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Lecture 6: Ekmanpumping/suction and the Taylor-
Proudman effect on a sphereAtmosphere, Ocean, Climate
DynamicsEESS 146B/246B
Ekman pumping/suction and the Taylor-Proudman effect on a sphere
• Vertical motions driven by the Ekman flow.• How the rigidity of the fluid imposed by the
Earth’s rotation translates these vertical motions into the horizontal flows that make up the ocean gyres Taylor-Proudmaneffect.
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
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
•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
Distribution of the Ekman pumping/suction
suction
30 m/y ≈1x10-4 cm/s
10 year mean dynamic topography
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. How does this work?
How does Ekman pumping/suction change the shape of a column of water in the ocean interior?
OCEAN INTERIOR
Two scenarios
•To increase the volume, the column could increase in cross-sectional area or lengthen.
Scenario 1: the cross-sectional area of the column to Ω increases
•The moment of inertia of the column increase thus the net spin must decrease by conservation of angular momentum
•Spin/vorticity is generated, a flow is accelerated.
Scenario 2: the length of the column increases
•If the bottom of the column moves down at the same rate as the Ekman pumping then the volume increases but the moment of inertia of the column does not change.
•No spin/vorticity is induced no acceleration.
w is constant in the direction of the rotation vector
Two scenarios
•Flow acceleration•Generation of vorticity•Non-zero Rossby
•No flow acceleration•No generation of vorticity•Zero Rossby
RELEVANT TO LARGE-SCALE CIRCULATION
How does this work on the spherical Earth
•The water column can change its volume without changing its cross-sectional area to Ω by moving meridionally while not tilting over.
•Ekman pumping/suction generates meridional flows. How strong are these currents?
Taylor Proudman Effect
•The components of the velocity do not vary in the direction parallel to the rotation vector.
•Fluid columns do not tilt over nor change their area.
•Expression of gyroscopic rigidity.
Quantifying the meridional flow
Volume conservation:
Quantifying the meridional flow
Amplification of vertical motions into horizontal motions
Ekman vertical velocity = 30 m/y ≈1x10-4 cm/s
Meridional flow = 0.5 cm/s
AMPLIFICATION