Ocean currents II

Wind-water interaction and drag forces Ekman transport circular and geostrophic flow General ocean flow pattern

Wind-Water surface interaction Water motion at the surface of the ocean (mixed layer) is driven by wind effects Friction causes drag effects on the water transferring momentum from the atmospheric winds to the ocean surface water

The drag force Wind generates vertical and horizontal motion in the water triggering convective motion causing turbulent mixing down to about 100m depth which defines the isothermal mixed layer The drag force FD on the water depends on wind velocity v

wavesofemergencethelyparticular

androughnesssurfaceondepending

areasectionalcrossACninteractiowaterwindfor

factoressdimensionltcoefficiendragCvACF

D

DaDD

0020

2

Katsushika Hokusai The Great Wave off Kanagawa

The Beaufort Scale is an empirical measure describing wind speed based on the observed sea conditions (1 knot = 0514 ms = 185 kmh)

For land and city people Bft 6 Bft 8

Bft 9 Bft 10 Bft 11 Bft 12

Bft 7

s

mBv 238360

A strong breeze of B=6 corresponds to wind speed of v=39 to 49 kmh at which long waves begin to form and white foam crests become frequent The drag force can be calculated to

2

2

2

3

3

2

5187518751212000010

0010512451200

mNAForNAs

mmA

m

kgF

Cs

m

h

kmv

m

kgvACF

DD

DaaDD

For a strong gale (B=12) v=35 ms the drag stress on the water will be

00250351200

367535120000250

3

2

2

3

Da

D

Cs

mv

m

kg

mNs

m

m

kgAF

Conversion from scale to wind velocity

Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z

sm

kgdz

fdzf

f

transportofdirectionvectordefines

ftermsvectorin

zuf

zz

zzz

Am

AF

D

D

0

0

ˆˆ

ˆ

ˆ

1ˆ

1

uM

Mzuz

z

τuz

uz

z

τuz

Ek

Ek

D

D

kg

N

mass

force

zA

mparameterCoriolissf

A

mufuAmAFvCAF ccaDDD

1

2

sin2

sin2

Ekman mass transport vector

dep

th v

ecto

r

Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is

zufz

f

MfMfz

D

EkEkD

sin2

90sin1 0

zuM

depth thdensity wi waterof increase linear moreless a is assumption

sm

kgdz

Ek

0

uMEk

Ekman transport

Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right

22

15

3

15015

150

1837000020101834

000201060

1001200

10183435sin1029272

10292735sin2

m

N

sm

kg

sm

kgsMfz

sm

kgm

s

m

m

kgzuM

ssf

sfMfz

EkD

Ek

EkD

Weak force done by winds of Basymp2 with h

km

s

m

m

kgsm

kg

Cv

D

D 339130

00101200

1

3

2

Typical surface wind stress conditions

Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums

sin2

2

vC

f

zMMfz aDD

EkEkD

Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2

at the southern latitude of 40oS

sm

kg

s

m

N

fM

ssf

sf

DEk

3

15

2

15015

150

1067210379

250

1037940sin1029272

10292740sin2

About 2 tons of water are shifted within 1 sec by 1 meter to the left

Determine the wind velocity for a typical drag coefficient CD=0002

h

km

s

m

m

kgsm

kgs

C

Mfv

C

Mfv

aD

Ek

aD

Ek 1290

12000020

1013210379

3

315

2

About B=1-2 on the Beauford Scale

Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts

Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon

Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

Wind-Water surface interaction Water motion at the surface of the ocean (mixed layer) is driven by wind effects Friction causes drag effects on the water transferring momentum from the atmospheric winds to the ocean surface water

The drag force Wind generates vertical and horizontal motion in the water triggering convective motion causing turbulent mixing down to about 100m depth which defines the isothermal mixed layer The drag force FD on the water depends on wind velocity v

wavesofemergencethelyparticular

androughnesssurfaceondepending

areasectionalcrossACninteractiowaterwindfor

factoressdimensionltcoefficiendragCvACF

D

DaDD

0020

2

Katsushika Hokusai The Great Wave off Kanagawa

The Beaufort Scale is an empirical measure describing wind speed based on the observed sea conditions (1 knot = 0514 ms = 185 kmh)

For land and city people Bft 6 Bft 8

Bft 9 Bft 10 Bft 11 Bft 12

Bft 7

s

mBv 238360

A strong breeze of B=6 corresponds to wind speed of v=39 to 49 kmh at which long waves begin to form and white foam crests become frequent The drag force can be calculated to

2

2

2

3

3

2

5187518751212000010

0010512451200

mNAForNAs

mmA

m

kgF

Cs

m

h

kmv

m

kgvACF

DD

DaaDD

For a strong gale (B=12) v=35 ms the drag stress on the water will be

00250351200

367535120000250

3

2

2

3

Da

D

Cs

mv

m

kg

mNs

m

m

kgAF

Conversion from scale to wind velocity

Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z

sm

kgdz

fdzf

f

transportofdirectionvectordefines

ftermsvectorin

zuf

zz

zzz

Am

AF

D

D

0

0

ˆˆ

ˆ

ˆ

1ˆ

1

uM

Mzuz

z

τuz

uz

z

τuz

Ek

Ek

D

D

kg

N

mass

force

zA

mparameterCoriolissf

A

mufuAmAFvCAF ccaDDD

1

2

sin2

sin2

Ekman mass transport vector

dep

th v

ecto

r

Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is

zufz

f

MfMfz

D

EkEkD

sin2

90sin1 0

zuM

depth thdensity wi waterof increase linear moreless a is assumption

sm

kgdz

Ek

0

uMEk

Ekman transport

Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right

22

15

3

15015

150

1837000020101834

000201060

1001200

10183435sin1029272

10292735sin2

m

N

sm

kg

sm

kgsMfz

sm

kgm

s

m

m

kgzuM

ssf

sfMfz

EkD

Ek

EkD

Weak force done by winds of Basymp2 with h

km

s

m

m

kgsm

kg

Cv

D

D 339130

00101200

1

3

2

Typical surface wind stress conditions

Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums

sin2

2

vC

f

zMMfz aDD

EkEkD

Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2

at the southern latitude of 40oS

sm

kg

s

m

N

fM

ssf

sf

DEk

3

15

2

15015

150

1067210379

250

1037940sin1029272

10292740sin2

About 2 tons of water are shifted within 1 sec by 1 meter to the left

Determine the wind velocity for a typical drag coefficient CD=0002

h

km

s

m

m

kgsm

kgs

C

Mfv

C

Mfv

aD

Ek

aD

Ek 1290

12000020

1013210379

3

315

2

About B=1-2 on the Beauford Scale

Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts

Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon

Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

The drag force Wind generates vertical and horizontal motion in the water triggering convective motion causing turbulent mixing down to about 100m depth which defines the isothermal mixed layer The drag force FD on the water depends on wind velocity v

wavesofemergencethelyparticular

androughnesssurfaceondepending

areasectionalcrossACninteractiowaterwindfor

factoressdimensionltcoefficiendragCvACF

D

DaDD

0020

2

Katsushika Hokusai The Great Wave off Kanagawa

The Beaufort Scale is an empirical measure describing wind speed based on the observed sea conditions (1 knot = 0514 ms = 185 kmh)

For land and city people Bft 6 Bft 8

Bft 9 Bft 10 Bft 11 Bft 12

Bft 7

s

mBv 238360

A strong breeze of B=6 corresponds to wind speed of v=39 to 49 kmh at which long waves begin to form and white foam crests become frequent The drag force can be calculated to

2

2

2

3

3

2

5187518751212000010

0010512451200

mNAForNAs

mmA

m

kgF

Cs

m

h

kmv

m

kgvACF

DD

DaaDD

For a strong gale (B=12) v=35 ms the drag stress on the water will be

00250351200

367535120000250

3

2

2

3

Da

D

Cs

mv

m

kg

mNs

m

m

kgAF

Conversion from scale to wind velocity

Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z

sm

kgdz

fdzf

f

transportofdirectionvectordefines

ftermsvectorin

zuf

zz

zzz

Am

AF

D

D

0

0

ˆˆ

ˆ

ˆ

1ˆ

1

uM

Mzuz

z

τuz

uz

z

τuz

Ek

Ek

D

D

kg

N

mass

force

zA

mparameterCoriolissf

A

mufuAmAFvCAF ccaDDD

1

2

sin2

sin2

Ekman mass transport vector

dep

th v

ecto

r

Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is

zufz

f

MfMfz

D

EkEkD

sin2

90sin1 0

zuM

depth thdensity wi waterof increase linear moreless a is assumption

sm

kgdz

Ek

0

uMEk

Ekman transport

Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right

22

15

3

15015

150

1837000020101834

000201060

1001200

10183435sin1029272

10292735sin2

m

N

sm

kg

sm

kgsMfz

sm

kgm

s

m

m

kgzuM

ssf

sfMfz

EkD

Ek

EkD

Weak force done by winds of Basymp2 with h

km

s

m

m

kgsm

kg

Cv

D

D 339130

00101200

1

3

2

Typical surface wind stress conditions

Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums

sin2

2

vC

f

zMMfz aDD

EkEkD

Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2

at the southern latitude of 40oS

sm

kg

s

m

N

fM

ssf

sf

DEk

3

15

2

15015

150

1067210379

250

1037940sin1029272

10292740sin2

About 2 tons of water are shifted within 1 sec by 1 meter to the left

Determine the wind velocity for a typical drag coefficient CD=0002

h

km

s

m

m

kgsm

kgs

C

Mfv

C

Mfv

aD

Ek

aD

Ek 1290

12000020

1013210379

3

315

2

About B=1-2 on the Beauford Scale

Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts

Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon

Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

The Beaufort Scale is an empirical measure describing wind speed based on the observed sea conditions (1 knot = 0514 ms = 185 kmh)

For land and city people Bft 6 Bft 8

Bft 9 Bft 10 Bft 11 Bft 12

Bft 7

s

mBv 238360

A strong breeze of B=6 corresponds to wind speed of v=39 to 49 kmh at which long waves begin to form and white foam crests become frequent The drag force can be calculated to

2

2

2

3

3

2

5187518751212000010

0010512451200

mNAForNAs

mmA

m

kgF

Cs

m

h

kmv

m

kgvACF

DD

DaaDD

For a strong gale (B=12) v=35 ms the drag stress on the water will be

00250351200

367535120000250

3

2

2

3

Da

D

Cs

mv

m

kg

mNs

m

m

kgAF

Conversion from scale to wind velocity

Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z

sm

kgdz

fdzf

f

transportofdirectionvectordefines

ftermsvectorin

zuf

zz

zzz

Am

AF

D

D

0

0

ˆˆ

ˆ

ˆ

1ˆ

1

uM

Mzuz

z

τuz

uz

z

τuz

Ek

Ek

D

D

kg

N

mass

force

zA

mparameterCoriolissf

A

mufuAmAFvCAF ccaDDD

1

2

sin2

sin2

Ekman mass transport vector

dep

th v

ecto

r

Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is

zufz

f

MfMfz

D

EkEkD

sin2

90sin1 0

zuM

depth thdensity wi waterof increase linear moreless a is assumption

sm

kgdz

Ek

0

uMEk

Ekman transport

Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right

22

15

3

15015

150

1837000020101834

000201060

1001200

10183435sin1029272

10292735sin2

m

N

sm

kg

sm

kgsMfz

sm

kgm

s

m

m

kgzuM

ssf

sfMfz

EkD

Ek

EkD

Weak force done by winds of Basymp2 with h

km

s

m

m

kgsm

kg

Cv

D

D 339130

00101200

1

3

2

Typical surface wind stress conditions

Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums

sin2

2

vC

f

zMMfz aDD

EkEkD

Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2

at the southern latitude of 40oS

sm

kg

s

m

N

fM

ssf

sf

DEk

3

15

2

15015

150

1067210379

250

1037940sin1029272

10292740sin2

About 2 tons of water are shifted within 1 sec by 1 meter to the left

Determine the wind velocity for a typical drag coefficient CD=0002

h

km

s

m

m

kgsm

kgs

C

Mfv

C

Mfv

aD

Ek

aD

Ek 1290

12000020

1013210379

3

315

2

About B=1-2 on the Beauford Scale

Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts

Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon

Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

For land and city people Bft 6 Bft 8

Bft 9 Bft 10 Bft 11 Bft 12

Bft 7

s

mBv 238360

A strong breeze of B=6 corresponds to wind speed of v=39 to 49 kmh at which long waves begin to form and white foam crests become frequent The drag force can be calculated to

2

2

2

3

3

2

5187518751212000010

0010512451200

mNAForNAs

mmA

m

kgF

Cs

m

h

kmv

m

kgvACF

DD

DaaDD

For a strong gale (B=12) v=35 ms the drag stress on the water will be

00250351200

367535120000250

3

2

2

3

Da

D

Cs

mv

m

kg

mNs

m

m

kgAF

Conversion from scale to wind velocity

Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z

sm

kgdz

fdzf

f

transportofdirectionvectordefines

ftermsvectorin

zuf

zz

zzz

Am

AF

D

D

0

0

ˆˆ

ˆ

ˆ

1ˆ

1

uM

Mzuz

z

τuz

uz

z

τuz

Ek

Ek

D

D

kg

N

mass

force

zA

mparameterCoriolissf

A

mufuAmAFvCAF ccaDDD

1

2

sin2

sin2

Ekman mass transport vector

dep

th v

ecto

r

Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is

zufz

f

MfMfz

D

EkEkD

sin2

90sin1 0

zuM

depth thdensity wi waterof increase linear moreless a is assumption

sm

kgdz

Ek

0

uMEk

Ekman transport

Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right

22

15

3

15015

150

1837000020101834

000201060

1001200

10183435sin1029272

10292735sin2

m

N

sm

kg

sm

kgsMfz

sm

kgm

s

m

m

kgzuM

ssf

sfMfz

EkD

Ek

EkD

Weak force done by winds of Basymp2 with h

km

s

m

m

kgsm

kg

Cv

D

D 339130

00101200

1

3

2

Typical surface wind stress conditions

Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums

sin2

2

vC

f

zMMfz aDD

EkEkD

Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2

at the southern latitude of 40oS

sm

kg

s

m

N

fM

ssf

sf

DEk

3

15

2

15015

150

1067210379

250

1037940sin1029272

10292740sin2

About 2 tons of water are shifted within 1 sec by 1 meter to the left

Determine the wind velocity for a typical drag coefficient CD=0002

h

km

s

m

m

kgsm

kgs

C

Mfv

C

Mfv

aD

Ek

aD

Ek 1290

12000020

1013210379

3

315

2

About B=1-2 on the Beauford Scale

Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts

Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon

Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

s

mBv 238360

A strong breeze of B=6 corresponds to wind speed of v=39 to 49 kmh at which long waves begin to form and white foam crests become frequent The drag force can be calculated to

2

2

2

3

3

2

5187518751212000010

0010512451200

mNAForNAs

mmA

m

kgF

Cs

m

h

kmv

m

kgvACF

DD

DaaDD

For a strong gale (B=12) v=35 ms the drag stress on the water will be

00250351200

367535120000250

3

2

2

3

Da

D

Cs

mv

m

kg

mNs

m

m

kgAF

Conversion from scale to wind velocity

Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z

sm

kgdz

fdzf

f

transportofdirectionvectordefines

ftermsvectorin

zuf

zz

zzz

Am

AF

D

D

0

0

ˆˆ

ˆ

ˆ

1ˆ

1

uM

Mzuz

z

τuz

uz

z

τuz

Ek

Ek

D

D

kg

N

mass

force

zA

mparameterCoriolissf

A

mufuAmAFvCAF ccaDDD

1

2

sin2

sin2

Ekman mass transport vector

dep

th v

ecto

r

Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is

zufz

f

MfMfz

D

EkEkD

sin2

90sin1 0

zuM

depth thdensity wi waterof increase linear moreless a is assumption

sm

kgdz

Ek

0

uMEk

Ekman transport

Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right

22

15

3

15015

150

1837000020101834

000201060

1001200

10183435sin1029272

10292735sin2

m

N

sm

kg

sm

kgsMfz

sm

kgm

s

m

m

kgzuM

ssf

sfMfz

EkD

Ek

EkD

Weak force done by winds of Basymp2 with h

km

s

m

m

kgsm

kg

Cv

D

D 339130

00101200

1

3

2

Typical surface wind stress conditions

Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums

sin2

2

vC

f

zMMfz aDD

EkEkD

Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2

at the southern latitude of 40oS

sm

kg

s

m

N

fM

ssf

sf

DEk

3

15

2

15015

150

1067210379

250

1037940sin1029272

10292740sin2

About 2 tons of water are shifted within 1 sec by 1 meter to the left

Determine the wind velocity for a typical drag coefficient CD=0002

h

km

s

m

m

kgsm

kgs

C

Mfv

C

Mfv

aD

Ek

aD

Ek 1290

12000020

1013210379

3

315

2

About B=1-2 on the Beauford Scale

Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts

Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon

Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z

sm

kgdz

fdzf

f

transportofdirectionvectordefines

ftermsvectorin

zuf

zz

zzz

Am

AF

D

D

0

0

ˆˆ

ˆ

ˆ

1ˆ

1

uM

Mzuz

z

τuz

uz

z

τuz

Ek

Ek

D

D

kg

N

mass

force

zA

mparameterCoriolissf

A

mufuAmAFvCAF ccaDDD

1

2

sin2

sin2

Ekman mass transport vector

dep

th v

ecto

r

Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is

zufz

f

MfMfz

D

EkEkD

sin2

90sin1 0

zuM

depth thdensity wi waterof increase linear moreless a is assumption

sm

kgdz

Ek

0

uMEk

Ekman transport

Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right

22

15

3

15015

150

1837000020101834

000201060

1001200

10183435sin1029272

10292735sin2

m

N

sm

kg

sm

kgsMfz

sm

kgm

s

m

m

kgzuM

ssf

sfMfz

EkD

Ek

EkD

Weak force done by winds of Basymp2 with h

km

s

m

m

kgsm

kg

Cv

D

D 339130

00101200

1

3

2

Typical surface wind stress conditions

Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums

sin2

2

vC

f

zMMfz aDD

EkEkD

Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2

at the southern latitude of 40oS

sm

kg

s

m

N

fM

ssf

sf

DEk

3

15

2

15015

150

1067210379

250

1037940sin1029272

10292740sin2

About 2 tons of water are shifted within 1 sec by 1 meter to the left

Determine the wind velocity for a typical drag coefficient CD=0002

h

km

s

m

m

kgsm

kgs

C

Mfv

C

Mfv

aD

Ek

aD

Ek 1290

12000020

1013210379

3

315

2

About B=1-2 on the Beauford Scale

Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts

Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon

Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

dep

th v

ecto

r

Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is

zufz

f

MfMfz

D

EkEkD

sin2

90sin1 0

zuM

depth thdensity wi waterof increase linear moreless a is assumption

sm

kgdz

Ek

0

uMEk

Ekman transport

Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right

22

15

3

15015

150

1837000020101834

000201060

1001200

10183435sin1029272

10292735sin2

m

N

sm

kg

sm

kgsMfz

sm

kgm

s

m

m

kgzuM

ssf

sfMfz

EkD

Ek

EkD

Weak force done by winds of Basymp2 with h

km

s

m

m

kgsm

kg

Cv

D

D 339130

00101200

1

3

2

Typical surface wind stress conditions

Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums

sin2

2

vC

f

zMMfz aDD

EkEkD

Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2

at the southern latitude of 40oS

sm

kg

s

m

N

fM

ssf

sf

DEk

3

15

2

15015

150

1067210379

250

1037940sin1029272

10292740sin2

About 2 tons of water are shifted within 1 sec by 1 meter to the left

Determine the wind velocity for a typical drag coefficient CD=0002

h

km

s

m

m

kgsm

kgs

C

Mfv

C

Mfv

aD

Ek

aD

Ek 1290

12000020

1013210379

3

315

2

About B=1-2 on the Beauford Scale

Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts

Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon

Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right

22

15

3

15015

150

1837000020101834

000201060

1001200

10183435sin1029272

10292735sin2

m

N

sm

kg

sm

kgsMfz

sm

kgm

s

m

m

kgzuM

ssf

sfMfz

EkD

Ek

EkD

Weak force done by winds of Basymp2 with h

km

s

m

m

kgsm

kg

Cv

D

D 339130

00101200

1

3

2

Typical surface wind stress conditions

Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums

sin2

2

vC

f

zMMfz aDD

EkEkD

Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2

at the southern latitude of 40oS

sm

kg

s

m

N

fM

ssf

sf

DEk

3

15

2

15015

150

1067210379

250

1037940sin1029272

10292740sin2

About 2 tons of water are shifted within 1 sec by 1 meter to the left

Determine the wind velocity for a typical drag coefficient CD=0002

h

km

s

m

m

kgsm

kgs

C

Mfv

C

Mfv

aD

Ek

aD

Ek 1290

12000020

1013210379

3

315

2

About B=1-2 on the Beauford Scale

Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts

Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon

Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

Typical surface wind stress conditions

Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums

sin2

2

vC

f

zMMfz aDD

EkEkD

Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2

at the southern latitude of 40oS

sm

kg

s

m

N

fM

ssf

sf

DEk

3

15

2

15015

150

1067210379

250

1037940sin1029272

10292740sin2

About 2 tons of water are shifted within 1 sec by 1 meter to the left

Determine the wind velocity for a typical drag coefficient CD=0002

h

km

s

m

m

kgsm

kgs

C

Mfv

C

Mfv

aD

Ek

aD

Ek 1290

12000020

1013210379

3

315

2

About B=1-2 on the Beauford Scale

Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts

Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon

Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

sin2

2

vC

f

zMMfz aDD

EkEkD

Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2

at the southern latitude of 40oS

sm

kg

s

m

N

fM

ssf

sf

DEk

3

15

2

15015

150

1067210379

250

1037940sin1029272

10292740sin2

About 2 tons of water are shifted within 1 sec by 1 meter to the left

Determine the wind velocity for a typical drag coefficient CD=0002

h

km

s

m

m

kgsm

kgs

C

Mfv

C

Mfv

aD

Ek

aD

Ek 1290

12000020

1013210379

3

315

2

About B=1-2 on the Beauford Scale

Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts

Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon

Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts

Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon

Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon

Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water

Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel

Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density

PaatmP

zsurface

zgPzP

PTSneglecting

PTSgz

P

gdz

dP

surface

refsurface

ref

5101

PakmPkmz

PakmPkmz

Pamm

kg

s

mPamPmz

7

7

6

32

5

10444

1011

10100100081910100100

Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo

Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude

Geostrophic flow

A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere

Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow

Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed

Pzu

Puz

ˆ1

01

ˆ

f

velocityflowayielding

fFF pc

With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km

L

z

f

gu

ref

surface

The pressure gradient is also affected along coastlines with upwards sloping ground level

Geostrophic ocean flow

With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km

L

z

f

gu

ref

surface

Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity

Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms

s

m

m

m

kg

m

kgs

s

m

u

sfsf

m

kg

m

kg

m

kg

L

z

f

gu

surface

ref

surface

13

3

15

2

15150

333

1030000002

041000

1000102927

819

10292710292730sin2

42226

Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m

Gulf stream flow velocity

Ocean current simulation for different temperature zones

NASAGoddard Space Flight Center Scientific Visualization Studio

The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force

Single water drop flow

Geostrophic flow induced variations in ocean surface height

The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height

6

2

614

101

819

1010110

L

m

s

ms

mms

g

uLf

kmLsfs

mufor 10001010 14

Ocean Surface Height

Example Gulf of Mexico

httpwwwaomlnoaagovphoddhosaltimetryphp

Flow pattern Water height

Altitude anomalies

Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level

Changing average sea altitude levels

Based on observational data such as tide level measurements and satellite based altimetry

Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level

Geostrophic flow

A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere

Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow

Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed

Pzu

Puz

ˆ1

01

ˆ

f

velocityflowayielding

fFF pc

With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km

L

z

f

gu

ref

surface

The pressure gradient is also affected along coastlines with upwards sloping ground level

Geostrophic ocean flow

With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km

L

z

f

gu

ref

surface

Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity

Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms

s

m

m

m

kg

m

kgs

s

m

u

sfsf

m

kg

m

kg

m

kg

L

z

f

gu

surface

ref

surface

13

3

15

2

15150

333

1030000002

041000

1000102927

819

10292710292730sin2

42226

Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m

Gulf stream flow velocity

Ocean current simulation for different temperature zones

NASAGoddard Space Flight Center Scientific Visualization Studio

The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force

Single water drop flow

Geostrophic flow induced variations in ocean surface height

The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height

6

2

614

101

819

1010110

L

m

s

ms

mms

g

uLf

kmLsfs

mufor 10001010 14

Ocean Surface Height

Example Gulf of Mexico

httpwwwaomlnoaagovphoddhosaltimetryphp

Flow pattern Water height

Altitude anomalies

Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level

Changing average sea altitude levels

Based on observational data such as tide level measurements and satellite based altimetry

Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level

Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed

Pzu

Puz

ˆ1

01

ˆ

f

velocityflowayielding

fFF pc

With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km

L

z

f

gu

ref

surface

The pressure gradient is also affected along coastlines with upwards sloping ground level

Geostrophic ocean flow

With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km

L

z

f

gu

ref

surface

Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity

Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms

s

m

m

m

kg

m

kgs

s

m

u

sfsf

m

kg

m

kg

m

kg

L

z

f

gu

surface

ref

surface

13

3

15

2

15150

333

1030000002

041000

1000102927

819

10292710292730sin2

42226

Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m

Gulf stream flow velocity

Ocean current simulation for different temperature zones

NASAGoddard Space Flight Center Scientific Visualization Studio

The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force

Single water drop flow

Geostrophic flow induced variations in ocean surface height

The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height

6

2

614

101

819

1010110

L

m

s

ms

mms

g

uLf

kmLsfs

mufor 10001010 14

Ocean Surface Height

Example Gulf of Mexico

httpwwwaomlnoaagovphoddhosaltimetryphp

Flow pattern Water height

Altitude anomalies

Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level

Changing average sea altitude levels

Based on observational data such as tide level measurements and satellite based altimetry

Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level

Geostrophic ocean flow

With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km

L

z

f

gu

ref

surface

Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity

Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms

s

m

m

m

kg

m

kgs

s

m

u

sfsf

m

kg

m

kg

m

kg

L

z

f

gu

surface

ref

surface

13

3

15

2

15150

333

1030000002

041000

1000102927

819

10292710292730sin2

42226

Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m

Gulf stream flow velocity

Ocean current simulation for different temperature zones

NASAGoddard Space Flight Center Scientific Visualization Studio

The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force

Single water drop flow

Geostrophic flow induced variations in ocean surface height

The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height

6

2

614

101

819

1010110

L

m

s

ms

mms

g

uLf

kmLsfs

mufor 10001010 14

Ocean Surface Height

Example Gulf of Mexico

httpwwwaomlnoaagovphoddhosaltimetryphp

Flow pattern Water height

Altitude anomalies

Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level

Changing average sea altitude levels

Based on observational data such as tide level measurements and satellite based altimetry

Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level

Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms

s

m

m

m

kg

m

kgs

s

m

u

sfsf

m

kg

m

kg

m

kg

L

z

f

gu

surface

ref

surface

13

3

15

2

15150

333

1030000002

041000

1000102927

819

10292710292730sin2

42226

Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m

Gulf stream flow velocity

Ocean current simulation for different temperature zones

NASAGoddard Space Flight Center Scientific Visualization Studio

The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force

Single water drop flow

Geostrophic flow induced variations in ocean surface height

The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height

6

2

614

101

819

1010110

L

m

s

ms

mms

g

uLf

kmLsfs

mufor 10001010 14

Ocean Surface Height

Example Gulf of Mexico

httpwwwaomlnoaagovphoddhosaltimetryphp

Flow pattern Water height

Altitude anomalies

Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level

Changing average sea altitude levels

Based on observational data such as tide level measurements and satellite based altimetry

Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level

Gulf stream flow velocity

Ocean current simulation for different temperature zones

NASAGoddard Space Flight Center Scientific Visualization Studio

The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force

Single water drop flow

Geostrophic flow induced variations in ocean surface height

The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height

6

2

614

101

819

1010110

L

m

s

ms

mms

g

uLf

kmLsfs

mufor 10001010 14

Ocean Surface Height

Example Gulf of Mexico

httpwwwaomlnoaagovphoddhosaltimetryphp

Flow pattern Water height

Altitude anomalies

Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level

Changing average sea altitude levels

Based on observational data such as tide level measurements and satellite based altimetry

Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level

Ocean current simulation for different temperature zones

NASAGoddard Space Flight Center Scientific Visualization Studio

The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force

Single water drop flow

Geostrophic flow induced variations in ocean surface height

The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height

6

2

614

101

819

1010110

L

m

s

ms

mms

g

uLf

kmLsfs

mufor 10001010 14

Ocean Surface Height

Example Gulf of Mexico

httpwwwaomlnoaagovphoddhosaltimetryphp

Flow pattern Water height

Altitude anomalies

Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level

Changing average sea altitude levels

Based on observational data such as tide level measurements and satellite based altimetry

Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level

The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force

Single water drop flow

Geostrophic flow induced variations in ocean surface height

The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height

6

2

614

101

819

1010110

L

m

s

ms

mms

g

uLf

kmLsfs

mufor 10001010 14

Ocean Surface Height

Example Gulf of Mexico

httpwwwaomlnoaagovphoddhosaltimetryphp

Flow pattern Water height

Altitude anomalies

Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level

Changing average sea altitude levels

Based on observational data such as tide level measurements and satellite based altimetry

Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level

Geostrophic flow induced variations in ocean surface height

The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height

6

2

614

101

819

1010110

L

m

s

ms

mms

g

uLf

kmLsfs

mufor 10001010 14

Ocean Surface Height

Example Gulf of Mexico

httpwwwaomlnoaagovphoddhosaltimetryphp

Flow pattern Water height

Altitude anomalies

Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level

Changing average sea altitude levels

Based on observational data such as tide level measurements and satellite based altimetry

Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level

6

2

614

101

819

1010110

L

m

s

ms

mms

g

uLf

kmLsfs

mufor 10001010 14

Ocean Surface Height

Example Gulf of Mexico

httpwwwaomlnoaagovphoddhosaltimetryphp

Flow pattern Water height

Altitude anomalies

Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level

Changing average sea altitude levels

Based on observational data such as tide level measurements and satellite based altimetry

Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level

Example Gulf of Mexico

httpwwwaomlnoaagovphoddhosaltimetryphp

Flow pattern Water height

Altitude anomalies

Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level

Changing average sea altitude levels

Based on observational data such as tide level measurements and satellite based altimetry

Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level

Changing average sea altitude levels

Based on observational data such as tide level measurements and satellite based altimetry

Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level