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

•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

Hadley cell in the lab

EQUATOREQUATOREQUATOR

SUBTROPICSSUBTROPICSSUBTROPICS

TRADE WINDS

Atmospheric circulation

Animation of water vapor in the atmosphere observed from a satellite

Trade winds

Westerlies

Westerlies

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

Distribution of the wind-stress

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

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

•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

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.

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

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

Ekman spiral and transport

WIN

D

S. HEMISPHERE

Ekmantransport

•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

•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

•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.