Dr. Goricsán István, 2008Balczó Márton, Balogh Miklós, 2009

Budapesti Műszaki és Gazdaságtudományi Egyetem, Áramlástan Tanszék1

Wind in the atmosphere

The atmospheric boundary layer

BUILDING AERODYNAMICSBME GEÁT MW08

27

TROPICAL CYCLONES

The tropical cyclone Catarina near the shore of Brazil, photographerd from the International Space Station, March 26, 2004

Eye of hurricane ‘Katrina’ Aug 28, 2005photographed from an airplane.

Hurricane (Atlantic Ocean), typhoon (Indian Ocean), Cyclone (PacificOcean)

28

TROPICAL CYCLONES

• From 26°C ocean temperature > very high evaporation

• Warm air transported by convection up to the tropopusecondensation relase of latent heat further heating further uprise low pressure

at the sea surface inducing strong horizontal flows to the eye (positive feedback)

• Warm dry air is entering the centre from above the hurricane’s eye

• Pressure difference 50 - 100mbar compared to the environment

• A hurrican is a thermodynamic machine cooling the ocean and transporting heat andmoisture into the higher levels of the atmosphere

29

TROPICAL CYCLONES

• Eye 15-40 km diamater• Eyewalls: max. speed 200-300 km/h. Moving velocity: 20-30km/h• High level outflow is counter-rotating• if reaching solid terrain, the driving force, latent heat transport is prohibited• If heading north, gets weakes and turns into an extratropical storm.

30

TROPICAL CYCLONES

Luis hurrikán1995 aug. 27-szept. 11.

31

TROPICAL CYCLONES

1 sec = 10 min90km

Hurrrivane Luis, Sept 1995

32

TROPICAL CYCLONES

The effects

• Wind damage (Épület, autók stb.)

• 15-20m waves on the shore

• Low pressure elevates water level

• High participation (300 mm/24h , Texas, 1921: 750mm!! – difficult to measure)

floodings (+ 5m)

Hurricane watch:

• Meteorological radar (from the 1950’s), satellites (from the 1970’s),

• Fly-in with manned or unmanned airplanes, to measure wind speed and pressures(dropsondes)

• Hurricane season: July - September

• 100 tropical lows annaually, from which 6-7 develop to hurricanes (wind higher thanBeaufort 12)

• Global climate change: oceans getting hotter (T< 26 C) higher probability!

National Hurricane Center (USA) szimulációja

33

Span Systems Inc.

Open ait theatre with tensile fabric roof(St Augustine, Florida, USA)

34

Open air theatre destroyed by a hurricane(Porthsmouth, Virginia, USA)

35

HURRICANE OBSERVATIONS

Unmanned Aerial vehicle

Dropsonde (verticalprofiling)

36

HURRICANE OBSERVATIONS

Unmanned Aerial vehicle

Dropsonde (verticalprofiling)

37

HURRICANE OBSERVATIONS

Unmanned Aerial vehicle

Dropsonde (verticalprofiling)

38

TROPICAL CYCLONES

Hurricane paths 1985-2005

• sea winds

• Urban winds

• orographic winds

• Can be strengthened by other effects : e.g: bora

39

LOCAL WINDS

different albedo, heat capacity of surfaces andconsequently varying temperature of air

daily periodocity

morning evening

Orographic wind

• In the morning: southern slopes warm updraft : wind from the valley

Anabatic wind

• In the late afternon: faster cooldown of slopes due to radiation (effect strongerwithout forest coverage) cold downdrafts

Catabatic wind

Thin layer of wind (some meters – some 10 meters), 2-4 m/s max. speed(can be blocked by buildings)

40

LOCAL WINDS

http://www.tpub.com/weather2/3-23.htm

Desert winds:

Cyclones generated above desert areas (high T)

and modified by local effects

Scirocco: Mediterranean sea

Samum: Palestine

Khamsin,

haboob: Egypt (causing transport of sand to the Alps - blood rain)

Brickfielder: Australia (very dry hot wind)

Pampero: Argentina

Mistral: catabatic wind strengthened by orographic effects in the valley of the Rhone river. (Bay of Biscaya, Western Franc: anticyclonic = high pressure, Gulf of Genova: low pressure)

Buran: eastern Asian cyclone, snow storm

Bora: High speed wind at the NE shore of Adriatic Sea coming from the mountains (up to 200km/h wind speed, and 14 days of endurance)

41

REGIONAL WINDS

Monsoon (- circulation)

• Seasonal reversing wind with annual changes of wind direction 2x a year (min. 120°)

• cause: ITCZ and asymmetric heating of land and sea

• Low pressure areas above desert areas in summer (Indus-plain, Tibetianhighlands, Siberia) ITCZ is moved towards the north

• Southeast trade winds turn to southwest (Coriolis force!) and transport moist air tothe land.

• In winter: cold dry winds from northeast (intensified trade wind)

• Orographic effects: pld. Himalaya

• Monsoon:

• North-Australia

• West Africa

• India

• East-Asia

• Gulf of Mexico (weak)

42

WINDS MODIFYING THE PLANETARY CIRCULATION

43

GLOBAL ATMOSPHERIC CIRCULATION - SUMMARY

Surface wind directions ans pressure in January (Weischet, 1977)T: low pressure; H: high pressure

44

GLOBAL ATMOSPHERIC CIRCULATION - SUMMARY

Surface wind directions ans pressure in July (Weischet, 1977)T: low pressure; H: high pressure

High temporal variability of wind speed and direction

• Wind observations in a fixed observation point:

45

WIND SPEED FLUCTUATIONS

( ) ( )trwvu

trV ,,⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

46

EXAMPLE OF STRUCTURES CAUSING WIND FLUCTUATIONS

Forrá

s: D

r. K

ristó

f Ger

gely

• Von Kármán vortex street– one specific frequency of vortex separation

• Mixture of frequencies

• Signalling the pass of vortices ofdifferent size

• Max. freq: some Hz (T = 0.1s)

► spectral analysis useful

47

ATMOSPHERIC TURBULENCE

Transformation from time domainto frequency domain:

48

FREQUENCY ANALYSIS OF SIGNALS

( ) ( )ωFtf ⇒

Euler formula:

Fourier-transformation: Conversion to time domain:( ) ( )πθπθθπ 2sin2cos2 ⋅+= ie i

( ) ( )∫+∞

∞−

−⋅= dtetfF tiωπω 2 ( ) ( )∫+∞

∞−

⋅= ωω ωπ deFtf ti2

F(ω) complex function: amplitude and phase

Az ampl. squared: powers spectrum

day/night

weathercyclonesfronts

seasons

49

WIND POWER SPECTRUM

• shows the contribution of met. Scales to the wind genesis

• right section of the plotis important when addressing building aerodynamics

turbulenceMean wind

( ) ( ) ( ) ( ) kt,rwjt,rvit,rut,rV ⋅+⋅+⋅=

( ) ( ) ( )∫==T

dttruT

rutru0

,1,

Mean wind:

Similarly :( )rv ( )rw

( ) ( ) ( )rut,rut,ru, −=Velocity fluctuation:

( )t,rv, ( )t,rw,

Similarly:

u(r,t)

w(r,t)

v(r,t)

V(r,t)

( )rv

( )rw

( )ru

( )t,rw,

( )t,ru,

( )t,rv,

50

DESCRIPTION OF TURBULENT FLOWS

( ) ( ) 0,10

,, == ∫T

dttruT

ru ( ) 0, =rv ( ) 0, =rw

Temporal average of fluctuations:

51

DESCRIPTION OF TURBULENT FLOWS

( ) ( ) ( ) ( )( ) ( )rdtrut,ruT1dtt,r'u

T1t,r'u 2

u

T

0

2T

0

22 σ=−== ∫∫Root mean square of fluctuations = squared deviation of velocity

Root mean square of fluctuations:

[ ]s/m,, wvu σσσ

uT u

uσ

=

uT v

vσ

=

uT w

wσ

=

Quotient of stnadard deviation and mean windvelocity [-]

• Laminar flows: verylow turbulenceintensity

• Growing flowvelocity: highturbulence (shownby stronger mixing)

52

DEFINITION OF TURBULENCE INTENSITY

53

TURBULENT KINETIC ENERGY

Kinetic energy of an elementar mass:2)t(V

21

m)t(E

=

2)t(V21

m)t(E =Average kinetic energy:

( )

( )2w

22v

22u

2

222

wvu21

wvu21

m)t(E

σ++σ++σ+

=++= ( ) ( ) ( )rurru 22u

2 =σ+

The total kinetic energy of the turbulent flow is larger than that of a laminarflow with the same mean wind velocity!

=m

Eössz

Kinetic energy of the mean flow:

( )222átlag wvu21

mE

++= +

Kinetic energy of fluctutations(turbulent kinetic energy, TKE):

( )2w

2v

2u2

1m

TKEσ+σ+σ=

day/night

weathercyclonesfronts

seasons

turbulenceMean wind

54

TURBULENT KINETIC ENERGY

• Area below the curve ~ TKE

• Distribution of TKE by frequency / vortex size

Large vortices in the atmospherefall a part to smaller ones.At the end, smallest vorticesdissipate their kinetic energy toheat. (because real flows areviscous)The spectrum of winf is formed bythis mechanism to a typical shape.

Turbulent energy cascade

55

TURBULENT KINETIC ENERGY SPECTRUM

Big whorls have little whorls That feed on their velocity,

And little whorls have lesser whorls And so on to viscosity.

(Lewis F. Richardson*, 1922)

*English mathematician, physicist, meteorologist (1881-1953), who created the concept of numerical weather prediction

Momentum transportfrom the mean flow: vortices aredeveloped on theedges of flowobstacles

Inertial domain: a energy of largestructures passedto smaller flowstructures

Molecular dissipation: kinetic energy turns intoheat

56

TURBULENS KINETIKUS ENERGIA SPEKTRÁLIS MEGOSZLÁSA

The planetary boundary layer (PBL), also known as the atmospheric boundary layer (ABL), is the lowest part of the atmosphere and its behavior is directly influenced by its contact with a planetary surface. Heat, momentum and moisture transportbetween earth and atosphere occurs in the ABL. Flow in the ABL is mostly turbulent, transport isdone by turbulent vortices (turbulent diffusion).

57

THE ATMOSPHERIC BOUNDARY LAYER

• Driving force: free atmosphere, gestrophic or cyclonic winds• On the surface : velocity = 0• Thermal convection• Surface roughness and elevation has major influence on its shape and

thickness• Thickness can vary in time ( – time scale ≤ 1day)• 3D flow – w cannot be neglected

58

THE ATMOSPHERIC BOUNDARY LAYER

Momentum equations:

59

EKMAN LAYERGeostrophic wind,

acting forces: Coriolis and pressure gradient force, flow || isobars

• Friction on the surface V < Vg

• Coriolis-force smaller wind directiondeflected towards the pressuregradient.

• Max.deflection : 45°

0np1fVg =

∂∂

ρ−

( )z

'w'vfUnp1

∂∂

+=∂∂

ρ

( )z

'w'ufV0∂

∂+=

X :

Y :

The ‘Fram’ in the ice

60

FRIDTJOF NANSEN’S EXPEDITION WITH FRAM (1893-1896)

• Journey of the FRAM (continuous)• Nansen and Johansen by cayak and hound

sledge (dashed) ‘Fram’s cross-sectionNansen (1861-1930)

61

EKMAN-SPIRAL, SUBLAYERS

Surface layer (Prandtl layer)

boundary layer thickness ~ 10% of tropospherewidth, ~ 1 km, but can vary between 200 m - 5 km

Surface layer: wind speed, temperature change with height.

Turbulence induced by surfaceroughness / obstacles and thermalconvection

constant flux of mass heat etc.

Wind direction approximatelyconstant

Typical height: 50 m, can varybetween 5-200 m

roughness or canopy layer: windspeed influenced strongly bybuildings, groves trees: chaotic (3D) dominance of turbulent movement.

62

BOUNDARY LAYER STRUCTURE ABOVE ROUGH TERRAIN

K)zln(u)z(u*

+⋅κ

=

• Turbulent momentum exchange betweenlayers:

63

LOGARITHMIC BOUNDARY LAYER PROFILE

zuK'w'u M ∂

∂==

ρτ

• K-theory: shear stsess proportianal to thegradient of the mean wind profile

• Turbulent vortices cause an additionalviscosity (turbulent viscosity)

• KM not constant, and can be determined usingturbulence models

ν>>MK

τ constant in the surface layer

( ) .állu'w'u 2* ===ρτ

u* - friction velocity(fictitious quantity with

velocity dimension)

zuK *M ⋅⋅κ=

Simple assumption: Km 0 at the surfaceκ – Kármán-constant = 0.41

zu

zu *

∂∂

=κ

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

κ=

0zzlnu)z(u

*

64

LOGARITHMIC BOUNDARY LAYER PROFILE

d0 – displacement height(if the whole boundary layer is shifted upwards)

z0 – roughness length

)z

dzln(1u

)z(u0

0*

−⋅

κ=

• d0+ ln z0 at U/Uref = 0

z0=0.1, α=0.185

)z

dzln(

1u

)z(u

0

0

*

−⋅

κ=

α

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=

0ref

0

ref dzdz

u)z(u

empirical power function

65

LOG-LAW AND POWER LAW WIND PROFILES

66

LOG-LAW AND POWER LAW WIND PROFILES

• Power law wind profiles measured in wind tunnel

67

WIND PROFILES FROM ON-SITE MEASUREMENTS

≈0.75⋅h≈0.75⋅h≈0≈0d0 [m]0.24 – 0.40.18 – 0.240.12 – 0.180.08 – 0.12a [-]

0.5 - 20.1 – 0.55⋅10-3 – 10-110-5 – 5⋅10-3z0 [m]

Forests, urban area

Suburban area, groves

Farmland, grass Ice, snow, calm water

description

very roughroughmediumsmoothSurface category

Forrás: http://www.gi.alaska.edu/~heike/Barrow2005/h_chargingADV.jpg

Forrás: http://earthobservatory.nasa.gov/Laboratory/Biome/Images/picgrassland.jpg

Forrás: http://www.aerometrex.com.au/AdelaideMetro/Suburban_Adelaide.jpg

Forrás: http://www.usatravel.hu/fckep/Image/Missouri/.thumb_Kansas_City.jpg

68

PROFILE PARAMETERS

*u u5,245,2 ⋅÷=σ

*v u2,2 ⋅=σ

*w u25,1 ⋅=σ5.0:8.0:1T:T:T wvu =

ATMOSPHERIC TURBULENCE IS ANISOTROPIC!69

TURBULENCE INTENSITY IN THE ATMOSPHERIC BOUNDARY LAYER

α

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=

0ref

0

ref dzdz

u)z(u

uT u

uσ

=

70

PROFILE PARAMETERS

( )( ) ( )DC

red

red2u

uu

fBE

fAz

z,fSf

⋅+

⋅=

σ⋅

71

WIND SPECTRA

Forrás: Yu et al (2008): HurricaneWind Power Spectra, Cospectra, and Integral Length Scales72

WIND SPECTRA

73

BOUNDARY LAYER GENERATION IN WIND TUNNELS

ábra: E. J. Plate. Engineering Meteorology (1982)

1. Confuser2. Turbulence generators3. Roughness elements4. Adjustable roof5. Flow preparation section6. Measurement section - model on turntable7. Fan8. Diffuser

74

BOUNDARY LAYER GENERATION IN WIND TUNNELS

75

BOUNDARY LAYER GENERATION IN WIND TUNNELS

closedtest section

5 or 7preparation section length [m]

0.5inlet turbulece intensity [%]

22max. wind speed [m/s]

1.4measurement section height [m]

2.2measurement section width [m]

2measurement section length [m]