parameterizing energy conversion on rough topography using...
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Parameterizing energy conversion on rough topography using bottom pressure sensors to measure form drag
Sally Warner, Parker MacCreadyUniversity of Washington
Jim Moum, Jonathan Nash, Aurélie MoulinOregon State University
February 21, 2012Ocean Sciences Conference, Salt Lake City, UT
Form drag and mixing
U0
Form dragpressure
Tidalenergyconversion
Form drag causes:
- internal wave generation
- eddy generation
- local mixing and dissipation
Experiment location
Seattle
Tacoma
Edwards et al., 2004
Puget Sound, WA
PointThree Tree
Previous work
McCabe et al., 2006
> Measured the internal form drag
> Measured the external form drag
Our goal> Measure the total form drag with bottom pressure sensors
Internal lee waves
EddyBottom
pressure
Why measure form drag?Find better parameterizations for form drag that can be implemented into larger scale models.
Fine grid resolution resolves form drag>> Drag coefficients well parameterized
Imagine sometopography with tides
Coarse grid resolution does not resolve form drag>> Drag coefficients unknown
Build model
New method: PPODsUse bottom pressure sensors (PPODs) to directly measure form drag.
lon
Three Tree Point Bathymetry
1 km
−122.4 −122.38 −122.36
47.43
47.44
47.45
47.46
47.47
47.4447.4547.46
−200
−100
0
lat
m
ridgetransect
−200
−100
0
Bathymetric height
m
headlandtransect
m−300 −200 −100 0
bottom lander (L1−L7)
autonomous Ppod (P1−P8)
Bottom pressure sensors: PPODs
New method: PPODsAugment bottom pressure sensors with shipboard ADCP, CTD, and microstructure measurements.
lon
Three Tree Point Bathymetry
1 km
−122.4 −122.38 −122.36
47.43
47.44
47.45
47.46
47.47
47.4447.4547.46
−200
−100
0
lat
m
ridgetransect
−200
−100
0
Bathymetric height
m
headlandtransect
m−300 −200 −100 0
bottom lander (L1−L7)
autonomous Ppod (P1−P8)
Shipboard transects with Chameleon profiler
−200
−150
−100
−50
0
dept
h [m
]
12:33
47.4447.44547.4547.45547.46−10
−5
0
5
10
botto
m p
ress
ure
anom
.[m
m e
quiv
. SSH
]
[lat]−10
−5
0
5
10
σθ
[kg m−3]
22.6
22.8
23
23.2
23.4
−200
−150
−100
−50
0
dept
h [m
]
12:33
47.4447.44547.4547.45547.46−10
−5
0
5
10
botto
m p
ress
ure
anom
.[m
m e
quiv
. SSH
]
[lat]−10
−5
0
5
Bottom pressure at max flood
high pressureanomaly on the upstream side
low pressureanomaly on the downstream side
total PPOD pressure– resting pressure– tidal height
= pressure anomaly
lon
1 km
−122.4
−122.38
−122.36
47.43
47.44
47.45
47.46
47.47
47.44
47.45
47.46
−200−100
0
lat
m
ridge
trans
ect
−200−100
0Ba
thym
etric
hei
ght
m
head
land
trans
ect
m
−300
−200
−100
0
current
−200
−150
−100
−50
0
dept
h [m
]
12:33
47.4447.44547.4547.45547.46−10
−5
0
5
10
botto
m p
ress
ure
anom
.[m
m e
quiv
. SSH
]
[lat]−10
−5
0
5
10
σθ
[kg m−3]
22.6
22.8
23
23.2
23.4
−200
−150
−100
−50
0
dept
h [m
]
12:33
47.4447.44547.4547.45547.46−10
−5
0
5
10
botto
m p
ress
ure
anom
.[m
m e
quiv
. SSH
]
[lat]−10
−5
0
5
Density at max flood
Internal lee wave visible in density section
Bottom pressure anomaly from the density section
internal pressure+ external pressure
= PPOD pressure
Internal lee waves
EddyBottom
pressure
−122.4
−122.3
9−
122.3
8−
122.3
7
47.4
4
47.4
45
47.4
5
47.4
55
47.4
6
47.4
65
lat
lon
Max e
bb tid
e
10/2
906:3
9
Sla
ck tid
e
10/2
909:5
8
Max flo
od tid
e
10/2
913:5
8
80 m
48 m
20 m
0.5
m/s
m
−300
−200
−100
0
Eddy currents at max flood
tidalcurrent
20 m48 m80 m
0.5 m/s
Eddy signature visable
Internal lee waves
EddyBottom
pressure
Dissipation at max flood
−200
−150
−100
−50
0
dept
h [m
]
12:33
47.4447.44547.4547.45547.46−10
−5
0
5
10
botto
m p
ress
ure
anom
.[m
m e
quiv
. SSH
]
[lat]−10
−5
0
5
10
σθ
[kg m−3]
22.6
22.8
23
23.2
23.4
−200
−150
−100
−50
0
dept
h [m
]
12:33
47.4447.44547.4547.45547.46−10
−5
0
5
10
botto
m p
ress
ure
anom
.[m
m e
quiv
. SSH
]
[lat]−10
−5
0
547.4447.44547.4547.45547.46
−250
−200
−150
−100
−50
0
dept
h [m
]
Ridge transect [lat]
12:33
log10(ε)
[W kg−1]
−8
−7
−6
−5
Energy dissipation ratein the lee wave is 5x10-5 W/kg
−200
−150
−100
−50
0
dept
h [m
]
12:33
47.4447.44547.4547.45547.46−10
−5
0
5
10
botto
m p
ress
ure
anom
.[m
m e
quiv
. SSH
]
[lat]−10
−5
0
5
10
σθ
[kg m−3]
22.6
22.8
23
23.2
23.4
−200
−150
−100
−50
0
dept
h [m
]
12:33
47.4447.44547.4547.45547.46−10
−5
0
5
10
botto
m p
ress
ure
anom
.[m
m e
quiv
. SSH
]
[lat]−10
−5
0
5
Time series of form drag
Spatial integral of pressure anomalies at every time step gives a time series of form drag
}
tidalvelocity
[m/s]
total form drag and power from PPODs
Large peaks of power during strong flood tides
−0.3
−0.2
−0.1
0
0.1
0.2
−1.5
−1
−0.5
0
0.5
1
1.5
totalinternal
10/26 10/28 10/30 11/1−5
0
5
10
15
20
25
−0.2
−0.1
0
0.1
−1
−0.5
0
0.5
1
−5
0
5
10
15
20
flood tide
−0.3
−0.2
−0.1
0
0.1
0.2
−1.5
−1
−0.5
0
0.5
1
1.5
total
10/26 10/28 10/30 11/1−5
0
5
10
15
20
25
−0.2
−0.1
0
0.1
−1
−0.5
0
0.5
1
−5
0
5
10
15
20
flood tide
form drag[N/m x 104]
power= drag x U
[W/m x 102]
Time series of form dragFlood tide
tidalvelocity
[m/s]
total form drag and power from PPODs
internal form drag and power from density
form drag[N/m x 104]
power= drag x U
[W/m x 102]
Large peaks of power during strong flood tides for both the total form drag and internal form drag
−0.3
−0.2
−0.1
0
0.1
0.2
−1.5
−1
−0.5
0
0.5
1
1.5
totalinternal
10/26 10/28 10/30 11/1−5
0
5
10
15
20
25
−0.2
−0.1
0
0.1
−1
−0.5
0
0.5
1
−5
0
5
10
15
20
flood tide
−0.3
−0.2
−0.1
0
0.1
0.2
−1.5
−1
−0.5
0
0.5
1
1.5
total
10/26 10/28 10/30 11/1−5
0
5
10
15
20
25
−0.2
−0.1
0
0.1
−1
−0.5
0
0.5
1
−5
0
5
10
15
20
flood tide
Time series of form dragFlood tide
Parameterizing form dragtotal
(from PPODs)internal
(from density)
−1.5
−1
−0.5
0
0.5
1
1.5
−0.2 −0.1 0 0.1 0.2
−2
−1
0
1
2
−0.2 −0.1 0 0.1 0.2tidal velocity
[m/s]
form drag[N/m x 104]
power= drag x U
[W/m x 102]
tidal velocity[m/s]
linear wave drag
bluff body drag
2 parameterizations:
DW
C hU UBBD T T=
12 0ρ
DW
NU hwaveT=
πρ
8 02
Drag coefficients in modelsIn a 5-km grid cell: > without Three Tree Point, just frictional drag CD = 3x10-3
> with Three Tree Point, frictional and form drag CD = 3x10-2
>>> Drag is 10x higer with form drag than just with frictional drag in this 5 km x 5 km box
5 km
5 km
Conclusions• Bottom pressure sensors (PPODs) provide a relatively
inexpensive — but accurate and easy — way to directly measure the total form drag on under-sea topography.
• The form drag at Three Tree Point is significantly larger than frictional drag.
• Using bottom pressure measurements, we have made a step towards better form drag parameterizations of tidal flow over oceanographic topography.
More PPODs and form drag:
Downslope flows and Bernoulli: Toward a direct measure of topographic form drag
Jim Moum, Uwe Stoeber and Jonathan Nash
Wednesday
#B2125
Eddy pressure from model
negative surface pressure anomaly
Internal lee waves
SurfaceeddyBottom
pressure
external pressure
[± 1 cm]
internal pressure
[± 1 cm]
total bottom pressure
[± 1 cm]
surface vorticity
[10-3 1/s]
positive internal pressure anomaly
external and internal pressures counteract each other
Bottom pressure anomalies
total PPOD pressure– resting pressure– tidal height
= pressure anomaly
47.4447.4547.46
−200
−100
0
lat
m
ridgetransect
Pressure anomalies along the ridge transect
−0.20
0.2tid
al c
urre
nts
[m s−1
]
−505
[m
m]
−505
[m
m]
−505
[m
m]
−505
[m
m]
−505
[m
m]
10/29 10/30 10/31
−505
[m
m]
Nor
th s
ide
Hea
dlan
d cr
est
Sout
h si
deebb tide flood
tideebb floodN
ort
hC
rest
Sou
th
Parameterizing form drag
linear wave drag
bluff body dragDW
C hU UBBD T T=
12 0ρ
DW
NU hwaveT=
πρ
8 02
0
100
200
300
400
500[W
m−1
]
ridge line headland line
totalbluff bodywave
totalbluff bodywave
internal
Edwards, et al.friction
average power[W/m]
0
100
200
300
400
500
[W m
−1]
ridge line headland line
totalbluff bodywave
totalbluff bodywave
internal
Edwards, et al.friction
internal (from density pertubations)
total(from PPODs)