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)

Height (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( Lz

zzkC r

mo

rd

22 )][ln( o

rd z

zkCNeutral =

Corrected =

Where is a stability function

But…how do we find this stability function???

)(Lzr

m

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)

Elev

atio

n (ft

) NA

VD88

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 DuneStation 2, Denuded DuneStation 3, Denuded DuneStation 1, Ponce ParkStation 2, Ponce ParkStation 3, Ponce ParkStation 4, Ponce Park

Dra

g C

oeff

icie

nt (C

d)

22 )][ln( o

rd z

zkC

What is Expected?• Corrected for Stability

22 )]()[ln( Lz

zzkC 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

oeffi

cien

t

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

Wind Vectors 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

Stat

ic S

tabi

lity/

Dra

g C

oeff

icie

nt

Drag Coeff icient

Station 2

0102030

0 5 10 15

Wind Speed (m/s)

Hei

ght (

ft)

Station 4

0102030

0 5 10 15

Wind Speed (m/s)

Hei

ght (

ft)

Station 3

0102030

0 5 10 15

Wind Speed (m/s)

Hei

ght (

ft)

Station 1

0102030

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

Stat

ic S

tabi

lity/

Dra

g Co

effic

ient

Drag Coeff icient

Station 1

0

20

40

2 4 6 8Wind Speed (m/s)

Hei

ght (

ft)

Station 2

02040

2 4 6 8

Wind Speed (m/s)

Hei

ght (

ft) Station 3

02040

2 4 6 8

Wind Speed (m/s)

Hei

ght (

ft)

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!