lecture 5: wind-stress and ekman layers - stanford … 5...wind-stress and ekman layers •...
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Lecture 5: Wind-stress and Ekman layers
Atmosphere, Ocean, Climate Dynamics
EESS 146B/246B
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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.
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Atmospheric circulation
•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
Ferrel cell
Polar cell
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Hadley cell in the lab
EQUATOREQUATOREQUATOR
SUBTROPICSSUBTROPICSSUBTROPICS
TRADE WINDS
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Atmospheric circulation
Animation of water vapor in the atmosphere observed from a satellite
Trade winds
Westerlies
Westerlies
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Winds at the surface of the ocean
•Winds measured at the sea surface via satellites reflect the large scale atmospheric circulation.
Westerlies
Westerlies
Trade Winds
Polar Easterlies
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Distribution of the wind-stress
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Relation between the wind-stress and the frictional force
stress= - momentum flux
x
z Force equals net flux of momentum into volume
Force per unit volume
MOMENTUM FLUX
Frictional Force=Force per unit mass
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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.
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Numerical simulation of wind-driven turbulence
WIND STRESS
The correlation between the vertical and horizontal turbulent velocity shows how turbulence transfers momentum downwards
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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
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Wind-driven acceleration without rotation
•Without rotation, friction accelerates a flow that diffuses downward, extending through the water column over time.
WIND-STRESS
Frictional force and accelerationDown-wind velocity
dept
h
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Wind-driven acceleration with rotationWIND-STRESS
dept
h
Frictional force
Acceleration
Down-wind velocity Coriolisforce
•With rotation, after a time friction is balanced by the Coriolis force.
•The wind-driven flow is confined to the surface in an Ekman layer thick.
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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
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Ekman spiral and transport
WIN
D
•The Ekman flow spirals with depth, a phenomenon known as the Ekman spiral.
Ekmantransport
•The net horizontal motion averaged in depth is to the right of the wind and is referred to as the Ekman transport.
N. HEMISPHERE
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Ekman spiral and transport
WIN
D
S. HEMISPHERE
Ekmantransport
•The Ekman transport is to the left of the wind in the Southern Hemisphere.
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Distribution of the wind-stress
•What is the structure of the Ekman transport given the distribution of the wind-stress?
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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
•When the Ekman vertical velocity is known as the Ekman pumping
•When the Ekman vertical velocity is known as the Ekman suction
Vertical motions associated with the curl of the wind-stress
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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.