Ocean Circulation: review

Transcription

1 Joe LaCasce Section for Meteorology and Oceanography December 2, 2014

2 Outline Physical characteristics Observed circulation Geostrophic, hydrostatic and thermal wind balances Wind-driven circulation Buoyancy-driven circulation

3 Ocean observations Woods Hole Oceanographic Inst.

4 Interpreting the observations Temperature, salinity and pressure density Sea surface height surface velocities Density profiles velocity profiles

5 Calculating density Density is determined from temperature, salinity and pressure: ρ = ρ(t, S, p) = ρ c [1 α T (T T ref ) + α S (S S ref ) +...] where: ρ c = 1000 kg m 3 Warm water is lighter than cold water Salty water is heavier than fresh water

6 Basic balances: incompressibility The full continuity equation is: ρ + u ρ + ρ( u) = 0 t In the ocean, ρ ρ c = const. So: u = x u + y v + z w = 0 Ocean velocities are approximately incompressible

7 Basic balances: hydrostatic dp dz = ρg

8 Basic balances: geostrophy The momentum equations can be scaled: t u + u u + f ˆk u = 1 ρ c p U fl U fl 1 p ρ c ful The Rossby number, ɛ U fl, is small at large scales, so the horizontal velocities are approximately: fu 1 ρ c y p, fv = 1 ρ c x p

9 Combined equations Integrating the hydrostatic relation from a depth z to the surface (at z = η), we find: p( z) = ρ c g η So the geostrophic velocities at the surface are: u g = g f y η, v g = g f x η Sea surface height can be used to estimate velocity

10 Surface geostrophic flow

11 Mean sea surface height, global

12 Basic balances: Thermal Wind Taking the vertical derivative of the geostrophic relations and inserting the hydrostatic balance: z u g = g ρ c f y ρ, z v g = g ρ c f x ρ

13 Subsurface velocity

14 Basic balances: summary Incompressibility Hydrostatic balance u = u x + v y + w z = 0 Geostrophic balance p z = ρg Thermal wind fu = 1 p ρ y, fv = 1 p ρ x

15 Ocean forcing The ocean is driven primarily by: Wind : forcing at the surface transfers momentum to the ocean, via waves and turbulent motion Heating : the sun warms the low latitudes more than the high latitudes, creating a large scale density gradient at the surface Evaporation/precipitation : fresh water removal and input at the surface can also affect surface density

16 Applied stress d u dt = 1 ρ c z τ

17 Ekman layer transport Add stress to geostrophic relations: fv = 1 ρ c x p + z fu = 1 ρ c y p + z τ x ρ c τ y ρ c Integrate vertically over the surface layer: 0 fv a dz fv E = 1 τ wx δ E ρ c 0 fu a dz fu E = 1 τ wy δ E ρ c

18 Ekman pumping

19 Sverdrup transport From the vorticity equation, we obtain: δe H βv dz βv I = 1 τ wy ( ρ c x τ wx y ) = 1 ρ c ˆk τ w This is the Sverdrup balance: the meridional (N-S) velocity is proportional to the curl of the wind stress

20 Sverdrup relation For example, if the wind blows east: βv I = y τ wx

21 Boundary currents Imagine a negative wind stress curl over a basin: But how does the fluid return north?

22 Boundary currents Actually two possibilities:

23 Stommel s Gulf Stream In Stommel s model, geostrophy is broken by bottom friction: fv = 1 ρ c x p ru fu = 1 ρ c y p rv Friction allows ageostrophic return flow

24 Stommel s Gulf Stream Now the Sverdrup relation is: βv = 1 τ wy ( ρ c x τ wx y ) r δe H ( v x u y ) dz Assume the deep velocities are depth-independent: βhv = 1 τ wy ( ρ c x τ wx y ) rh( v x u y ) Also have assumed δ E H

25 Stommel s Gulf Stream Break velocity into two parts: v = v I + v B, with: βv I = 1 wy ( τ ρ c H x τ wx y ) in the interior, and: βv B = r( v B x u B y ) in the boundary layer. The boundary current is narrow so: βv B r v B x

26 Stommel s Gulf Stream Now consider the shear in the boundary current:

27 Stommel s Gulf Stream Western boundary current Eastern boundary current βv B r v B x r v B x < 0 βv B > 0 r v B x > 0 βv B < 0

28 Stommel s Gulf Stream Works the other way too. If the interior flow is northwards, the boundary currents go south: West : r v B x > 0 βv B < 0

29 The Pacific gyres

30 Observations: Pacific

31 Observations: Atlantic

32 Buoyancy forcing

33 Zonally-averaged buoyancy forcing

34 Thermally-driven flow What type of flow do we expect, with warming at low latitudes and cooling at high latitudes? From thermal wind: z u g = g ρ c f y ρ In the northern hemisphere: y ρ > 0, f > 0 z u g > 0 In the southern hemisphere: y ρ < 0, f < 0 z u g > 0

35 Thermally-driven flow

36 Surface velocities in a thermally-driven box G. Brostom (2010)

37 Surface velocities in a thermally-driven ocean L. Denstad (2014)

38 Stommel-Arons abyssal layer

39 Stommel-Arons model Same equations as for Gulf Stream: fv = 1 ρ c x p ru fu = 1 ρ c y p rv Cross-multiply to make a vorticity equation: βv = f w z r( v x u y )

40 Stommel-Arons model In the abyssal layer, assume no vertical shear: z u = z v = 0 Integrate vorticity equation vertically, with flat bottom: βh A v = fw T rh a ( v x u y ) where H A is the layer depth and w T is vertical velocity at top

41 Basin interior Away from boundaries, Sverdrup balance: βh A v = fw T Stommel assumed that w T = W constant upwelling so: v = fw βh A > 0 everywhere in the interior

42 Basin interior

43 Boundary current Flow returns in deep western boundary current βv B = r( v B x u B y ) r v B x West : r v B x > 0 v B < 0

44 Stommel-Arons circulation

45 Transports from observations, and the conveyor belt

46 Summary Wind-forcing drives gyres with western boundary currents Buoyancy forcing drives a meridional overturning circulation which is global in extent. Largely driven by surface heating/cooling, although sensitive to fresh water input (melting) How these two interact is not well understood Extremely important for the climate system