 # Wind-driven circulation II

## Presentation on theme: "Wind-driven circulation II"— Presentation transcript:

Wind-driven circulation II
●Wind pattern and oceanic gyres ●Sverdrup Relation ●Vorticity Equation

Surface current measurement from ship drift
Current measurements are harder to make than T&S The data are much sparse.

Surface current observations

Surface current observations

Drifting Buoy Data Assembly Center, Miami, Florida
Atlantic Oceanographic and Meteorological Laboratory, NOAA

Annual Mean Surface Current Pacific Ocean, 1995-2003
Drifting Buoy Data Assembly Center, Miami, Florida Atlantic Oceanographic and Meteorological Laboratory, NOAA

Schematic picture of the major surface currents of the world oceans
Note the anticyclonic circulation in the subtropics (the subtropical gyres)

Relation between surface winds and subtropical gyres

Surface winds and oceanic gyres: A more realistic view
Note that the North Equatorial Counter Current (NECC) is against the direction of prevailing wind.

Mean surface current tropical Atlantic Ocean
Note the North Equatorial Counter Current (NECC)

Consider the following balance in an ocean of depth h of flat bottom
Sverdrup Relation Consider the following balance in an ocean of depth h of flat bottom (1) (2) Integrating vertically from –h to 0 for both (1) and (2), we have (neglecting bottom stress and surface height change) (3) (4) where are total zonal and meridional transport of mass sum of geostrophic and ageostropic transports

(3) and (4) can be written as
Define We have (3) and (4) can be written as (6) (5) Differentiating , we have

We have Sverdrup equation
Using continuity equation And define We have Sverdrup equation Vertical component of the wind stress curl If The line provides a natural boundary that separate the circulation into “gyres”

is the total meridional mass transport
Geostrophic transport Ekman transport Order of magnitude example: At 35oN, -4 s-1, 2  m-1 s-1, assume x10-1 Nm-2 y=0

Alternative derivation of Sverdrup Relation
Construct vorticity equation from geostrophic balance (1) Assume =constant (2) Integrating over the whole ocean depth, we have

where is the entrainment rate from the surface Ekman layer at 45oN The Sverdrup transport is the total of geostrophic and Ekman transport. The indirectly driven Vg may be much larger than VE.

then

set x =0 at the eastern boundary,
Since , we have set x =0 at the eastern boundary, Further assume In the trade wind and equatorial zones, the 2nd derivative term dominates:

Mass Transport Since Let , ,  where  is stream function.
Problem: only one boundary condition can be satisfied.

1 Sverdrup (Sv) =106 m3/s