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Skyler Goldman, Meteorology, DMES RELATIONSHIP BETWEEN ROUGHNESS LENGTH, STATIC STABILITY, AND DRAG COEFFICIENT IN A DUNE ENVIRONMENT

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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

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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

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Neutral vs. Corrected Drag Coefficient Overall goal is to draw comparisons between drag coefficient and wind profiles. 1 st Type of drag coefficient (C d ) –Neutral (dependent on roughness length (z o ) Increasing roughness length (z o ) (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 upwards as z o increases.

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Neutral Drag Coefficient K = von Karman constant (0.4) Z r = Reference height (6.5 ft) Z o = Roughness length Higher the roughness length, higher the drag coefficient

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2 nd 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 regime produces steeper wind profiles Diagram from: Air-sea Interaction: Laws and Mechanisms, Csanady Structure of the Atmospheric Boundary Layer, Sorbjan

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Corrected Drag Coefficient Neutral = Corrected = Where is a stability function But…how do we find this stability function???

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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)

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Courtesy of Cory Hodes Profiles vary spatially and temporally BEACH DUNE CREST WEST OF DUNE

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Finding Stability To find stability function, a series of equations are used –1 st – Find static stability using temperature, pressure, and humidity data –2 nd – Determine Richardson Number Ri Number = static stability / windshear –Richardson Number is then related to a buoyancy parameter –3 rd – Use buoyancy parameter to correct neutral drag coefficient

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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 Roughness lengths from Sarah Collins Beach profile map from John Hearin Station 2 WATER Station 1 Station 3

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What is Expected? Corrected for Stability Our data (Arya 2001)

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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?

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LOW DRAG HIGH DRAG Wind Vectors Wind Vectors decrease When subjected to more drag Z Z Wind Speed GREATER CHANGE IN WIND SPEED OVER HEIGHT LITTLE CHANGE IN WIND SPEED OVER HEIGHT

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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….

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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 z o can vary due to: –wind speed –fetch –wave height for station 1 which is located near the high tide line.

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Questions… Break is next, followed by: Emily Teske!

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