Turbulence and Mixing in Shelf Seas

John Simpson, Tom Rippeth, Neil Fisher,Mattias Green Eirwen Williams, Phil Wiles, Matthew Palmer

Funded by the NERC, EU (OAERRE, MABENE, C2C) and Dstl

With technical support from Ray Wilton, Ben Powell& the officers and crew of the Prince Madog

.School of Ocean Sciences,

University of Wales Bangor, Menai Bridge,LL59 5EY, UK

Ysgol Gwyddorau Eigion,Prifysgol Cymru Bangor,

Porthaethwy

Visit our web site at:www.sos.bangor.ac.uk/research/tmiss/index.html

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• Motivation• Measurement capabilities

• Mapping ε in shelf regimes with FLY• ADCP variance method for Production

• Mixing in the pycnocline of the shelf seas

Turbulent processes in shelf seas

Motivation ?

• Key environmental control of:

Fluxes of nutrients/ particles etc. (Mixing) Particle aggregation/disaggregation

Predator-prey encounter rates

• Tests of Turbulence Closure schemes for models

zK

z

v

z

u

z

EK

zt

Ezxq y

Which Properties ? Diffusion TKE production Buoyancy Dissipation

ADCP Variance method

FLYDissipationProfiler

S1 M1

Mixed station M1 observed ε

ε Model MY2.2(with diffusion)

Model MY2.0(no diffusion)

Time(days)

Stratified station S1

T°C

ε (Wm-3)

ε Model MY2.2

ε observed

Model – Observation Inter-comparison

BIG discrepancy between the predicted (using MY2.2 closure scheme) and observed levels of (Simpson et al., 1996).

• ie. The model fails to reproduce the critical dissipation and thus mixing within the thermocline.Bottom

Boundary Layer

Log10 [0 (Wm-3)]

Model

Obs.

Missing physical processes within the model?

S1

z

z

Nzte

A

z

u

2);4/cos(2

))2/22cos(1(22

22

2

zteAN

z

uNP

zz

z

The velocity shear in a boundary layer forced by an oscillating pressure gradient X=A cos ωt

is given by (Lamb p.622):

The corresponding TKE production will be:

2/2

2/24 zN

zz

which increase with height above bed at a rate

zN

2

So that the production (and hence ε ) will exhibit an M4 phase lag of :

The phase of TKE production ?

Phase lag (hours)

Mixed Nz=0.4m2s-1

StratifiedNz=0.025m2s-1

PHASE AMPLITUDE

MixedNz=0.13m2s-1

Liverpool Bay ROFI

186.7 186.8 186.9 187 187.1 187.2 187.3 187.4 187.5 187.6 187.7

T em p era tu re (d eg ree s C )

0

5

10

15

20

25

30

35

Hei

ght a

bove

Bed

(m

)

1 4 .61 4 .71 4 .81 4 .91 5 .01 5 .11 5 .21 5 .31 5 .41 5 .51 5 .61 5 .71 5 .81 5 .91 6 .0

186.7 186.8 186.9 187 187.1 187.2 187.3 187.4 187.5 187.6 187.7

D ec im a l D ay

S a lin ity (P S U )

0

5

10

15

20

25

30

35

Hei

ght a

bove

Bed

(m

)

3 2 .4 5

3 2 .5 5

3 2 .6 5

3 2 .7 5

3 2 .8 5

3 2 .9 5

3 3 .0 5

3 3 .1 5

3 3 .2 5

3 3 .3 5

LB2

Temperature

Salinity

Cycle of epsilon with density

186.7 186.8 186.9 187 187.1 187.2 187.3 187.4 187.5 187.6 187.7

D ecim al D ays

0

5

10

15

20

25

30

35H

eigh

t abo

ve B

ed (

m)

-5.50

-5.00

-4.50

-4.00

-3.50

-3.00

-2.50

-2.00

-1.50

JPO 31,2458-2471 (2001)

Log W/m3

E p silo n (L o g1 0

W m - 3 )

0

5

10

15

20

25

30

35

Hei

ght a

bove

Bed

(m

)

-5 .5 0

-5 .0 0

-4 .5 0

-4 .0 0

-3 .5 0

-3 .0 0

-2 .5 0

-2 .0 0

-1 .5 0

186.7 186.8 186.9 187 187.1 187.2 187.3 187.4 187.5 187.6 187.7

D ec im a l D ay s

U /z (s - 1 )

0

5

10

15

20

25

30

35

Hei

ght a

bove

Bed

(m

)

-0 .0 4

-0 .0 3

-0 .0 2

-0 .0 1

0

0 .0 1

0 .0 2

O b se rv a tio n s - E p s ilo n (L o g1 0

W m - 3 ) w ith D en s ity co n to u rs (k g m - 3 )

0

5

10

15

20

25

30

35

Hei

ght a

bove

Bed

(m

)

-5 .5 0

-5 .0 0

-4 .5 0

-4 .0 0

-3 .5 0

-3 .0 0

-2 .5 0

-2 .0 0

-1 .5 0

186.7 186.8 186.9 187 187.1 187.2 187.3 187.4 187.5 187.6 187.7

D ecim al D ays

C A N U T O w ith N u d g in g -E p s ilo n (L o g1 0

W m - 3 ) w ith D en s ity co n to u rs (k g m - 3 )

0

5

10

15

20

25

30

35

Hei

ght a

bove

Bed

(m

)

-5 .5 0

-5 .0 0

-4 .5 0

-4 .0 0

-3 .5 0

-3 .0 0

-2 .5 0

-2 .0 0

-1 .5 0

GOT Model

k-epsilon +Canuto

Hans Burchard

Karsten Bolding

R a tio o f S h ea r P ro d u c tio n to D iss ip a tio n ra te .

0

5

10

15

20

25

30

35

Hei

ght a

bove

Bed

(m

)

186.7 186.8 186.9 187 187.1 187.2 187.3 187.4 187.5 187.6 187.7

D ec im a l D ay s

R a tio o f B u o y an cy P ro d u c tio n to D iss ip a tio n ra te .

0

5

10

15

20

25

30

35

Hei

ght a

bove

Bed

(m

)

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

-0 .50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

C A w ith N udging

P/ε

B/ε

ADCP Variance Method

z

v

z

uP yx

bbb coswsinvb 444

z

w4

v4

b4

4 3

y

2sin2

bb'w'v

23

24

y