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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.

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atmospheric boundary layers and turbulence i

Atmospheric boundary layers and turbulence I

Wind loading and structural response

Lecture 6 Dr. J.D. Holmes

atmospheric boundary layers and turbulence
Atmospheric boundary layers and turbulence

Wind speeds from 3 different levels recorded from a synoptic gale

atmospheric boundary layers and turbulence3
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 turbulence4
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 turbulence5
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 turbulence6
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 turbulence7
Atmospheric boundary layers and turbulence
  • logarithmic law applied to two different heights
  • or with zero-plane displacement :
atmospheric boundary layers and turbulence8
Atmospheric boundary layers and turbulence
  • Surface drag coefficient :

Non-dimensional surface shear stress :

from logarithmic law :

atmospheric boundary layers and turbulence10
Atmospheric boundary layers and turbulence
  • Power law
  •  = changes with terrain roughness and height range

zref = reference height

atmospheric boundary layers and turbulence11
Atmospheric boundary layers and turbulence
  • Matching of power and logarithmic laws :

zo = 0.02 m  = 0.128 zref = 50 metres

atmospheric boundary layers and turbulence12
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 constanta- empirical constant

a lies between 0.01 and 0.02

substituting :

Implicit relationship between zo and U10

atmospheric boundary layers and turbulence13
Atmospheric boundary layers and turbulence
  • Mean wind speed profiles over the ocean:

Assumeg = 9.81 m/s2 ;a= 0.0144 (Garratt) ; k =0.41

Applicable to non-hurricane conditions

atmospheric boundary layers and turbulence14
Atmospheric boundary layers and turbulence
  • Geostrophic drag coefficient
  • Relationship between upper level and surface winds :

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 Lettau Log law

U10, terrain 1  u*,terrain 1  Ug  u*,terrain 2  U10, terrain 2

atmospheric boundary layers and turbulence15
Atmospheric boundary layers and turbulence
  • Aircraft flights down to 200 metres
  • Mean wind profiles in hurricanes :
  • 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 turbulence16

North West Cape

US Navy antennas

Exmouth

EXMOUTH

GULF

100 km

Atmospheric boundary layers and turbulence
  • Mean wind profiles in hurricanes :
  • Northern coastline of Western Australia
  • Profiles from 390 m mast in late nineteen-seventies
atmospheric boundary layers and turbulence17
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 =U100 forz  100 m

atmospheric boundary layers and turbulence18
Atmospheric boundary layers and turbulence
  • Doppler radar
  • Mean wind profiles in thunderstorms (downbursts) :
  • 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 turbulence19
Atmospheric boundary layers and turbulence

Model of Oseguera and Bowles (stationary downburst) :

  • Mean wind profiles in thunderstorms (downbursts) :

R = 1000 m

r/R = 1.121

z* = 200 metres

 = 30 metres

 = 0.25 (1/sec)

atmospheric boundary layers and turbulence20
Atmospheric boundary layers and turbulence

Add component constant with height (moving downburst) :

  • Mean wind profiles in thunderstorms (downbursts) :

R = 1000 m

r/R = 1.121

z* = 60 metres

 = 50 metres

 = 1.3 (1/sec)

Uconst = 35 m/s

atmospheric boundary layers and turbulence21
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 turbulence22

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

Components of turbulence :

atmospheric boundary layers and turbulence23
Atmospheric boundary layers and turbulence

Turbulence intensities :

  • standard deviation of u(t) :

Iu = u /U (longitudinal turbulence intensity)(non dimensional)

Iv = v /U (lateral turbulence intensity)

Iw = w /U (vertical turbulence intensity)

atmospheric boundary layers and turbulence24
Atmospheric boundary layers and turbulence

Turbulence intensities :

near the ground, u  2.5u*

Iu = u /U

from logarithmic law

v  2.2u*

w  1.37u*

atmospheric boundary layers and turbulence25
Atmospheric boundary layers and turbulence

Turbulence intensities :

rural terrain, zo= 0.04 m :

atmospheric boundary layers and turbulence26
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) :