and AMOC strength increase with vertical diffusivity Vertical mixing is primarily driven by winds and tides, hence mechanically-driven

6 Drake Passage Effect Toggweiler and Samuels (1993) Strength of AMOC appears to linearly increase with strength of zonal wind at altitude of Drake Passage

7 Buoyancy only Whitehead and Wang (JPO,28) Buoyancy + Stirring Turbulent stirring causes overturning to increase

8 Buoyancy-Driven or Mechanically-Driven? What about Mechanically-controlled buoyancy-driven circulation? Tailleux (29); Tailleux and Rouleau (21)

9 The same value of potential energy (PE) may reveal very different situations No available PE Some Available PE PE = PEr + APE Hughes et al., (JPO, 29) Lorenz (1955) theory of available potential energy

10 Boussinesq Momentum Equations Coriolis Buoyancy + Wind Wind Du u Dt + f z u + 1 ρ h (p p r (z)) = z A v z (p p r ) z = g( ρ( S,θ,z) ρ (z)) r

11 G(KE) G(APE) Wind-driven route B versus KE APE buoyancy-driven route D(KE) D(APE) Gregory and Tailleux (211) Clim. Dyn. wind heating cooling light light dense dense Wind-driven route Buoyancy-driven route KE B< APE KE B> APE

12 Energetics: Filter out Coriolis Multiply by horizontal velocity ρ D Dt u 2 2 = u i h p + ρ z A v z u 2 2 ρ A v u z 2 Integrate vertically De ρ k Dt dz u = u i h (p p r ) dz + u iτ s ρ A v z H H H 2 dz APE to KE conversion Wind work Viscous Dissipation

13 From Gregory and Tailleux, 211 Local APE to KE Conversion (mw.m -2 ) H ui h P dz Buoyancy-Driven Regions (High Latitudes, Western Boundaries) Wind-Driven Regions (ACC, Equator,...)

14 Isolation of the wind forcing and viscous dissipation H ρ u i z A v H u u dz = u iτ ρ A z s s v z 2 dz Isolation of the buoyancy forcing and mixing? H u i h (p p r )dz = Buoyancy +Mixing+... Buoyancy-driven theory seeks to link pressure gradient work to surface buoyancy fluxes and interior mixing processes

15 Local Definition of Available Potential Energy = Work of buoyancy force from rest state to actual state = quadratic positive definite for small amplitude e a (S,θ,z) = ( ) z g ρ(s,θ,z') ρ r (z') dz' N 2 z z r 2 z r (S,θ ) ρ ( ) 2 APE density satisfies local evolution equation ρ De a Dt = (ρ ρ r )gw ρ αg(z z r ) Dθ Dt + ρ βg(z z r ) DS Dt Manipulate and integrate vertically u i (p p r )dz = ρ g z r βs (E P) αq H c p H H ρ K N De 2 v r dz ρ a Dt dz i H p'udz Production by surface buoyancy fluxes Dissipation by Mixing Horizontal Transfers

16 State Dependent Wind and Buoyancy Forcing Wind Forcing depends on Ocean Surface Velocity G(KE) = S u s iτ s dx dy Buoyancy Forcing depends on Lorenz Reference Depth G(APE) = g z ρ βs (E P) αq r S c p dx dy

17 Buoyancy-Driven Theory of the AMOC Unknown Proportionality Factor Ψ AMOC = k atlantic Atlantic g z r ρ β(e P) αq dxdy c p Mechanically-controlled Reference Depth (e.g., mixing) Buoyancy Forcing

18 Lorenz (1955) theory of available potential energy and its moist extension (1978,1979) Tailleux, ARFM, 213

19 1.5 Depth (meters) Decimal Logarithm of zonally-averaged APE density Latitude Zonally-averaged Depth (meters) Reference position Tailleux 213, Saenz et al. (215) Latitude 5 55

20 From Zemkova et al. (JPO, 215)

21 Seasonally averaged APE generation rate from ECCO2 DJF JJA From Zemkova et al. (JPO, 215) MAM SON

22 Increasing mixing controls G(APE) through increasing thermocline depth

23

24 Bryan (JPO, 1987): Thermocline depth and AMOC strength increase with vertical diffusivity Vertical mixing is primarily driven by winds and tides, hence mechanically-driven

25 Buoyancy only Whitehead and Wang (JPO,28) Buoyancy + Stirring Stirring causes stratification to deepen, increasing APE production, increasing overturning

26 Increase in zonal wind at Drake Passage increases net heating over ACC, which in steady state requires increasing net cooling in Northern Polar Regions thus increasing G(APE) and AMOC

27 Hasumi and Suginohara (1999)

28 Climate Change

29 From Gregory and Tailleux, 211 Global warming reduces APE production by buoyancy Global warming increases APE production by the wind

30 Conclusions Buoyancy-driven theory posits that AMOC strength proportional to APE production rate by high-latitude cooling. Physics of proportionality constant not really understood though: research needed! APE production rate is state dependent. Ocean is a mechanically-controlled heat engine. Mixing and winds helps buoyancy forcing out. Determination of ocean stratification as important as determination of formation rates for inferring past AMOC variations