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## Atmospheric boundary layers and turbulence I

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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

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 stressa - 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 constanta- empirical constant

a lies between 0.01 and 0.02

substituting :

Implicit relationship between zo and U10

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 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 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

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 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 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 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 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 turbulence

Turbulence represents the fluctuations (gusts) in the wind speed

It can usually be represented as a stationary random process

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 turbulenceComponents of turbulence :

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 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 turbulence

Probability density :

- The components of turbulence (constantU) can generally be represented quite well by the Gaussian, or normal, p.d.f. :

for u(t) :

for v(t) :

for w(t) :

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