[PPT] - (x,y), W(y)=(y1/2) 2 1/4, =20, =0.01 1 0.9 0.8 0.7 0.6 0.5 PowerPoint Presentation

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x/L y ψ(x,y), W(y)=(y−1/2)2−1/4, β=20, ν=0.01 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

120
60

+ 60

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Kallberg et al. 1995 (ERA-40 reanalysis)

Wind Forcing

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Ocean Currents

80
60
40
20

20 40 60 80 100 150 200 +120°

180 °
120 °
60 °

0° + 60°

75 °
60 °
45 °

15 ° 0° 15° +45° +60° +75°

Time-averaged (16-year) ocean circulation

Wunsch, 2011

Transport streamfunction (106 m3/s = 1 Sverdrup)

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Haidvogel, McWilliams, Gent, J. Phys. Oceanography 1992

Numerical Simulations: Time-averaged Instantaneous Eddies

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Haidvogel, McWilliams, Gent, J. Phys. Oceanography 1992

Instantaneous Sea-surface temperature Gulf-stream ‘rings’

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tracer informa-

f

Furthermore, for ‐ rs tem- Gouretski

The surface sources of global ocean waters. Oceanic volume that has originated in each 2° by 2° surface location (11,113 origination sites), scaled by the surface area of each box to make an equivalent thickness, d. The color-scale follows a base ten logarithm of the field.

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Antarctic Bottom Water (AABW) North Atlantic Deep Water (NADW) Antarctic Intermediate Water (AAIW)

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Averaging, across an ocean in longitude

Meridional Overturning Circulation (MOC)

(sometimes called the Thermohaline Circulation, THC)

−30 −30 −30 − 3 −27 −27 −27 − 2 7 −24 −24 −24 − 2 4 −21 −21 −21 − 2 1 −18 −18 −18 − 1 8 −15 −15 −15 − 1 5 −12 −12 −12 −12 −12 − 9 −9 −9 −9 − 9 −6 −6 −6 −6 −6 −3 −3 −3 −3 −3 3 3 3 3 3 3 3 3 3 3 6 6 6 6 6 6 6 6 6 9 9 9 9 9 9 9 9 −3 − 3 −3 − 3 −3 −3 −3 12 1 2 12 12 12 15 15 15 15 − 6 − 6 − 6 −6 18 18 18 12 12 1 2 − 9 − 9 −9 15 15 21 21 21 21 1 8 −3 − 3 − 3 −3 − 6 −6 21 21 2 4 24 −15 24 −18 − 9 −21 30 −24 −6 −6 −27 2 7 −30 2 1 −3 30 −3 15 −12

Latitude Depth, (m) −60 −40 −20 20 40 60 −5000 −4000 −3000 −2000 −1000

Nikurashin and Vallis, 2011

Atlantic MOC (1 Sv = 106 m3/s)

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Mignotti + Woods, 2015

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MI THERMO PYCNOCLI ABYSS Abyss Thermocline Mixed layer

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500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000

20 20 21 21 22 22 23 23 24 24 25 25 25 26 26 26 26 26 26.5 26.5 26.5 26.5 26.5 26.6 26.6 26.6 26.6 26.6 26.6 26.7 26.7 26.7 26.7 26.7 26.7 26.8 26.8 26.8 26.8 26.8 26.8 26.9 26.9 26.9 26.9 26.9 26.9 27 27 27 27 27 27 27.1 27.1 27.1 27.1 27.1 27.1 27.2 27.2 27.2 27.2 27.2 27.2 27.2 27.3 27.3 27.3 27.3 27.3 27.3 27.3 27.4 27.4 27.4 27.4 27.4 27.4 27.4 27.5 27.5 27.5 27.5 27.5 27.5 27.5 27.52 27.52 27.52 27.52 27.52 27.52 27.52 27.54 27.54 27.54 27.54 27.54 27.54 27.54 27.56 27.56 27.56 27.56 27.56 27.56 27.56 27.58 27.58 27.58 27.58 27.58 27.58 27.58 27.6 27.6 27.6 27.6 27.6 27.6 27.6 27.62 27.62 27.62 27.62 27.62 27.62 27.62 27.64 27.64 27.64 27.64 27.64 27.64 27.64 27.66 27.66 27.66 27.66 27.66 27.66 27.66 27.68 27.68 27.68 27.68 27.68 27.68 27.68 27.7 27.7 27.7 27.7 27.7 27.7 27.7 27.7 27.72 27.72 27.72 27.72 27.72 27.72 27.72 27.72 27.74 27.74 27.74 27.74 27.74 27.74 27.74 27.74 27.76 27.76 27.76 27.76 27.76 27.76 27.76 27.76 27.78 27.78 27.78 27.78 27.78 27.78 27.78 27.78 27.8 27.8 27.8 27.8 27.8 27.8 27.8 27.8 27.82 27.82 27.82 27.82 27.82 27.82 27.82 27.82 27.82 27.84 27.84 27.84 27.84 27.84 27.84 27.84 27.84 27.84 27.86 27.86 27.86 27.86 27.86 27.86 27.86 27.86 27.88 27.88 27.88 27.88 27.88 27.88

km Lat

50
40
30
20
10

10 20 30 40 50 60

Eq. N S

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Kunze et al. JPO, 2006

Inferred diffusivity, North-South Atlantic section Munk value

Problem: Observations of ocean mixing typically find

‘Missing’ Mixing

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κT ' 1.1 ⇥ 10−5m2 s−1

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Inoue + Smyth 2009

Mixing Efficiency

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Boundary Mixing

1978 ARMI: BRIEF REPORT

Fig.

8. Simplified

sketch

f

boundary mixing

f

continuous stratification into layers and subsequent transport

f

mixed layers into interior

f basin

either by along-isopycnal diffusion

r by advection.

Bottom-generated turbulence due to motion

f the

water stirs the background stratification into layers (arrow at right); it is suggested that layers

f

different

rigins

and densities interleave as they decay and flatten to form a nearly uniform stratification again (arrow at left).

mixing-advection model is illustrated in Figure 8 with a steep boundary, these processes may

ccur

wherever isopycnals in- tersect the bottom, even on a large flat abyssal plain over which there exist isopycnal slopes due to the mesoscale eddy field. The depth

f each
f the

steps will be roughly controlled by a Froude number criterion F • 1, as described by Armi and

Millard [1976] and Armi [1977]. We take, for the estimate which follows,

50 m as

an average thickness but note that the thickness

f individual

layers at any location will depend

n

the local velocity.

The horizontal extent

f each

layer across isobaths is pre- sumed to be the projection

f each

layer along the slope, i.e.,

h/a. The extent
f each

layer along isobaths is unknown but is also presumably limited, as evidenced by the horizontal

variability found at station KN 60/4 (Figure 2). We visualize

the boundary mixing process as forming many iaminae each

f

approximately 50-m depth; no individual lamina extends com- pletely around the basin, although at any point on the boundary one is always present. We will estimate the vertical eddy diffusion within each layer at the boundary following Clauser [1956], i.e.,

Kvboun a

•u,h

where u, is the friction velocity

(1)

u, (2) and h is the height

f the mixed

layer; with a mean velocity, U

10

cm/s, and h • 50 m: K%oun a

l0

2 cmV'/s. This estimate for

the vertical eddy diffusivity at the boundary must be thought

f only as a very rough estimate.

In fact, Armi [1977] has pointed

ut that within the boundary

mixed layer and above the Ekman layer scale, very little is known of the turbulence. We also assume that the horizontal

r along-isopycnal

ex-

change is rapid. We do not understand how the character

f

the individual mixed layers formed at the boundaries is lost in

the interior. One possibility is that layers

f different
rigins

and densities interleave as they decay and flatten. With enough interleaving a nearly uniform stratification may result. The vertical

r cross-isopycnal

mixing at the boundary must serve the entire basin. We will equate the vertical transport at the boundary with the total transport represented as total area times the 'average' flux. The ratio

f the

surface area along the boundary for the mixed layers bounding any isopycnal surface

to the surface area within the considered circular basin of

diameter L is given by

rLh/ce

4h

Ar •r(L/2)•. aL (3)

The apparent, or 'average,' eddy diffusivity for the basin,

Kv• ..... , is then given by

Kv, .... '•' gvbound'A r (4)

With typical values, e.g., L • 4 X 10 a kin, a -- •.-•o, and Kv, .... •

I cm•'/s, in agreement with the historical estimates [cf. Munk,

1966].

CONCLUSION

Data have 'been presented here to suggest that turbulent mixing in the deep

cean

is a two-part process:

1. Vertical mixing

at boundaries and topographic features

ccurs

within finite layers. The vertical extent

f the layers

is

limited by the stable background density field and the velocity

f the flow which causes

the boundary-generated shear and

turbulence.

2. The layers

formed are advected along constant density surfaces into the interior and eventually lose their step charac-

ter.

The combined effect

f these

two processes may be paramet- rically disguised as a vertical eddy diffusivity in one-dimensional models. A crude estimate shows that the two processes can account for all the vertical eddy diffusion apparent in one-

dimensional

models. The actual mechanism is far from a

simple

ne-dimensi,onal

process. It involves complicated dy- namics both at the boundary and in the interior about which

we have much to learn.

Acknowledgments. I am very grateful for the assistance

f the

W.H.O.I. buoy group, Nan Bray, and Mary Raymer with the presentation of these results. The current speeds and directions shown in Figure I were provided through the courtesy

f W. Schmitz.

Trish Pettigrew carefully drew the conceptual sketch shown in Figure 8. This research is based

n research

supported by the Office of Naval Re- search under contracts N00014-76-C-0197 and NR 083-400 and by the

,

National Science Foundation under grant OCE 76-81190. The sugges- tions from the reviewers and editor for improving the original manu- script are sincerely appreciated. This is contribution 4060 from the Woods Hole Oceanographic Institution, Woods Hole, Massachusetts.

ARm: BmF•F R•POgT 1973

SALINITY PPT

34;,.85 34;86 :•,.87 34;88 34,89 34;90 34;91

4920' 4960' 5000' 5040- 5080. 5120-

5160'

m 5200-

5240'

D 5280 a_ 5320-

5;560-

ß

5400- 5480. 5520. 5560- 5600

POT TEMP øC

1.72 1.74 1.76 1.78 I.,80 I.,82 I.,84

(s

i ,"

.,.

! /'

NEPHELS (arbitrary)

; ½ ;

KN60/4/E P

DATE 76-10-5

Ne:;;

LOW

NO. I

LAT 35 • 57.3 LONG. 53 • 45.5

34,.92 34193

1.86

:54.88
34.89
:5490
Fig. 2. Profile

taken at station KN 60/4 (refer to_Figure 1) downstream

f the Corner Rise.

Shown are potential temperature 0, salinity S, and light scattering N, versus pressure

depth. Also superposed

is a scatter plot of potential temperature versus salinity which includes the historical data of Worthington and Metcalf[1961]. The multiple layers are due to advection

f mixed

layers formed at their respective isopyc- hal depths

n the Corner Rise.

The water mass in each layer has the same characteristic as the background water mass. Both down and up traces

f potential

temperature and light scattering are shown; the up traces are dotted and only shown below 5200

dbar. Light scattering

is shown increasing to the left to emphasize similarity with potential temperature and salinity traces.

30 cm/s (refer to Figure 3b of Armi and Millard [1976]. This compares well with the velocity measured at the location of profile KN 60/4 (Figure 2) and

ther

velocities shown for the Sohm Abyssal Plain region in Figure 1. The flow is thus energetic enough to have mixed these layers. As the flow moves by the Corner Rise, these layers presumably detach and are then carried into the interior. The layers are distinct at the location

f station

KN 60/4 only 3-4 days downstream

f the

Corner Rise, 100 km away. Similar step structures are also evident in the near-surface 800-m depth profiles

f Wunsch

[1970, 1972]. He shows a systematic change in the temperature

gradient as measured with a STD as the Bermuda Islands are

approached and suggests the possibility that the stirring mech- anism is the breaking of internal waves. The profiles made as the package was both lowered and raised are shown for station KN 60/4 (Figure 2). The character of the profile obtained as the package was raised was identical, i.e., multiple layers were again

found. However, as

the profiler got above the first bottom layer, the numbers and locations

f the layered

structures were found to be different. For example, instead

f the three-step

structure found on the way down between 5300 and 5500 dbar, only two larger steps were found on the way up. In the approximately 20 min between crossing 5400 dbar on the way down and the subsequent crossing

n the way up, advection
f 30 cm/s can

alone account for a Lagrangian spatial separation

f •400 m.

The structures found a few hundred meters above the bottom have limited horizontal extent.

The included 'nephelometer shows that the light-scattering profile has a structure nearly identical to that of the salinity and potential temperature profiles. The small 1- to 2-tzm parti- cles, the concentration

f which the nephelometer

is most sensitive to, have a very slow settling rate of •10 m/yr [cf. McCave, 1975]. For the advective processes with which we are dealing here they are essentially passive tracers. It appears as though the particulate matter was also mixed, to form the various nepheloid layers seen, from a background gradient

f

particulate matter just as the potential temperature and salinity were. If the material had been resuspended from the bottom at the depths

n the Corner Rise

where the mixed layers were formed, the concentration in each layer would be a function of the amount of locally resuspended material; in contrast, the concentration appears predetermined by the background gradient, and little local resuspension has oc-

curred.

Water mass

anomalies. Some profiles made along 55øW

show an anomalous water mass at a potential temperature between 1.80 and 1.81øC. This anomaly is evident in the profile made at station KN 60/9 (Figure 3) as the 150-m-thick layer sandwiched between the uniform stratification above and the bottom mixed layer below. This bottom layer and the stratification above lie on a straight 0 versus S characteristic, parallel to the Worthington and Metcalf [ 1961] characteristic shown. The anomalous layer sandwiched between is •0.0015%o saltier than the background water mass would be at the same potential temperature of 1.81øC. The anomalous layer found at station KN 60/9 is seen at the same potential density (a4 = 45.96) as the bottom layer at station KN 60/7 (Figure 4). The anomaly is due to a higher concentration

f water with Norwegian Sea water character-

istics [cf. Worthington, 1976]. Similar anomalous water was seen in the Geosecs station 28 profile [Bainbridge et al., 1976]

at 39ø0.0'N, 43ø59.0'W near the bottom of the submarine

canyon to the east.

Recently, in August 1977, similar anomalous water was also

found

n an R/V Oceanus

cruise at station OC 31/1 (Figure 5)

ver the northern

Hatteras Abyssal

Plain. The nephelometer

used on this cruise was of a new type developed at Woods

Hole. It measured

forward angle (•6-8 ø) scattered light from

a collimated white light source. This profile, as well as those

f

Figure 6, was added to the paper because it illustrates the

persistence

f the

thin anomalous layer

ver

large distances

and long times; at 31ø43.8'N, 70ø44.9'W, station OC 31/1

was to the west of the area included in the map shown in

Figure 1. The profile illustrates the usual well-mixed bottom

Armi, 1972

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FIG. 4. Dependence of the time-averaged overturning circulation upon the vertical diffusion coefficient

(surface buoyancy flux is fixed, with Q0 5 200 W m22). The maximum streamfunction quoted is that for a two-dimensional flow in a basin of 1-m width, while the density range is Dr 5 rbottom rtop. The 208C isotherm is shown in gray.

Available Potential Energy and Irreversible Mixing in the Meridional Overturning Circulation

GRAHAM O. HUGHES, ANDREW MCC. HOGG, AND ROSS W. GRIFFITHS

The Australian National University, Canberra, Australia

Stabilizing buoyancy input Destabilizing buoyancy input Destabilizing buoyancy input

Horizontal convection

Hughes and Griffiths 2008

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Wunsch and Ferrari, 2004

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Video: Ryan Abernathy

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0.01 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0.01 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0.01 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0.01 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001

0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

0.01 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0.01 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001

0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

Matt Colebrook

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Figure 1 Changes in surface air temperature caused by a shutdown

f North Atlantic Deep Water

(NADW) formation in a current

cean–atmosphere circulation
model. Note the hemispheric see-

saw (Northern Hemisphere cools while the Southern Hemisphere warms) and the maximum cooling

ver the northern Atlantic. In this

particular model (HadCM3)7, the surface cooling resulting from switching off NADW formation is up to 6 C. It is further to the west compared with most models, which tend to put the maximum cooling near Scandinavia. This probably depends on the exact location of deep-water formation (an aspect not well represented in current coarse-resolution models) and on the sea-ice distribution in the models, as ice-margin shifts act to amplify the cooling. The largest air temperature cooling is thus greater than the largest sea surface temperature (SST) cooling. The latter is typically around 5 C and roughly corresponds to the observed SST difference between the northern Atlantic and Pacific at a given latitude. In most models, maximum air temperature cooling ranges from 6 C to 11 C in annual mean; the effect is generally stronger in winter.

–4 –2 2 4 180°W 90°W 0° 90°E 180°E 90°N 90°S 45°S 45°N 0° Temperature change (°C)

Rahmstorf, Nature, 2002

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‘Cold’ ‘Off’

Depth (km) Depth (km) Depth (km)

‘Warm’ 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 30°S 30°N 60°N 90°N

Freshwater forcing (Sv) –0.1 0.1 NADW flow (Sv) 20 Stommel bifurcation Present climate? Bistable regime

60 55 50 45 40 35 30 25 20 15 10 42 40 38 36 16 18 20 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 YD H1 H5 H4 H3 H2 H0 Time (kyr ago) SST (°C) δ18O (°/°°) Bølling H6?