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
Which Properties ?
Diffusion
TKE production
Buoyancy
Dissipation
E
 
E 
u
v


 y
 Kz

 Kq
  x
t
z 
z 
z
z
z
ADCP Variance method
FLY
Dissipation
Profiler
M1
Mixed station M1
observed ε
Time(days)
ε Model MY2.2
(with diffusion)
Model MY2.0
(no diffusion)
Stratified station S1
T°C
ε (Wm-3)
ε observed
ε Model MY2.2
Model – Observation Inter-comparison
Model
S1
Obs.
Bottom
Boundary
Layer
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.
Log10 [0 (Wm-3)]
Missing physical processes within the model?
The phase of TKE production ?
The velocity shear in a boundary layer forced by an oscillating pressure gradient X=A cos ωt
is given by (Lamb p.622):
u
A
 2 e z cos(t  z   / 4);
z



2N z
The corresponding TKE production will be:
 u 
P  N z  
 z 
N z A2  2  2 z

e (1  cos( 2t  2z   / 2))
2
2

So that the production (and hence ε ) will exhibit an M4 phase lag of :
 4  2 z   / 2 
2
z  /2
Nz
which increase with height above bed at a rate
2
Nz
PHASE
Mixed
Nz=0.4m2s-1
Stratified
Nz=0.025m2s-1
Phase lag (hours)
AMPLITUDE
Mixed
Nz=0.13m2s-1
Liverpool Bay ROFI
Temperature (degrees C)
35
LB2
Temperature
Height above Bed (m)
30
25
20
15
10
5
0
186.7 186.8 186.9 187 187.1 187.2 187.3 187.4 187.5 187.6 187.7
16.0
15.9
15.8
15.7
15.6
15.5
15.4
15.3
15.2
15.1
15.0
14.9
14.8
14.7
14.6
Salinity (PSU)
35
33.35
30
Salinity
Height above Bed (m)
33.25
25
33.15
33.05
20
32.95
15
32.85
32.75
10
32.65
5
32.55
0
186.7 186.8 186.9 187 187.1 187.2 187.3 187.4 187.5 187.6 187.7
Decimal Day
32.45
Height above Bed (m)
Cycle of epsilon with density
Log W/m3
35
-1.50
30
-2.00
-2.50
25
-3.00
20
-3.50
15
-4.00
10
-4.50
-5.00
5
-5.50
0
186.7 186.8 186.9
187
187.1 187.2 187.3 187.4 187.5 187.6 187.7
Decimal Days
JPO 31,2458-2471
(2001)
Epsilon (Log
10
Wm-3)
-1.50
35
-2.00
Height above Bed (m)
30
-2.50
25
-3.00
20
-3.50
15
-4.00
10
-4.50
5
-5.00
-5.50
0
U/z (s-1)
Height above Bed (m)
35
30
0.02
25
0.01
20
0
15
-0.01
10
-0.02
5
-0.03
0
186.7
186.8
186.9
187
187.1
187.2
187.3
Decimal Days
187.4
187.5
187.6
187.7
-0.04
Observations - Epsilon (Log
10
Wm-3) with Density contours (kg m-3)
-1.50
35
-2.00
30
Height above Bed (m)
-2.50
25
-3.00
20
-3.50
15
-4.00
-4.50
10
-5.00
5
-5.50
0
CANUTO with Nudging -Epsilon (Log
10
Wm-3) with Density contours (kg m-3)
-1.50
35
-2.00
30
k-epsilon +Canuto
Hans Burchard
Karsten Bolding
-2.50
Height above Bed (m)
GOT Model
25
-3.00
20
-3.50
15
-4.00
-4.50
10
-5.00
5
-5.50
0
186.7
186.8
186.9
187
187.1
187.2
187.3
Decimal Days
187.4
187.5
187.6
187.7
Ratio of Shear Production to Dissipation rate.
35
2.00
30
P/ε
Height above Bed (m)
1.75
1.50
25
1.25
20
1.00
0.75
15
0.50
10
0.25
0.00
5
-0.25
0
-0.50
Ratio of Buoyancy Production to Dissipation rate.
35
0.40
B/ε
Height above Bed (m)
30
0.30
0.20
25
0.10
20
0.00
15
-0.10
-0.20
10
-0.30
5
-0.40
0
186.7
186.8
186.9
187
187.1
187.2
187.3
Decimal Days
187.4
187.5
187.6
187.7
-0.50
ADCP Variance Method
z
v4
b4
b  b  b
b4  v4 sin  w4 cos 
2
2


b 4  b3
y  v' w ' 
2 sin 2
w4
4
3

y
u
v
P   x
 y
z
z