1. Upwelling and Downwelling in the deep ocean: how much is there of both?
Trevor J McDougall, Raf Ferrari & Ryan Holmes
Munk Centennial Symposium, Scripps, 15 May 2017
Ocean Physics, School of Mathematics and Statistics

2. An ocean mixing conundrum
The very dense Bottom Water Plume (BWP) sinks to the sea floor, entraining fluid as it sinks.

3. My interest in this boundary mixing topic began in 1989 …
An ocean mixing conundrum
My interest in this boundary mixing topic began in 1989 …
This exceedingly simple idea gave a vertical stretching of the opposite sign to that assumed in the Stommel-Arons circulation…..

4. An ocean mixing conundrum
The one-dimensional part of the Munk (1966) Abyssal Recipes paper proposed a balance between diapycnal advection and the vertical divergence of diapycnal diffusion, or
and given the amount of Bottom Water to be upwelled across density surfaces, and given a value of the vertical diffusivity D followed.

5. Using the Osborn (1980) relationship,
An ocean mixing conundrum
Using the Osborn (1980) relationship,
the Abyssal Recipes balance requires that the dissipation increases with height, since

6. An ocean mixing conundrum
But the modern measurements of diapycnal mixing in the deep ocean have shown that is is bottom-intensified, and is mainly caused by the internal tide interacting with rough bottom topography.
The largest values of dissipation are found near the sea floor, with dissipation decreasing with height on each vertical cast.

7. An ocean mixing conundrum

8. An ocean mixing conundrum

9. The simplified connection between upwelling and dissipation.
Assuming that the equation of state to be linear, there is a very simple relationship between dianeutral upwelling and dissipation,
which has used the Osborn (1980) relationship
with the 0.2 number being a typical value in the stratified ocean interior.

10. So…
How does Bottom Water rise through isopycnals given that on each vertical water column
is negative?

11. The resolution of the ocean mixing conundrum relies on the ocean not having vertical walls.
That is, the sloping nature of the sea floor is crucial.

12. The resolution of the ocean mixing conundrum requires sloping side boundaries
Assume a linear equation of state and consider the conservation of
(i) mass and (ii) density in a control volume bounded by two density
surfaces and the sloping sea floor.
That is, rather than studying a single water column we will do a
budget study over a finite volume.

13. Upwelling and Downwelling in the Abyss
(ignoring )

14. Upwelling and Downwelling in the Abyss

15. Upwelling and Downwelling in the Abyss
This result is an application of the
Walin (1982) method of volume-integrated
buoyancy conservation
where

16. Seamounts cause net downwelling
Seamounts have net downwelling surrounding them, thus acting as a sink to the surrounding ocean.

17. Upwelling and Downwelling in the Abyss
Now to express in terms of the
diffusive buoyancy flux using

18. Upwelling and Downwelling in the Abyss
(ignoring )
We now have all three dianeutral volume transports
in terms of the imposed buoyancy flux field,
and

19. Upwelling and Downwelling in the Abyss

20. Global Upwelling and Downwelling in the Abyss
The volume-integrated buoyancy budget is
and combining the above equations gives the main results

21. Global Upwelling and Downwelling in the Abyss
For illustrative purposes take to be constant,
and

22. The vertical ocean circulation

23. Global Upwelling and Downwelling in the Abyss
Taking the net dianeutral upwelling from Lumpkin and Speer (2007)

24. Global Upwelling and Downwelling in the Abyss

25. Global Upwelling and Downwelling in the Abyss

26. Global Upwelling and Downwelling in the Abyss
summary slide
The volume-integrated buoyancy budget is
and combining the above equations gives the main result,

27. Global Upwelling and Downwelling in the Abyss
The new view of the abyssal diapycnal flow is then of intense
upwelling in the turbulent bottom boundary layer (~50m deep)
and strong downwelling in a region about 4 degrees of latitude
away from the boundaries.

28. The Stommel-Arons circulation needs to be drastically revised, with the upwelling and downwelling being very close to the continental boundaries

29. Global Upwelling and Downwelling in the Abyss
The constant vertical diffusivity D case therefore had
increasing with height!
Use of the Bryan & Lewis profile of the vertical
diffusivity in ocean models also yields upwelling
in the interior of the abyssal ocean.

30. Global Upwelling and Downwelling in the Abyss
How does the abyss manage to upwell rather than having fluid sink through isopycnals?
needs to be an increasing function of buoyancy b

31. Global Upwelling and Downwelling in the Abyss
How does the abyss manage to upwell rather than having fluid sink through isopycnals?

32. Global Upwelling and Downwelling in the Abyss
How does the abyss manage to upwell rather than having fluid sink through isopycnals?

33. The Direction of Lateral Mixing in the Ocean

34. The Direction of Lateral Mixing in the Ocean

36. The Direction of Lateral Mixing in the Ocean
The observations show that density inversions occur only at the micro- and fine- scales. That is, the Thorpe scale is observed to be about the same as the Ozmidov scale.
This implies that density inversions only occur during active three-dimensional almost-isotropic turbulence, and we are justified in parameterising this small-scale turbulent mixing with an isotropic diffusivity of 0.1 – 1 Munk.
Now we treat this small-scale mixing process separately to the lateral stirring and mixing. During the lateral mixing there can be no density inversions. This leads to the direction of mixing of mesoscale eddies being along the locally-referenced potential density surface.

37. The End