• The lowest part of the atmosphere that is in direct interaction with the Earth's surface; it responds to surface forcings with a time scale of about an hour or less. It is highly turbulent .
• Boundary layer depth is variable, typically between 100-3000 m
• Ratio of boundary layer depth to radius of earth: ~1 km/6400 km

Physical processes that act to modify wind velocity, temperature, moisture, pollution.
• Frictional drag
• Heat transfer from/to the ground
• Terrain-induced drag
Energy balance at surface:

Q
*
S

Q
E

Q
H

Q
G
-----------------------------------------------------------------------------------------------------------
• Evaporation and Transpiration
• Emissions of gases (e.g., pollutants)
Boundary Layer flow: wind tunnel visualizations
Skin (surface) temperature time series measured over a diurnal cycle.


Q
*
S
 
Q
H

Q
E

Q
G
 
Q stor
Q s
* : Net solar radiation
Q
H
: Sensible heat flux
Q
E
: Latent heat flux
Q
G
: Ground heat flux

• Microscale portion of the meteorological spectrum, i.e., phenomena with spatial scales between approximately 1 mm and 2 km ; temporal scales between mili-seconds and an hour .
• Note that all these scales of motion are inter-related through TURBULENCE : energy transfers or cascades from the larger scales to the smaller scales, eventually dissipating .

Property
Turbulence
Mixing
Vertical Transport
Winds
Thickness
Boundary Layer
Almost continuously turbulent over its whole depth
Free Atmosphere
Mostly Laminar . Turbulence in convective clouds, and sporadic clear-air turbulence in thin layers of large horizontal extent
Rapid turbulent mixing vertical and horizontal
in the
Small molecular diffusion . Often rapid horizontal transport by mean wind.
Turbulence dominates
Mean wind dominates [slow vertical transport]
Near logarithmic wind speed profile in the surface layer. Subgeostrophic , crossisobaric flow common
Varies between 100 m to 3 km in time and space. Diurnal oscillations over land
Winds nearly geostrophic
Less variable . 8-18 km. Slow time variations.

Q: Why is it important to study the boundary layer?
• We spend most of our lives in the boundary layer.
• Daily weather forecasts of dew, fog, frost, max and min temperature are really boundary layer forecasts.
• Virtually all water vapor that reaches the free atmosphere is first transported through the boundary layer by turbulent processes.
• Cloud Condensation Nuclei are lofted into the air from the surface by boundary layer processes.

• Turbulence and gustiness affect architecture and the design of structures .
• Wind energy: Wind turbines extract energy from boundary layer winds.
• Wind stress on water surface: primary energy source for water currents in lakes & oceans .
• Crops are grown in the boundary layer. Pollen is transported by boundary layer processes.
• Basic understanding of high-Reynolds-number boundary layer flows
• Air pollution , etc., etc., etc. .......

• Air Pollution
• atmospheric transport and diffusion of pollutants
• prediction of local, urban, and regional air quality
• Mesoscale Meteorology
• urban boundary layers and the heat island effect
• land/sea breezes
• drainage and valley flows
• development of fronts and cyclones
• Agricultural and forest Meteorology / Hydrometeorology
• prediction of surface temperatures and frost conditions
• soil temperature and moisture
• evaporation, evapotranspiration and water budgets
• energy balance of a plant canopy
• Urban Planning and Management
• prediction and abatement of ground fogs
• heating and cooling requirements
• flow dispersion around buildings
• prediction of road surface temperatures and icing
• Wind Energy / Renewable Energies
• Fluid Mechanics & Turbulence in high-Re boundary layers

• TURBULENCE THEORY
• EXPERIMENTS:
• Point sensors mounted on towers (~1m to ~100 m)
• Balloons
• Aircraft-borne sensors
• Satellite-borne sensors
• Remote sensing techniques: sodars, radars, lidars
• Laboratory experiments: wind tunnels, water tanks/flumes
• NUMERICAL SIMULATIONS:
• LES (Large-Eddy Simulation)
• Weather models
• Global Circulation Models (GCMs)
[grid size ~10 m]
[grid size ~1-10 km]
[grid size ~100 km]

T (C)
34
32
30
28
5600 5650 5700 5750 5800 5850 5900
Data points (sampling rate = 20 Hz)
5950 6000

Digital Elevation Map (DEM) from airborne LIDAR

SODAR (SOund Detection And Ranging)

LIDAR (LIght Detection And Ranging)

Example: Applications to turbine-wake measurements
Kasler et al. (2010)
Trujillo et al. (2011)
Iungo et al. (2013)

Large-Eddy Simulation (LES)

~10km
~10km w

Within the boundary layer, the wind can usually be decomposed [artificially] into 3 categories:
• Mean Wind:
• The mean wind is important for horizontal transport of quantities such as moisture, heat, momentum, and pollutants - i.e., advection.
• typical speeds are 2-10 m/s
• friction slows the winds near the surface, the wind velocity is 0 m/s right at ground level
• Waves:
• occur mostly at night in the nocturnal boundary layer.
• transport little heat, moisture and other scalar variables like pollutants
• are effective at transporting energy and momentum, however.

LES of stable boundary layer – u-velocity field
Kelvin-Helmholtz (K-H) waves in the ‘ inversion layer ’
Instability at the interface between two horizontal parallel streams of different velocities and densities, with heavier fluid at the bottom.

• The vertical transport of moisture, heat, momentum, and pollutants is dominated by turbulence. Q: What is turbulence?
• Unsteady; three-dimensional
• Random-like (but not really: coherent structures)
• Turbulence increases MIXING and transport rates (fluxes)
• It can be visualized as consisting of irregular swirls of motion called eddies
• Continuous spectrum of eddy sizes - anywhere from the integral scale ( L
I
~
100-3000 m) to the Kolmogorov scale ( L
K
= η ~ 1 mm).
Turbulence is one of the unresolved problems in classical physics
• Chaotic system [high sensitivity to initial conditions]
• Governing equations (Navier-Stokes equations) are known , but no analytical solution in turbulent flows

o How long would it take for sugar on the bottom of a coffee cup to diffuse and dissolve uniformly in stagnant coffee?
In that case, coffee will diffuse only due to molecular diffusion (zero advection). The molecular diffusion time can be estimated using: t

L 2
D
For sugar in water: D m

10

9 2

1 m s
(Typical values in air: D m

10

5 m s

1
)
Assuming: L

0.05
m t

30 days !!!
o If turbulence is introduced (e.g., by stirring the coffee), full mixing takes place in just a few seconds.
As we will see, it is common to model turbulence by using a
‘ turbulent/eddy diffusion coefficient ’ (eddy diffusivity)
D t

D m

Re



Re


U

LT
-1
Velocity scale (e.g., average velocity or r.m.s.) [ ]
L

 
Kinematic viscosity [ L T -1 ]
Re

Reynolds found approximately: o Re < 2300 : Laminar Flow o Re > 2300 : Turbulent Flow

‘ Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity ’
Richardson (1922)
Integral scale
L ~ 1 km
(in ABL)
Range of flow scales
Kolmogorov scale
η ~ 1 mm
L

~ Re
3/ 4
Energy production
(Inertial effects)
(Energy cascade) Energy dissipation
(Viscous effects)

What Turbulent Jet Flow has higher Reynolds number?
Re ~ 1,500 Re ~ 5,000
Werner et al (1990, J Fluid Mech)
Re ~ 20,000

• Difficult to obtain an instantaneous snapshot of all eddies within the ABL.
• To study turbulence from a continuous record of measurements from a single point, we need to assume that the turbulence is frozen.
• As the mean flow advects the eddies past the sensor, the fundamental properties of the eddies remain unchanged, or frozen.
• Mathematically, how can we express Taylor ’ s hypothesis?
For any variable, ξ, the total derivative is equal to zero , i.e., d ξ /dt = 0 if it is “ frozen ” .
or since d ξ /dt = 0 , (1) can be written as:
(1)
(2)
Assuming that the flow is entirely in the x direction (with average wind u ) :
(3)

X
T (C)
34
32
30
28
5600 5650 5700 5750 5800
Time scale
5850 5900 5950 6000
Data points (sampling rate = f = 20 Hz) t (=number points / f)
Spatial scale dX = − U * dt using Taylor ’ s hypothesis

• Q: Can we always use Taylor ’ s (frozen flow) hypothesis?
Only when the turbulent eddies evolve with a time scale much longer than the time it takes the eddies to get advected past the sensor.
• Criterion: σ u
<< U
Willis and Deardorff (1976) σ u
< 0.5 U

1.
Temperature (T)

2. Dew-point temperature (T
3. Mixing ratio (r)
4. Specific humidity (q)

5. Potential temperature (θ) - Poisson equation:
It is conserved for adiabatic processes.

 z



C g p z

T g

 z C p

 r


 g v d
C p q d
)

C p
=specific heat at constant pressure
 v

T d
: Temperature at which the air becomes saturated for a given water vapor pressur e e
Lapse Rate:  

T
 z
ADIABATIC case:
Temperature that an air parcel with absolute temperature T and pressure P would have if brought adiabatically to the pressure of 1000-mb
(100 KPa)
 
= –( Dry adiabatic lapse rate )= 9.8 ° C/km ad
 
 z

0

T

  z C g p

5. Virtual Temperature (T v
) - for unsaturated air, T v
is given by
T v

T

1 0.61
q

6. Virtual Potential Temperature (θ v
) given by
 v
    q

• Definition of ATMOSPHERIC STABILITY based on θ v
Temperature at which dry air has the same density as moist air at the same pressure q is the specific humidity
Atmospheric stability:
• NEUTRAL



 z
V
Dry Adiabatic lapse rate + NO convection
• UNSTABLE
• STABLE

Superadiabatic lapse rate

Subadiabatic lapse rate

 
 z
V

 
 z
V

0


0


Hydrostatic Equation:
First Law of
Thermodynamics:

P
 z
   g [1] dU
 dH
 dW
Change in internal energy
Heat exchange
[More details in Arya (2001)]
Work on the volume

C dT p
 dH
 dP
[2]
Assuming adiabatic conditions (i.e., no exchange of heat with surroundings, i.e., dH=0 )
Combining equations [1] and [2]:
  ad
 
T
 z
 ad
  g
 
9.8 K km
C p

1
(dry adiabatic lapse rate)
Ideal gas law
P
 
R T air dP
 
C dT p
 

P C T p
-1 dP R dT air
 
Integrating from to
P o
,

 
T

P o

R air
C p

P


T

P o
 0.286

P

For dry air: C p
=1005 J K -1 kg -1 and R=287.04 J K -1 kg -1
R
*
R air
 m air
Absolute gas constant:
R*=8.314 J K -1 mole -1