skyler goldman, meteorology, dmes relationship between roughness length, static stability, and drag...
TRANSCRIPT
Skyler Goldman, Meteorology, DMES
RELATIONSHIP BETWEEN ROUGHNESS LENGTH, STATIC STABILITY, AND DRAG COEFFICIENT IN A DUNE ENVIRONMENT
Introduction to the subject• Drag (Wind) coefficient- quantifies the drag or
resistance of an object in a fluid environment such as air or water. – A lower drag coefficient indicates the object will have
less aerodynamic or hydrodynamic drag. – Less Drag = Less Resistance!!
• For small scale flow (dune environment), a better characterization of the surface drag can go a long way towards understanding and modeling the air flow.
• Understanding what affects wind flow and magnitude is important to meteorology and engineering
Data Collected• Temperature and wind
collected using anemometer attached to stadia rod and elevated from 6.5 ft to 25 ft over seven different stations (vegetated and non-vegetated) on six different days
Courtesy of Sarah Collins
Neutral vs. Corrected Drag Coefficient
• Overall goal is to draw comparisons between drag coefficient and wind profiles.
• 1st Type of drag coefficient (Cd)– Neutral (dependent on roughness length (zo)
Increasing roughness length (zo)
(Figures from Beljaars, A. The Parameterization of the Boundary Layer, 5/1992. European Centre for Medium-Range European Weather Forecasts)
Heigh
t (m)
Wind Speed (m/s)
The impact of surface friction on atmosphere extends upwardsas zo increases.
Neutral Drag Coefficient
22 )][ln( o
rd z
zkC
K = von Karman constant (0.4)Zr = Reference height (6.5 ft)Zo = Roughness length
Higher the roughness length, higher the drag coefficient
2nd Type of Drag Coefficient• Corrected
(dependent on stability factor and roughness)
MOMENTUM
• Momentum moves downward more easily in unstable air than stable. • Near surface, unstable regimeproduces steeper wind profiles
Diagram from: Air-sea Interaction: Laws and Mechanisms, CsanadyStructure of the Atmospheric Boundary Layer, Sorbjan
Corrected Drag Coefficient
22 )]()[ln( L
z
z
zkC r
mo
rd
22 )][ln( o
rd z
zkC
Neutral =
Corrected =
Where is a stability function
But…how do we find this stability function???
)(L
zrm
Correcting for Stability…
• According to theory, the [drag] coefficients are a function of buoyancy and wind shear.
• The exact relationship is not known but is approximated using observed wind, temperature and moisture profiles near the surface.
- (Arya 2001)
Courtesy of Cory Hodes
Profiles vary spatially and temporally
BEACH DUNE CREST WEST OF DUNE
Finding Stability
• To find stability function, a series of equations are used– 1st – Find static stability using temperature,
pressure, and humidity data– 2nd – Determine Richardson Number
• Ri Number = static stability / windshear
– Richardson Number is then related to a buoyancy parameter
– 3rd – Use buoyancy parameter to correct neutral drag coefficient m
What is Expected?• Neutral
– Higher the roughness length, higher the drag coefficient
– Roughness Lengths:
• Vegetated (Ponce)– Station 1: 0.17 ft– Station 2: 0.21 ft– Station 3: 2.44 ft– Station 4: 0.59 ft
• Non Vegetated (Denuded):– Station1: 0.45 ft– Station 2: 2.5 10^-3
ft– Station 3: 1.11 ft
22 )][ln( o
rd z
zkC
Roughness lengths from Sarah CollinsBeach profile map from John Hearin
Wind Flow Survey Profile 6/9/10
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
0 50 100 150 200 250 300 350 400
Horizontal Station from Monument (ft)
Ele
vatio
n (ft
) N
AV
D88
MHHW
R-155T Out
R-155T ReturnStation 2
WATER
Station 1
Station 3
Roughness Length vs. Drag Coefficient
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 0.5 1 1.5 2 2.5 3Roughness
Length (Zo, ft)
Station 1, Denuded Dune
Station 2, Denuded Dune
Station 3, Denuded Dune
Station 1, Ponce Park
Station 2, Ponce Park
Station 3, Ponce Park
Station 4, Ponce Park
Dra
g C
oe
ffic
ien
t (C
d)
22 )][ln( o
rd z
zkC
What is Expected?
• Corrected for Stability
22 )]()[ln( L
z
z
zkC r
mo
rd
Our data
(Arya 2001)
Richardson Number vs. Drag Coefficient
0.0001
0.001
0.01
0.1
1
10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
Richardson Number
Dra
g C
oeff
icie
nt
Station 1: Denuded z_o = 0.45
Station 2: Denuded z_o = 0.0025
Station 3: Denuded z_o = 1.11
Station 1: Ponce z_o = 0.17
Station 2: Ponce z_o = 0.21
Station 3: Ponce z_o = 2.44
Station 4: Ponce z_o = 0.59
Putting it all together…• Based on formulas…
– High stability = low drag– Low stability = high drag
– High roughness length = high drag– Low roughness length = low drag
• Yet…how does this affect the wind profile?
LOWDRAG
HIGH DRAG
Win
d V
ectors
Wind Vectors decreaseWhen subjected to moredrag
Z Z
Wind Speed Wind Speed
GREATER CHANGE IN WIND SPEED OVER
HEIGHT
LITTLE CHANGEIN WIND SPEED OVER HEIGHT
Final Question…
• Evidence of direct relationship between roughness and stability
• Evidence of indirect relationship between drag and stability
• Wind profiles = little wind changes over height with low drag
• Wind profiles = large wind changes over height with high drag
• BUT…do these statements hold with actual data….
5/26/2010
-0.3
-0.1
0.1
0.3
0.5
0.7
0.9
Station 1, Mean HighWater
Station 2, Base of Dune Station 3, Top of Dune Station 4, A1A
Sta
tic
Sta
bili
ty/ D
rag
Co
effi
cien
t
Drag Coeff icient
Station 2
0
10
20
30
0 5 10 15
Wind Speed (m/s)
Hei
ght (
ft)
Station 4
0102030
0 5 10 15
Wind Speed (m/s)
Hei
gh
t (f
t)
Station 3
0102030
0 5 10 15
Wind Speed (m/s)
Hei
ght (
ft)
Station 1
0
10
20
30
0 5 10 15
Wind Speed (m/s)
Hei
ght (
ft)
6/9/2010
0
0.05
0.1
0.15
0.2
0.25
0.3
Station 1: Mean High Water Station 2: Top of Dune Station 3: Between Dune andA1A
Sta
tic
Sta
bil
ity/
Dra
g C
oef
fici
ent
Drag Coeff icient
Station 1
0
20
40
2 4 6 8
Wind Speed (m/s)
Hei
gh
t (f
t)
Station 2
02040
2 4 6 8
Wind Speed (m/s)
Hei
gh
t (f
t)
Station 3
0
20
40
2 4 6 8
Wind Speed (m/s)
Hei
gh
t (f
t)
Conclusions
• Wind profiles on 26 May 2010 appear to be consistent with corrected drag estimates
• This is not true of all sampled days as estimates of zo can vary due to:– wind speed– fetch– wave height for station 1 which is
located near the high tide line.
Questions…
Break is next, followed by:Emily Teske!