Atmospheric Boundary - Wind Engineering - Lecture Slides, Slides of Environmental Law and Policy

Download Atmospheric Boundary - Wind Engineering - Lecture Slides and more Slides Environmental Law and Policy in PDF only on Docsity!

Atmospheric boundary layers and

turbulence I

0

5

10

15

20

25

30

35

0 1 2 3 4 5 Time (minutes)

Wind speed (m/s)

153 metres 64 metres 12 metres

Wind speeds from 3 different levels recorded from a synoptic gale

• Mean wind speed profiles :
  • Logarithmic law

 0 - surface shear stress a - air density

isafunctionof (z,ρ τ )

dz

dU

a 0

z

u   constant. dz

dU

U  ( 1 / k ). u  log e z constant

integrating w.r.t. z :

u = friction velocity =  ( 0 /a)

• Logarithmic law
  • k = von Karman’s constant (constant for all surfaces)

log (z/z )

k

u

U(z) ^  e 0

• zo = roughness length (constant for a given ground surface)

logarithmic law - only valid for z >zo and z < about 100 m

• logarithmic law applied to two different heights
  • or with zero-plane displacement :

 

e^2 o

e 1 o 2

1 log z /z

log z /z U(z )

U(z ) 

 

e^2 h o

e 1 h o 2

1 log (z z )/z

log (z z )/z U(z )

U(z ) 

• Surface drag coefficient :

Non-dimensional surface shear stress :

from logarithmic law :

2 10

2 2 10

0

U

u

U

 ^ 



 

o

10 e z

log k

u U

2

log 

o

e (^) z

k 

• Power law
  •  = changes with terrain roughness and height range

  

z U z U

log ( / )

e zref z 0



zref = reference height

• Matching of power and logarithmic laws :

0

20

40

60

80

100

0.0 0.5 1.0 1.

Height, z (m)

Logarithmic law Power law

zo = 0.02 m  = 0.128 zref = 50 metres

• Mean wind speed profiles over the ocean:

Assume g = 9.81 m/s^2 ; a = 0.0144 (Garratt) ; k =0.

Applicable to non-hurricane conditions

 U 10 (m/s) Roughness Length (mm )

10 0.

15 0.

20 1.

25 2.

30 3.

• Relationship between upper level and surface winds :
• Geostrophic drag coefficient

Rossby Number :

balloon measurements : Cg = 0.16 Ro-0.

g

U

u C (^) g 

o

g fz

U

Ro 

(Lettau, 1959)

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

Log law Lettau Lettau Log law

Can be used to determine wind speed near ground level over different terrains :

• 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

• 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

10

100

1000

0.0 1.0 2. U(z)/U(10)

Height z, (m)

log ( 10 / 0. 3 )

log ( / 0. 3 ) U (^) z U 10 e

 e^ z for z < 100 m

Uz =U 100 for z  100 m

• Mean wind profiles in thunderstorms (downbursts) :

Model of Oseguera and Bowles (stationary downburst) :

R = 1000 m r/R = 1. z*^ = 200 metres  = 30 metres  = 0.25 (1/sec) 0

200

400

600

0 20 40 60 Wind speed (m/s)

Height (m)

r/R = 1.

• Mean wind profiles in thunderstorms (downbursts) :

Add component constant with height (moving downburst) :

R = 1000 m r/R = 1. z*^ = 60 metres  = 50 metres  = 1.3 (1/sec) 0

200

400

600

0 20 40 60 80 100 Wind speed (m/s)

Height (m)

Uconst = 35 m/s