Wind Driven Circulation

- wind energy to the ocean is a “wind stress”

- wind directly drives currents at ~2 - 3% of wind speed

- wind directly drives currents to right/left of wind in NH/SH

- wind driven currents set up variations in sea level

- surface waves transport wind energy over long distances

- turbulent mixing dissipates energy from wind

Geography 104 - “Physical Geography of the World’s Oceans”

Wind Stress (overview)

- forces give rise to ocean circulation

- wind stress is a frictional force parallel (tangential) to the sea surface per unit area

- effect of wind stress is to accelerate ocean’s surface layer

Wind Stress (details)

- (Greek letter tau) represents wind stress

- ρacDu2

ρa is air density (1 kg m-3)

cD is a drag coefficient (~1.4x10-3)

U2 is wind velocity (m2 s-2)

- units are Newtons (force) per meter squared

F = ma or 1 Newton = 1 N = 1 kg m s-2

N m-2 = kg m-1 s-2

Wind Stress (details)

wind speed

drag coefficient

exact processes creating wind stress are complex

Wind Stress (summary)

- many processes contribute to the transfer of momentum from the atmosphere to the ocean

- turbulent friction- capillary waves- wind waves

Wind Stress Bottom Line: process is turbulent; force proportional to wind speed squared (u2)

Coupling between two ocean layers is larger under greater winds. Transfer of momentum is due to turbulent water parcels, rather than just individual molecules

wind stress acts on surface layer, surface layer acts on underlying layer, underlying layer acts on layer below that,………..

winds contribute to upper ocean mixed layer (along with heat and salt)

Vagn Walfrid Ekman (1874-1954)

Ekman Flow – theory for direct wind driven currents published by Ekman in 1905

Wind driven flow named after Ekman because he knew how to do math!

Fridtjof Nansen – deserves much credit for Ekman flow

Nansen was a scientist – explorer

Later dedicated his life to refugee issues

Won Nobel Peace Prize in 1922

Nansen’s Fram

• Nansen built the Fram to reach North Pole

• Unique design to be locked in the ice

• Idea was to lock ship in the ice & wait

• Once close, dog team set out to NP

Fram locked in ice

1893 -1896 - Nansen got to 86o 14’ N

Ekman Flow

• Nansen noticed that movement of the ice-locked ship was 20-40o to right of the wind

• Nansen figured this was due to a steady balance of wind stress, friction & Coriolis forces

• Ekman later developed a mathematical framework based on Nansen’s observations

Ekman Flow

motion at the surface is 45° to right (NH) of wind

Ekman surface flow development

water parcel

surface flow development

water parcel

time = 0

wind force

surface flow development

surface current

time = 1

surface flow development

Coriolis force

friction force

time = 2

surface flow development

time = 3

surface currentturns to right (NH) due to Coriolis

surface flow development

time = 4 (force balance; wind, friction, Coriolis)

surface current 45° to right (NH) of wind

surface flow development

time = 4 time = 4 (force balance)

vector addition (decomposition)

surface flow development

time = 4

components of friction & Coriolis forces opposite wind force

time = 4 (force balance)

surface flow development

time = 4

surface current at 45° to right of wind

time = 4 (force balance)

surface flow development

time = 4

force balance where: friction + Coriolis = wind

time = 4 (force balance)

Ekman Flow

motion at the surface is 45° to right (NH) of wind

ice drift

wind direction

ice drift

Ekman Transport

• The ocean is like a layer cake

• A layer is accelerated by the one above it & slowed by the one beneath it

• Top layer is driven by

• Transport of momentum into interior is turbulent and inefficient

Ekman spiral

Ekman spiral, another view

Ekman spiral, plan view (looking down)

DE is depth of Ekman layer (top ~100 m)

Ekman flow, Ekman spiral, Ekman transport

Ekman transport is 90° to right (NH) of wind

Ekman transport refers to movement of Ekman layer

Friction force in Ekman layer

No friction force for layer coupling beneath Ekman layer

Ekman layer movement

Coriolis force

Ekman layer balance: wind force = Coriolis force

Ekman layer movement

Coriolis force is 90° to right of Ekman transport in NH

Coriolis force

Ekman spiral in observations

Price et al. 1987, Science

theory

observerd

Ekman transport in observations

Price et al. 1987, Science

Readings (Surface and Deep Circulation):Text Chapter 9 (pgs 165 – 170)Reader pgs. 63 – 72