Lecture 2 Atmospheric Boundary Layer

Size: px

Start display at page:

Download "Lecture 2 Atmospheric Boundary Layer"

Dayna Horton
5 years ago
Views:

1 Lecture Atmospheric Boundary Layer H. J. Fernando Ariona State niversity Region of the lower atmosphere where effects of the Earth surface are felt Surface fluxes of momentum, buoyancy.. Neutral, Convective, Stable and Transitional Boundary Layers

2 Atmospheric Boundary Layer (flat terrain) ij u u x x x P f x t j i j i j i j i j i 1 ~ ~ Horiontal homogeneity Steady (Boun Layer) 3 3 ~ ~ 1 x x P f i i y (y low P High P x e Fig Ekman Spiral in the Northern Atmosphere y (y low P High P x e Fig Ekman Spiral in the Northern Atmosphere P f x P f g i g 1 1 ~ ~ ~ ~ Geostrophy 0 P= g. ~

4 3 3 x f f i g + = ~ ~ f v v f y g x g 50 m (1-4. ~ ) ( ) * * g g fv u a H H fv u a Surface layer small change of stress y (y low P High P x e Ekman Spiral in the Northern Atmosphere d v v f H H g x x 0 0 u * Boundary Layer fow i g x P f 1 = ~ ~ x x P f i i x f i g ) = ( ~ ~ ~

5 low P g f f v v g g x y High P y (y e x ( v) (,0), = g at e Fig Ekman Spiral in the Northern Atmosphere g g v 0 at = 0 u' w x K ; y = K v (K theory)

6 e g e e cos 1 e g e V e cos f K e Ekman Spiral y (y low P High P x e Fig Ekman Spiral in the Northern Atmosphere g

7 Ekman Layer Height K h E ~ 300m f Sutton (1953) used this as the ABL height under neutral conditions K u* h E Tennekes (198).5u h ABL 0 * ~ 1km f With Stratification? - - Stable or nstable

8 Lecture a Convective Boundary Layers And Convective Flows

9 (m) ABL EVOLTION Virtual potential temperature (K)

10 T 0 q 0 = gq C 0 p buoyancy flux Non- Penetrative and Penetrative Convection h 1 N h q0t 1 q0 t N 1

11 (m) ABL EVOLTION Virtual potential temperature (K)

12 Formation and Breakdown of an Inversion Layer in El Paso

14 nstable Boundary Layer (flat terrain)

15 Stable Boundary Layer (flat terrain)

16 Convection between horiontal surfaces,,,, f k H q T o 4 0 Ra T f k H q k Td g H T a T r k P, [Rayleigh-Benard ; Chandrasekhar 1961] ( ) ) ( ~ ~ * * Deardorff W q B R H L H q W f =

17 1 3 Nu Ra Thermals Molecular Goldstein and Chu (1973) Sparrow et. al. (1970)

18 Plumes - Convective

19 1 3 Nu Ra Thermals Molecular Goldstein and Chu (1973) Sparrow et. al. (1970)

20 Dave Fult s experiments

21 u. u ~ u ~ 1 p Irregular vortex patterns (Higher Ra/smaller Ta) Geostrophic Turbulence

22 Onset of Rotational Effects k j jk H H H u Ro u w x u u t u T u L 1 x p u p H 0 0 u L L x x u V H Re / ) ( ~ H H H H L q fl u Ro = = ~100 km ( ) / / / ) ( ) ( ~ f q L f q L q R H o

23 Sea Surface Temperature, July ( o C )

25 Non-Rotating Plume

26 Rotating Plume Fernando, Dyn. Atmos. Oceans, 000

28 Atmospheric Surface layer

29 Monin-Obukhov (1954) Similarity Theory -- For flat terrain surface layer Parameters Heat Flux Q 0, Stress τ 0 = u * buoyancy flux q 0 = gq 0 0C p Q 0 τ 0 temperature flux H Q = ( w ) 0 = 0 C p Define the scaling variables: velocity scale u temperature scale T u 1/ * w 0 w * u* 0 w 0 Convection T * 0 w 0 Stratification stable : T* 0

30 Monin-Obukhov scale L * = 1 u 3 * w g Θ 1 u = q 3 * 0

31 Non dimensional relations Z u* Ø m (/L * ) wind shear) Any F( u G( u * *,, q,, L 0 * ) ) * Z T = Ø h (/L * ) (thermal stratification) Ø w = w u * (variability of w) Ø θ = w T * 3 Ø ε (/L * ) u* (variability in θ) (dissipation)

32 Kaimal & Finnigan 1994

33 Z L * g w 3 u* Z bw d uw dz Ri f given that d * dz u Z ; uw u * L * shear dominates : L * Buoyancy (outer layer)

34 With a slope

35 Thermal blob (IV) (III) (II) (I) (IV) Detachment occurs when Ra Ra c gt 3 c 10 3 (III) (II) (I) Princevac & Fernando, Phys. Fluids, 19, 007

36 Convection in Complex Terrain

37 T-Rex Observations (NCAR)

38 Fully developed upslope flow () E ~ c c= b h I frontal wave h W upslope flow, (x,, t) S F S x=l V H frontal wave (x) S x x x=l x=0

39 Prandtl s Solutions Initial temp distribution T = T 0 + Γ gt b g d b d N 0 0 T0 g Initial hydrostatic p s bsin ssin ncos

40 Now give a perturbation, b and corresponding velocity u ' s b s b u 0 n u b + v = sin ' 0 s p and g b sin / / / N s b s b 0 ' sin ' 4 4 b v N n b nl Ae b l n cos ' / 4 1 sin 4 N v l

41 Velocity along the slope, constant (eddy?) coefficients u A vn 1 e n l sin n l constant heat flux boundary condition q0 b/ A q 0 l / n

42 [S] [M] [I] [E] h S S S S x=0 h front wave x=l x=l T h c= b h x x h W S I E S MS mi V I S C () C S S F S c= b h I pslope - Theoretical Model F W x t b x P W x t ˆ ˆ ˆ ˆ ˆ ˆ ) ( ˆ ) ( t h f t m S u 0 S F S F } } 0 ˆ ˆ h ˆ ˆ L * S C S S ˆ * F h w * ˆ F u Hunt, Fernando & Princevac J. Atmos. Sci., 60, 003

43 Theory - p-slope Velocity For small M u 1 3 w * where F g h q ) w S * ( 0 h 4 (?) u (Experiments) Ariona State niversity Environmental Fluid Dynamics

44 Experimental setup - Schematic Ariona State niversity Environmental Fluid Dynamics

45 Balloons

46 Height [m] VTMX velocity profile VTMX Velocity Profile /08/00 5:53PM (Qnet = 91 W/m^) 10/14/00 4:58PM (Qnet = 49 W/m^) Velocity [m/s] Ariona State niversity Environmental Fluid Dynamics

Daily Averaged m [m/s] 4.5 p-slope velocity VTMX Daily Averaged m VS w * 1/3 (October 1-5, 7, 14-17) (Days with low synoptic wind condition) M u 1 3 w * 4 3.5 3.

47 Daily Averaged m [m/s] 4.5 p-slope velocity VTMX Daily Averaged m VS w * 1/3 (October 1-5, 7, 14-17) (Days with low synoptic wind condition) M u 1 3 w * Laboratory Data VTMX Sonic Data VTMX Balloon Data during IOP Linear (VTMX Sonic Data) y = x Daily Averaged w * 1/3 [m/s] Ariona State niversity Environmental Fluid Dynamics

48 Geophysical Convection

49 A continuum of scales Large scale -- deep convection/hadley Cells (~ km) Thunderstorms (~50mkm) Slope flows ( km) Atmospheric Plumes -- Microbursts ( km) CBL (100m to km)

50 Drivers of Environmental Motions 1 f u b ~ ~ Hadley Circulation cold p warm SN Tides g ~ Moon

51 T T a b k P d T d a b a b T a b Td g r a a T ; 4 4 Ro 4 4 1

53 Atmospheric Convection

54 CONVECTION OVER RBAN AREAS

55 Phoenix Metropolis rban Heat Island -- rban air can be significantly hotter than the countryside

56 HI in satellite image of Phoenix

57 Brael et al. 000

58 March 19, 008, 5pm to 10pm Infrared imaging of Phoenix

59 HI Experiment

61 Convective Scaling Vs. Data Variation or horiontal variance (normalied). (Solid Curve -- Laboratory) (Fernando et al., Dyn. Atmos. Oceans, 13,95-11, 1989) Variation of vertical variance (normalied).

62 Wind Shear Found at all Altitudes

Sergej S. Zilitinkevich 1,2,3. Helsinki 27 May 1 June Division of Atmospheric Sciences, University of Helsinki, Finland 2

Sergej S. Zilitinkevich 1,2,3. Helsinki 27 May 1 June Division of Atmospheric Sciences, University of Helsinki, Finland 2 Atmospheric Planetary Boundary Layers (ABLs / PBLs) in stable, neural and unstable stratification: scaling, data, analytical models and surface-flux algorithms Sergej S. Zilitinkevich 1,2,3 1 Division