Lecture 5: Wind-stress and
Ekman layers
Atmosphere, Ocean, Climate
Dynamics
EESS 146B/246B
Wind-stress and Ekman layers
• Distribution of the wind and wind-stress
over the oceans.
• Wind-driven turbulence.
• Ekman layers
• Ekman transport and pumping/suction.
Atmospheric circulation
Polar cell
Ferrel cell
Hadley cell
•Rotation causes the atmospheric circulation to form three overturning cells:
the Hadley, Ferrel, and Polar cells.
•The Coriolis force causes winds to veer to the east or west, driving the trade
winds, westerlies, and polar easterlies.
Hadley cell in the lab
SUBTROPICS
SUBTROPICS
TRADE
WINDS
EQUATOR
EQUATOR
Atmospheric circulation
Westerlies
Trade winds
Westerlies
Animation of water vapor in the atmosphere observed from a satellite
Winds at the surface of the ocean
Polar Easterlies
Westerlies
Trade Winds
Westerlies
•Winds measured at the sea surface via satellites reflect the large scale
atmospheric circulation.
Distribution of the wind-stress
Relation between the wind-stress and the
frictional force
stress= - momentum flux
MOMENTUM
FLUX
z
Force equals net flux of
momentum into volume
x
Force per unit volume
Frictional Force=Force per unit mass
Turbulence in the upper ocean
•Winds blowing over the ocean induce sheared flows and waves that generate
turbulence. This turbulence transfers the momentum imparted by the winds down
into the ocean.
Numerical simulation of wind-driven
turbulence
WIND STRESS
The correlation between
the vertical and horizontal
turbulent velocity shows
how turbulence transfers
momentum downwards
Parameterization of the turbulent
momentum flux
•Turbulence tends to flux momentum down the gradient of the mean flow
in an analogous fashion to the viscous transfer of momentum.
•Thus the turbulent flux of momentum can be parameterized in terms of
a down-gradient flux with an eddy viscosity
Typical eddy viscosity in
the upper ocean
Kinematic (molecular)
viscosity of water
Wind-driven acceleration without rotation
depth
WIND-STRESS
Down-wind velocity
Frictional force and acceleration
•Without rotation, friction accelerates a flow that diffuses downward, extending
through the water column over time.
Wind-driven acceleration with rotation
depth
WIND-STRESS
Down-wind velocity
Frictional force
Acceleration
•With rotation, after a time
Coriolis
force
friction is balanced by the Coriolis force.
•The wind-driven flow is confined to the surface in an Ekman layer
thick.
Ekman force balance and transport
•In the Ekman layer the frictional force is balanced by the Coriolis force.
•Integrating the force balance in
the vertical yields the net mass
transport per unit length
associated with the Ekman flow
Ekman spiral and transport
WIND
Ekman
transport
N. HEMISPHERE
•The Ekman flow spirals with depth, a phenomenon known as the Ekman spiral.
•The net horizontal motion averaged in depth is to the right of the wind and is referred to
as the Ekman transport.
Ekman spiral and transport
WIND
Ekman
transport
S. HEMISPHERE
•The Ekman transport is to the left of the wind in the Southern Hemisphere.
Distribution of the wind-stress
•What is the structure of the Ekman transport given the distribution of the wind-stress?
Ekman pumping/suction
•Convergence/divergence of the Ekman transport drives vertical motions:
assume w=0 at z=0
vertical velocity
at the beneath
the Ekman layer
Vertical motions
associated with
the curl of the
wind-stress
•When
the Ekman vertical velocity is known as the Ekman pumping
•When
the Ekman vertical velocity is known as the Ekman suction
Distribution of the Ekman pumping/suction
suction
•The Ekman vertical velocity is quite weak ~10s m/year but it is responsible for
driving the circulation of the ocean gyres and the ACC.