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

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 integrating w.r.t. z : u  = friction velocity =  (  0 /  a )

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

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

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 z ref = reference height

Atmospheric boundary layers and turbulence Matching of power and logarithmic laws : z o = 0.02 m  = z ref = 50 metres

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

Atmospheric boundary layers and turbulence Mean wind speed profiles over the ocean: Assume g = 9.81 m/s 2 ; a = (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 : C g = 0.16 Ro (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 :

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

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

Atmospheric boundary layers and turbulence Mean wind profiles in hurricanes : In region of maximum winds : steep logarithmic profile to m Nearly constant mean wind speed at greater heights for z < 100 m  U z =  U 100 for z  100 m

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 m

Atmospheric boundary layers and turbulence Mean wind profiles in thunderstorms (downbursts) : Model of Oseguera and Bowles (stationary downburst) : R = 1000 m r/R = 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 = z * = 60 metres  = 50 metres = 1.3 (1/sec) U const = 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) 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)

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)

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 *

Atmospheric boundary layers and turbulence Turbulence intensities : rural terrain, z o = 0.04 m :

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) :

End of Lecture 6 John Holmes