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Atmospheric boundary layers and turbulence I Wind loading and structural response Lecture 6 Dr. J.D. Holmes
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Atmospheric boundary layers and turbulence Wind speeds from 3 different levels recorded from a synoptic gale
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Atmospheric boundary layers and turbulence Features of the wind speed variation : Increase in mean (average) speed with height Turbulence (gustiness) at each height level Broad range of frequencies in the fluctuations Similarity in gust patterns at lower frequencies
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Atmospheric boundary layers and turbulence Mean wind speed profiles : Logarithmic law 0 - surface shear stress a - air density integrating w.r.t. z : u = friction velocity = ( 0 / a )
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Atmospheric boundary layers and turbulence Logarithmic law k = von Karman’s constant (constant for all surfaces) z o = roughness length (constant for a given ground surface) logarithmic law - only valid for z >z o and z < about 100 m
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Atmospheric boundary layers and turbulence Modified logarithmic law for very rough surfaces (forests, urban) z h = zero-plane displacement z h is about 0.75 times the average height of the roughness
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Atmospheric boundary layers and turbulence logarithmic law applied to two different heights or with zero-plane displacement :
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Atmospheric boundary layers and turbulence Surface drag coefficient : Non-dimensional surface shear stress : from logarithmic law :
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Atmospheric boundary layers and turbulence Terrain types :
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Atmospheric boundary layers and turbulence Power law = changes with terrain roughness and height range z ref = reference height
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Atmospheric boundary layers and turbulence Matching of power and logarithmic laws : z o = 0.02 m = 0.128 z ref = 50 metres
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Atmospheric boundary layers and turbulence Mean wind speed profiles over the ocean: Surface drag coefficient ( ) and roughness length (z o ) vary with mean wind speed g - gravitational constant a - empirical constant substituting : a lies between 0.01 and 0.02 (Charnock, 1955) Implicit relationship between z o and U 10
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Atmospheric boundary layers and turbulence Mean wind speed profiles over the ocean: Assume g = 9.81 m/s 2 ; a = 0.0144 (Garratt) ; k =0.41 Applicable to non-hurricane conditions
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Atmospheric boundary layers and turbulence Relationship between upper level and surface winds : Geostrophic drag coefficient Rossby Number : balloon measurements : C g = 0.16 Ro -0.09 (Lettau, 1959) U 10, terrain 1 u *,terrain 1 U g u *,terrain 2 U 10, terrain 2 Log law Lettau Lettau Log law Can be used to determine wind speed near ground level over different terrains :
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Atmospheric boundary layers and turbulence Mean wind profiles in hurricanes : Aircraft flights down to 200 metres Sonic radar (SODAR) measurements in Okinawa Drop-sonde (probe dropped from aircraft - tracked by satellite) : recently started Tower measurements not enough usually in outer radius of hurricane and/or higher latitudes
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Atmospheric boundary layers and turbulence Mean wind profiles in hurricanes : Northern coastline of Western Australia Exmouth EXMOUTH GULF North West Cape US Navy antennas 100 km Profiles from 390 m mast in late nineteen-seventies
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Atmospheric boundary layers and turbulence Mean wind profiles in hurricanes : In region of maximum winds : steep logarithmic profile to 60-200 m Nearly constant mean wind speed at greater heights for z < 100 m U z = U 100 for z 100 m
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Atmospheric boundary layers and turbulence Mean wind profiles in thunderstorms (downbursts) : Doppler radar Model of Oseguera and Bowles (stationary downburst): Some tower measurements (not enough) r - radial coordinate R - characteristic radius z * - characteristic height out of the boundary layer - characteristic height in the boundary layer - scaling factor Horizontal wind profile shows peak at 50-100 m
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Atmospheric boundary layers and turbulence Mean wind profiles in thunderstorms (downbursts) : Model of Oseguera and Bowles (stationary downburst) : R = 1000 m r/R = 1.121 z * = 200 metres = 30 metres = 0.25 (1/sec)
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Atmospheric boundary layers and turbulence Mean wind profiles in thunderstorms (downbursts) : Add component constant with height (moving downburst) : R = 1000 m r/R = 1.121 z * = 60 metres = 50 metres = 1.3 (1/sec) U const = 35 m/s
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Atmospheric boundary layers and turbulence Turbulence represents the fluctuations (gusts) in the wind speed It can usually be represented as a stationary random process
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Atmospheric boundary layers and turbulence Components of turbulence : u(t) - longitudinal - parallel to mean wind direction - parallel to ground (usually horizontal) ground U+u(t) w(t) - right angles to ground (usually vertical) w(t) v(t) - parallel to ground - right angles to u(t) v(t)
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Atmospheric boundary layers and turbulence Turbulence intensities : standard deviation of u(t) : I u = u / U (longitudinal turbulence intensity) (non dimensional) I v = v / U (lateral turbulence intensity) I w = w / U (vertical turbulence intensity)
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Atmospheric boundary layers and turbulence Turbulence intensities : v 2.2u * I u = u / U from logarithmic law w 1.37u * near the ground, u 2.5u *
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Atmospheric boundary layers and turbulence Turbulence intensities : rural terrain, z o = 0.04 m :
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Atmospheric boundary layers and turbulence Probability density : for u(t) : The components of turbulence (constant U) can generally be represented quite well by the Gaussian, or normal, p.d.f. : for v(t) : for w(t) :
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End of Lecture 6 John Holmes 225-405-3789 JHolmes@lsu.edu
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