Surface Wave Enhanced Turbulence as an important source energy

maintaining/regulating Thermohaline Circulation

Rui Xin HuangWoods Hole Oceanographic Institution, Woods Hole, USA

A Joint Study with Wei WangPhysical Oceanography Lab, Ocean University of China

9/15/2006 1

Why should we care about surface waves?

1) Surface waves affect the upper ocean only?

2) Most OGCMs assume kappa drops to 0.1 Munk below the mixed layer.

3) This is wrong! Due to surface wave enhance turbulence, kappa can be much larger than 0.1 below the base of mixed layer, and this strong mixing can affect the THC greatly.

9/15/2006 2

9/15/2006 3

Three schools: What drives THC?a) Pushing by deepwater formation

b) Pulling by deep mixing

c) Pulling by wind stress & surface waves

9/15/2006 4

Heating Cooling Heating Cooling CoolingHeating

. .

Wind

New energetic theory of THC1) Mechanical energy is required for

overcoming friction/dissipation2) Surface heating/cooling cannot

maintain THC observed in the oceans.Sandstrom Theorem and the new

debate3) Deep mixing is proposed as an important

mechanism in maintaining THC

9/15/2006 5

9/15/2006 6Wang, W. and R. X. Huang, 2005, Journal of Fluid Mechanics

Inverse energy cascade in the oceans:

1) Large-scale gravitational potential energy

Tidal energy

Small scale mixing

GPE of large scale ocean circulation

2) Wind stress small scale waves

Small scale mixing

GPE of large-scale ocean circulation9/15/2006 7

Outline• The role of wind waves on the energy

budget of the ocean• Observed distribution of wave-breaking

enhanced dissipation rate• Numerical experiments with idealized

surface-intensified diffusivity• Circulation driven by realistic surface wave

enhanced diffusivity• Conclusion

9/15/2006 8

9/15/2006 9

Mechanical energy balance in the oceansGeostrophic Currents

EkmanDrift

Freshwater Flux

0.05

KE

GPE

Mean State

Geothermal Heat

0.007

3.10.9

Salt Fingering 0.008 Cabbeling ??

Internal Waves & TurbulenceMean Currents

Open OceanTidal Mixing

0.18

DirectConversion0.9

0.3?

Costal &Marginal SeaMixing??

0.04

Wind Energy Input

KE & GPE

Surface Waves

BeachProcess

ViscousDissipation

????

LoadingAtmospheric

Baroclinic Instability

ConvectiveAdjustment

DissipationTidal

3.5Bottom Drag

0.4?

60

18−20

0.5−2 ?

Surface WaveEnhancedMixing

Breaking& Dissipation

WavesSurface

0.24?

Motivation• Thermal energy to mechanical energy

conversion rate

• Need more energy? Strong mixing applies to place with strong stratification!

• Upper ocean where surface wave enhanced turbulence is the right place

zp g kρ− ∇ ⋅ =u

9/15/2006 10

Surface wave energy input (mW/m/m, Wang & Huang, 2004)

9/15/2006 11

Wind energy is more important:1) It is much larger than tidal energy (64 vs 0.9TW)2) It dominates the circulation in the upper ocean

3) It varies greatly on time scale shorter than 100 yr

Increased 15% since 1980

9/15/2006 12Huang, R. X., W. Wang, and L. L. Liu, 2006, Deep Sea Research II

Surface wave enhanced mixing, wind-driven upwelling and deep tidal mixing

9/15/2006 13

Cooling

. .

Wind Heating

Stratification

500−2000mWeak stratificationweak mixing

2500−bottomVery weak stratificationStrong mixing

Wind−drivenupwelling

Tidal−drivendeep mixing

DeepwaterformationSurface wave

enhanced mixing

Strong stratificationStrong mixingLarge source of GPE

0−500m

Small source of GPE

Small source of GPE

How much GPE can be generated?(in units of TW, assuming conversion efficiency of 0.2)

• Tidal dissipation: In open ocean, 0.8X0.2=0.16• Wind to geostrophic currents; 0.9?• A substantial portion of this is transferred to

meso-scale eddies• How meso-scale eddies loose their energy

remains unclear --- breaking down of balance? Bottom form drag? Bottom friction? Lee waves in ACC?

• Final contribution may be much smaller, this will an important subject for future study.

• Wave enhanced turbulence: 1-2 ??.9/15/2006 14

Can Surface Waves affect THC?

9/15/2006 15

• Vertical mixing in deep ocean can drive THC. How can surface waves affect mixing through generation of internal waves and turbulence in the ocean ?.

• Answer: Enhanced mixing in the upper ocean can drive strong THC

• At the upper ocean, there is a mixed layer and there is no stratification there; thus, mixing cannot generated GPE.

• Answer: • 1) can be 0, infinite or finite.• 2) The base of mixed layer might be a site of

large source of GPE.0 × ∞

Surface enhanced mixing

Strong meridional overturning

More heat penetration into the thermocline

Strong Meridional baroclinic pressure difference

Stronger poleward heat flux

9/15/2006 16

Dynamic structure of the turbulent boundary layer in the upper ocean

9/15/2006 17

9/15/2006 18

Diffusivity profiles Observations and theory

10−2

10−1

100

101

102

103

104

10−1

100

101

102

KT

z

Gemmrich 1999Moum et al. 1995Michett et al. 2004Chereskin 1995Stevens et al. 2004

Dissipation Rate ProfilesTwo-segment models

• The Craig & Banner (1994) model

• The Hybrid model (Baumert, 2005)

( ) ( ) ( )3 1/ 2* 0

0 0

1 3 ,n

ww q b

u zz BS z zz z z z

ε ακ

−⎡ ⎤⎛ ⎞⎢ ⎥= + <⎜ ⎟+ +⎢ ⎥⎝ ⎠⎣ ⎦

( )( ) ( )

3 3/2 3*w 0 *w

5/200

150u u= ,z+zz+z b

zz z zεκκ

+ <

9/15/2006 19

9/15/2006 20

Surface wave enhanced turbulence dissipation

10−6

10−4

10−2

100

102

10−2

10−1

100

101

102

103

104

ε Hs / F

z / H

s

CB94 (Full)CB94 (Simple)Baumert 2005Baumert 2005(Modified)Wall LawTerray 1996Drennan 1996Anis & Moum 1995Kocsis et al. 1999Michett et al. 2004Ravens et al. 2000

Wave enhanced turbulence dissipation rate in mW/m/m

9/15/2006 210 200 400 600 800

−80

−60

−40

−20

0

20

40

60

80

GW/degree

b) Zonal distribution

30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W

80S

60S

40S

20S

0

20N

40N

60N

80N

a) Surface Wave Enhanced Dissipation Rate, in GW/grid

10

10

10

10

20

20

20

20

20

40

40

40

40

40

40

40

40

40

80 80

80

80 80

80

120 120

120120

120

120

200 200

200200

200

300

300400

III. Idealized Numerical experiments

9/15/2006 22

• A mass-conserving model, PCOM (pressure-coordinate ocean model, Huang et al., 2001)

• Temperature relaxation, linear equation of state

• A 60X60 degree model, mimicking the North Atlantic

• Flat bottom, 5000 m deep.• Spin up from a state of rest and T=0^oC.• No freshwater flux forcing• No wind stress forcing --- wind stress is to

provide small-scale turbulence energy only.• Vertical mixing profiles specified a priori.

Surface-enhanced vs Bottom-enhanced mixing

kappa profiles

9/15/2006 23

A1 B1 E1 F1

MOC(Sv) 8.50 16.40 8.55 16.44

PHF(PW) 0.063 0.255 0.063 0.255VM(GW) 6.96 34.86 6.87 34.90CV(GW) 6.17 28.87 6.21 28.91

9/15/2006 24

Result from Set 2

9/15/2006 25

MOC/PHF vsGPE source and PE->KE transfer

100

101

102

0

5

10

15

20

Verical mixing (GW)

Sv

a) MOC vs Vert. Mix.

10−2

100

102

0

5

10

15

20

PE−>KE (GW)

Sv

b) MOC vs PE−>KE conversion

100

101

102

10−2

10−1

100

Vertical Mixing (GW)

PW

c) PHF vs Vert. Mix.

10−2

100

102

10−2

10−1

PE−>KE (GW)

PW

d)PHF vs PE−>KE conversion

1.163 4.168ln VMEψ = +

9/15/2006 26

GPE due to vertical mixing and convective adjustment

−10 −5 0 5 10 15−1

−0.9

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

GW per 100m

Dep

th, k

m

CV (κ=0.1)VM (κ=0.1)Net (κ=0.1)CV (κ surface−enhanced to 10)VM (κ surface−enhanced to 10)Net (κ surface−enhanced to 10)

It is always surface trapped

GPE source/sink ( GW/2 degree/100m )

9/15/2006 27

0 10 20 30 40 50 60−0.5

−0.45

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

Dept

h, k

m

a) Vert. Mixing, κ=0.1

0

0

0.02

0.02

0.04

0.06

0.08

0.1

0.12

0.140.160.180.2

0 10 20 30 40 50 60−0.5

−0.45

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0b) Conv. Adjust., κ=0.1

−0.2−0.1

−0.02

0

0 10 20 30 40 50 60−0.5

−0.45

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

Latitude

Dept

h, k

m

c) Vert. Mixing, κ=0.1 (Enhanced to 10cgs)

0.1

0.1

0.20.3

0.40.5

0.6

0.7

0.80.91

0 10 20 30 40 50 60−0.5

−0.45

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

Latitude

d) Conv. Adjust., κ=0.1 (Enhanced to 10cgs)

−0.3

−0.2

−0.1−0.02

0

0

0

0

0

GPE usable and generated

9/15/2006 280 10 20 30 40 50 60

0

20

40

60

80

100

120

Latitude

Gw

/2o L

atitu

de

ba

nd

a) Wave breaking energy rate

For all gridsFor stratified grids

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

Latitude

Gw

/2o L

atitu

de

ba

nd

b) GPE generated from the model

From stratified grids,κ0=0.1

From all grids,κ0=0.1

From stratified grids,κ0=0.02

From all grids,κ0=0.02A huge amount of

energy is wasted in the unstratified part of the water column

9/15/2006 29

Poleward heat flux

0 10 20 30 40 50 600

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45Poleward Heat Flux

Latitude

PW

κ=0.1−100κ=0.02−100κ=0.1−10κ=0.02−10κ=0.1−100κ=0.02−100κ=0.1−1−100κ=0.02−1−100κ=0.263

Equatorward shift due toSurface-enhanced mixing

IV. THC driven by wave enhanced turbulence

• A. Wind stress treated as a source of kinetic energy for turbulence and internal wave only, i.e., there is no large-scale wind stress

• B. Wind stress contribute to large-scale wind-driven circulation and small scale mixing in the upper ocean

9/15/2006 30

9/15/2006 31

IV. A. Wave enhanced turbulence only

• Temperature relaxation and no freshwater flux.

• Wind interpreted as meridional-vertical distribution of wave enhanced turbulence dissipation rate average over the North Atlantic Ocean (60x60 degrees).

• Mixing coefficient sets to be < 100cm^2/s.

2/ , 0.2Nκ αε α= =

Diffusivity profiles inferred from Arabic Sea Experiment

Asuume: kappa=200/100 in ML, kappa=0.1 below ML

9/15/2006 320 50 100 150 200 250 300 350−150

−100

−50

0

Day

Dep

th (m

)

10−4

10−3

10−2

−150

−100

−50

0

κ (10−4m2/s)

Annual meanmixed layer depth

A

B

a) MIxed layer depth b) Annual mean mixing profile

Implications

• For models that do not resolve the diurnal cycle of mixed layer, strong diffusion just below the base of the mixed layer is neededin order to simulate the dynamic effect of surface wave enhanced turbulence in the upper ocean.

9/15/2006 33

9/15/2006 34

Result from Set 3

Energy balance of the model ocean

9/15/2006 35

10−5

10−4

10−3

10−2

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

Dep

th (

km)

κ

y=31oNy=41oN

0 10 20−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0T

10−5

10−4

10−3

10−2

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

κ (m2/s)

Dep

th (

km)

y=19oNy=41oN

0 10 20−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

oC

10−4

10−3

10−2

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0Input/Output Energy

y=31oN, inputy=31oN, outputy=41oN, inputy=41oN, output

0 50 100−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0Accumulated Energy

10−4

10−3

10−2

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

E (mW/m3)

y=19oN, inputy=19oN, outputy=41oN, inputy=41oN, output

0 50 100−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

%

a) b) c) d)

e) f) g) h)

IV. B. How does wind stress change the dynamical picture?

9/15/2006 36

Wind stress profile

−0.5 0 0.5 10

10

20

30

40

50

60

Latit

ude

τx (dyn/cm2)

a) Wind Stress

5 10 15 20 25 30 35 40 45 50 55

5

10

15

20

25

30

35

40

45

50

55

Longitude

b) Streamfunction (Sv)

−21

−18

−15

−15

−12

−12

−9

−9

−9−6

−6

−6

−6

−3

−3

−3

−3

0

0

0

0

0

0

3

3

3

3

3

3

6

6

6

6

9

9

12

15

How does adding on the wind stress modify the dynamical picture?

• Introducing the wind-driven gyres modifies stratification in the upper ocean, and thus enhances the generation of GPE through mixing.

• Other processes, such as the seasonal cycle and the diurnal cycle of the mixed layer can also help to maintain a strong stratification in the ocean, and thus gives rise to a large source of GPE generated by wave enhanced turbulence dissipation. 9/15/2006 37

9/15/2006 38

Temperature sections

0 10 20 30 40 50 60−1

−0.9

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0a)κ=0.1, No Wind/Waves

Latitude

Dep

th (k

m)

33

5

5

7

7

9111315171921

0 10 20 30 40 50 60−1

−0.9

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0b) κ=0.1, Wind only

Latitude

3

3

5

577

911

1315171921

0 10 20 30 40 50 60−1

−0.9

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0c)κ=0.1, Waves only

Latitude

Dep

th (k

m)

3

3 5

5 77

911

13151719

21

0 10 20 30 40 50 60−1

−0.9

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0d) κ=0.1, Wind & Waves

Latitude

3

3

5

5

7

79

1113

1517

1921

9/15/2006 39

Overturning streamfunction

0 10 20 30 40 50 60

−4.5

−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

a) κ=0.1

Dep

th (k

m)

22

2

2

2

4

4

4

6

6

8

0 10 20 30 40 50 60

−4.5

−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

b) κ=0.1, Wind only−4 −2

0

0 0

00

2

22 2

2

22

2 244

4

4

4

4

6

6

6

6

6

8

8

8

8

10

10

10

12

12

12

1414

16

0 10 20 30 40 50 60

−4.5

−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

c) κ=0.1, Waves only

Latitude

Dep

th (k

m)

0

22

22

2

2

2

4

4

44

4

4

6

6

6

88

8

10

1012

0 10 20 30 40 50 60

−4.5

−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

d) κ=0.1, Wind & Waves

Latitude

−4−2

0

0

0

00

22

22

2

2

2

2

4

444

4

4

4

4

6

6

6

6

6

8

8

8

8

10

10

10

10

12

12

12

14

14

14

16

16

9/15/2006 40

Diff. in Temp & MOC, with wave Wind - No Wind

0 10 20 30 40 50 60−1000

−900

−800

−700

−600

−500

−400

−300

−200

−100

0a)∆ T, Wind − No Wind

Latitude

De

pth

(m

)

−2

−1.5 −1

−1

−0.5−0.5

0

0

0

0.5

0.5

1

1

1

1.5

1.5

1.5

2

2

2

2.5

2.5

2.5

3

3

3.5

4

0 10 20 30 40 50 60

−4.5

−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

b)∆ ψ, Wind − No Wind

Latitude

De

pth

(km

)

−4

−2

−2

0

0

0

0

0

00 0

22

2

2

2

2

44

4

4

6810121416

WarmingCooling Surface wind-driven gyres

Enhanced

MOC

GPE balance, with/without wind

Enhanced GPE usable and generated from the model

0 10 20 30 40 50 600

1

2

3

4

5

6

7

8

Latitude

Gw

/2o L

atit

ude b

and

a) Wave energy for stratified grids

Waves & WindWaves only

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

1.2

Latitude

Gw

/2o L

atit

ud

e b

an

d

b) GPE generated from the model

Stratified grids,Waves onlyAll grids,Waves onlyStratified grids,Waves & WindAll grids,Waves & Wind

9/15/2006 41

0 5 10 15 200

2000

4000

6000

8000

10000

12000

A1

Wa1

Wi1

WW1

A2

Wa2

Wi2

WW2

a) MOR & TKE

MOR (Sv)

TKE

(1012

J)

0 5 10 15 20 25 300.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

GPE due to VM (GW)

PH

F (1

015 W

)A1

Wa1

Wi1

WW1

A2

Wa2Wi2

WW2

b) GPE & PHF

9/15/2006 42

Conclusion:– Wind energy input through surface waves may be one

of the most important unknowns– Relatively weak stratification in combination of strong

stirring in the upper ocean may produce large amount of GPE

– Surface wave enhanced turbulence may be one of the most important source of GPE driving THC

– Parameterizing wave enhanced turbulence is an important aspect of OGCM

– Including the seasonal/diurnal cycles may substantially increase the source/sink of GPE

9/15/2006 43