M2-Ekman Layer

Section 2: The Planetary
Boundary Layer
Chapter 5 in “Dynamic Meteorology”
The planetary boundary layer is that
portion of the atmosphere in which the
flow field is strongly influenced directly by
interaction with the surface of the earth.
How does the surface of the earth influence the flow
Eddies transport heat, moisture and momentum.
The mechanical impact of all subgrid-scale motions upon an
observable flow is collectively called a frictional force.
Force Balance
At the surface
Within the PBL
Top of the PBL
p −2δp
p −2δp
p −2δp
p −δp
p −δp
p −δp
PGF ~ Co
Three-way balance
PGF ~ Fr
A Tea Cup Experiment
Ekman pumping (or Ekman suction)
and Secondary Circulation
The flow in the free atmosphere is indirectly affected by the friction near
the surface through Ekman pumping or Ekman suction.
Mass convergence into low pressure centers and mass divergence
out of high pressure centers will eventually destroy the weather
systems while forcing upward vertical motion in low and downward
vertical motion in high.
Equations in the PBL
Do we have a closed equation set?
No! Closure assumptions must be made to approximate the unknown
fluxes in terms of the mean state variables.
Assume horizontal homogeneous…
Assume horizontal homogeneous…
Assume force balance in the PBL…
Apply the flux-gradient theory
Assume the vertical flux of a given field is proportional to the
local gradient of the mean:
u'w'  K m ( )
v'w'  K m ( )
u' '  K h ( )
where Km is the eddy viscosity coefficient and Kh is the eddy diffusion of heat.
Assuming Km is a constant, we have:
We will examine the effect of friction on the
wind in the Ekman layer:
 How does the wind field change with height?
 What determines the Ekman pumping (or
Ekman suction)?
 How is the Ekman layer coupled to the free
 The Ekman layer solution does not apply to the surface
 The flux-gradient approximation may not be valid.
 Km is not a constant in the PBL.
 The atmosphere is not neutral.
Barotropic, neutral atmosphere
Stable Stratification
Spin-down above the PBL
Adiabatic cooling
 BL drag + free atmosphere rotation 
convergence over cyclonic circulation 
upward mass transport out of the Ekman layer
 divergence above the Ekman layer  spindown of the cyclone in the free atmosphere
 BL drag + free atmosphere rotation 
convergence over cyclonic circulation 
Ekman pumping  adiabatic cooling (stable
stratification)  thermal wind balance

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