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
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. 4.7.1 Ekman Spiral in the Northern Atmosphere y (y low P High P x e Fig. 4.7.1 Ekman Spiral in the Northern Atmosphere P f x P f g i g 1 1 ~ ~ ~ ~ Geostrophy 0 P= g. ~
3 3 x f f i g + = ~ ~ f v v f y g x g 50 m 10 10 10 50 0 1 - (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 = ~ ~ 3 3 1 x x P f i i 3 3 - - x f i g ) = ( ~ ~ ~
low P g f f v v g g x y High P y (y e x ( v) (,0), = g at e Fig. 4.7.1 Ekman Spiral in the Northern Atmosphere g g v 0 at = 0 u' w x K ; y = K v (K theory)
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. 4.7.1 Ekman Spiral in the Northern Atmosphere g
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
Lecture a Convective Boundary Layers And Convective Flows
(m) ABL EVOLTION 0 00 180 160 140 1641-1644 1657-1701 171-174 1738-1741 1756-1800 1814-1817 1835-1838 1856-1900 10 100 80 60 40 0 0 87 88 89 90 91 9 93 94 Virtual potential temperature (K)
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
(m) ABL EVOLTION 0 00 180 160 140 1641-1644 1657-1701 171-174 1738-1741 1756-1800 1814-1817 1835-1838 1856-1900 10 100 80 60 40 0 0 87 88 89 90 91 9 93 94 Virtual potential temperature (K)
Formation and Breakdown of an Inversion Layer in El Paso
nstable Boundary Layer (flat terrain)
Stable Boundary Layer (flat terrain)
Convection between horiontal surfaces,,,, f k H q T o 4 0 Ra T f k H q k Td g 3 4 4 H T a T r k P, [Rayleigh-Benard ; Chandrasekhar 1961] ( ) ) ( ~ ~ * * 1971 10 0 8 3 1 0 Deardorff W q B R H L H q W f =
1 3 Nu Ra Thermals Molecular Goldstein and Chu (1973) Sparrow et. al. (1970)
Plumes - Convective
1 3 Nu Ra Thermals Molecular Goldstein and Chu (1973) Sparrow et. al. (1970)
Dave Fult s experiments
u. u ~ u ~ 1 p Irregular vortex patterns (Higher Ra/smaller Ta) Geostrophic Turbulence
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 1 3 1 0 1 / ) ( ~ H H H H L q fl u Ro = = ~100 km ( ) 1 3 0 1 0 3 1 10 / / / ) ( ) ( ~ f q L f q L q R H o
Sea Surface Temperature, July -10.0 33. ( o C )
Non-Rotating Plume
Rotating Plume Fernando, Dyn. Atmos. Oceans, 000
Atmospheric Surface layer
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
Monin-Obukhov scale L * = 1 u 3 * w g Θ 1 u = q 3 * 0
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)
Kaimal & Finnigan 1994
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)
With a slope
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
Convection in Complex Terrain
T-Rex Observations (NCAR)
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
Prandtl s Solutions Initial temp distribution T = T 0 + Γ gt b g d b d N 0 0 T0 g Initial hydrostatic 0 1 0 p s bsin ssin ncos
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
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
[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 3 1 3 4 * F h w...... * ˆ F u Hunt, Fernando & Princevac J. Atmos. Sci., 60, 003
Theory - p-slope Velocity For small M u 1 3 w * where 1 1 3 1 3 3 F g h q ) w S * ( 0 h 4 (?) u (Experiments) Ariona State niversity Environmental Fluid Dynamics
Experimental setup - Schematic Ariona State niversity Environmental Fluid Dynamics
Balloons
Height [m] VTMX velocity profile VTMX Velocity Profile 350 300 50 00 150 10/08/00 5:53PM (Qnet = 91 W/m^) 10/14/00 4:58PM (Qnet = 49 W/m^) 100 50 0 0 0.5 1 1.5.5 3 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 3.5 Laboratory Data VTMX Sonic Data VTMX Balloon Data during IOP Linear (VTMX Sonic Data) y = 4.1458x 1.5 1 0.5 0 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 Daily Averaged w * 1/3 [m/s] Ariona State niversity Environmental Fluid Dynamics
Geophysical Convection
A continuum of scales Large scale -- deep convection/hadley Cells (~ 10000 km) Thunderstorms (~50mkm) Slope flows (10-100 km) Atmospheric Plumes -- Microbursts ( km) CBL (100m to km)
Drivers of Environmental Motions 1 f u b ~ ~ Hadley Circulation cold p warm SN Tides g ~ Moon
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
Atmospheric Convection
CONVECTION OVER RBAN AREAS
Phoenix Metropolis rban Heat Island -- rban air can be significantly hotter than the countryside
HI in satellite image of Phoenix
Brael et al. 000
March 19, 008, 5pm to 10pm Infrared imaging of Phoenix
HI Experiment
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).
Wind Shear Found at all Altitudes