Wind loading and structural response Lecture 6 Dr

Wind loading and structural response Lecture 6 Dr. J. D. Holmes Atmospheric boundary layers and turbulence I

Atmospheric boundary layers and turbulence Wind speeds from 3 different levels recorded from a synoptic gale

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

Atmospheric boundary layers and turbulence • Mean wind speed profiles : • Logarithmic law 0 - surface shear stress a - air density u = friction velocity = ( 0/ a) integrating w. r. t. z :

Atmospheric boundary layers and turbulence • Logarithmic law • k = von Karman’s constant (constant for all surfaces) • zo = roughness length (constant for a given ground surface) logarithmic law - only valid for z >zo and z < about 100 m

Atmospheric boundary layers and turbulence • Modified logarithmic law for very rough surfaces (forests, urban) • zh= zero-plane displacement zh is about 0. 75 times the average height of the roughness

Atmospheric boundary layers and turbulence • logarithmic law applied to two different heights • or with zero-plane displacement :

Atmospheric boundary layers and turbulence • Surface drag coefficient : Non-dimensional surface shear stress : from logarithmic law :

Atmospheric boundary layers and turbulence • Terrain types :

Atmospheric boundary layers and turbulence • Power law • = changes with terrain roughness and height range zref = reference height

Atmospheric boundary layers and turbulence • Matching of power and logarithmic laws : zo = 0. 02 m = 0. 128 zref = 50 metres

Atmospheric boundary layers and turbulence • Mean wind speed profiles over the ocean: • Surface drag coefficient ( ) and roughness length (zo) vary with mean wind speed (Charnock, 1955) g - gravitational constant a - empirical constant a lies between 0. 01 and 0. 02 substituting : Implicit relationship between zo and U 10

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

Atmospheric boundary layers and turbulence • Relationship between upper level and surface winds : • Geostrophic drag coefficient Rossby Number : balloon measurements : Cg = 0. 16 Ro-0. 09 (Lettau, 1959) Can be used to determine wind speed near ground level over different terrains : Log law Lettau Log law U 10, terrain 1 u*, terrain 1 Ug u*, terrain 2 U 10, terrain 2

Atmospheric boundary layers and turbulence • Mean wind profiles in hurricanes : • Aircraft flights down to 200 metres • Drop-sonde (probe dropped from aircraft - tracked by satellite) : recently started • Sonic radar (SODAR) measurements in Okinawa • Tower measurements • not enough • usually in outer radius of hurricane and/or higher latitudes

Atmospheric boundary layers and turbulence • Mean wind profiles in hurricanes : North West Cape US Navy antennas Exmouth EXMOUTH GULF 100 km • Northern coastline of Western Australia • Profiles from 390 m mast in late nineteen-seventies

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 Uz = U 100 for z 100 m

Atmospheric boundary layers and turbulence • Mean wind profiles in thunderstorms (downbursts) : • Doppler radar • Some tower measurements (not enough) • Horizontal wind profile shows peak at 50 -100 m • Model of Oseguera and Bowles (stationary downburst): r - radial coordinate R - characteristic radius z* - characteristic height out of the boundary layer - characteristic height in the boundary layer - scaling factor

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)

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) Uconst = 35 m/s

Atmospheric boundary layers and turbulence Turbulence represents the fluctuations (gusts) in the wind speed It can usually be represented as a stationary random process

Atmospheric boundary layers and turbulence Components of turbulence : • u(t) - longitudinal - parallel to mean wind direction - parallel to ground (usually horizontal) • v(t) - parallel to ground - right angles to u(t) • w(t) - right angles to ground (usually vertical) w(t) v(t) U+u(t) ground

Atmospheric boundary layers and turbulence Turbulence intensities : • standard deviation of u(t) : Iu = u / U (longitudinal turbulence intensity) Iv = v / U (lateral turbulence intensity) Iw = w / U (vertical turbulence intensity) (non dimensional)

Atmospheric boundary layers and turbulence Turbulence intensities : near the ground, u 2. 5 u* Iu = u / U from logarithmic law v 2. 2 u* w 1. 37 u*

Atmospheric boundary layers and turbulence Turbulence intensities : rural terrain, zo = 0. 04 m :

Atmospheric boundary layers and turbulence Probability density : • The components of turbulence (constant U) can generally be represented quite well by the Gaussian, or normal, p. d. f. : for u(t) : for v(t) : for w(t) :

End of Lecture 6 John Holmes 225 -405 -3789 JHolmes@lsu. edu