Question: Why 45o, physics or math?

and are perpendicular to each other

45o relation holds for boundary layer solution

Physics: Coriolis force is balanced by vertical mixing (friction) for Ekman flow

If Az is constant,

45o relation is not likely to hold

Only if B=0, i.e., as z-

Question: Why 45o, physics or math?

and are not likely perpendicular to each other

Physics: Coriolis force is balanced by vertical mixing (friction) for Ekman flow

If Az is not constant,

45o relation is not likely to hold even for boundary layer solution

Wind-driven circulation II

Wind pattern and oceanic gyres

Sverdrup Relation

Vorticity Equation

What generate the gyre circulation?

Surface current measurement from ship drift

Current measurements are harder to make than T&SThe data are much sparse.

http://www.aoml.noaa.gov/phod/dac/gdp_drifter.php

Surface current observations

Surface current observations

A climatology of near-surface currents and SST for the world, at one degree resolution, derived from satellite-tracked surface drifting buoy observations. Most recent data included: 1 January 2011. Reference:Lumpkin, R. and Z. Garraffo, 2005: Evaluating the Decomposition of Tropical Atlantic Drifter Observations. J. Atmos. Oceanic Techn. I 22, 1403-1415.Lumpkin, R. and S. L. Garzoli, 2005: Near-surface Circulation in the Tropical Atlantic Ocean. Deep-Sea Res. I 52(3),495-518, 10.1016/j.dsr.2004.09.001.

http://www.aoml.noaa.gov/phod/dac/drifter_climatology.html

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

Annual Mean Surface CurrentPacific 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.

Sverdrup RelationConsider 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)

where

(3)

(4)

are total zonal and meridional transport of mass

sum of geostrophic and ageostropic transports

Differentiating , we have

Define We have

(3) and (4) can be written as

(5) (6)

Using continuity equation

And define

Vertical component of the wind stress curl

We have Sverdrup equation

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 10-11 m-1 s-1, assume x10-1 Nm-2 y=0

then

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

A More General Form of Sverdrup Equation

Surface stress curl

Bottom stress curl

Bottom topography effectVanish if the bottom is flatOr flow follows topographic contour