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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