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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-
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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
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Wind-driven circulation II
Wind pattern and oceanic gyres
Sverdrup Relation
Vorticity Equation
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What generate the gyre circulation?
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Surface current measurement from ship drift
Current measurements are harder to make than T&SThe data are much sparse.
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http://www.aoml.noaa.gov/phod/dac/gdp_drifter.php
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Surface current observations
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Surface current observations
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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
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Drifting Buoy Data Assembly Center, Miami, Florida Atlantic Oceanographic and Meteorological Laboratory, NOAA
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Annual Mean Surface CurrentPacific Ocean, 1995-2003
Drifting Buoy Data Assembly Center, Miami, Florida Atlantic Oceanographic and Meteorological Laboratory, NOAA
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Schematic picture of the major surface currents of the world oceans
Note the anticyclonic circulation in the subtropics (the subtropical gyres)
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Relation between surface winds and subtropical gyres
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Surface winds and oceanic gyres: A more realistic view
Note that the North Equatorial Counter Current (NECC) is against the direction of prevailing wind.
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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
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Differentiating , we have
Define We have
(3) and (4) can be written as
(5) (6)
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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”
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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
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then
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Since , we have
set x =0 at the eastern boundary,
Further assume
In the trade wind and equatorial zones, the 2nd derivative term dominates:
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Mass Transport
Since
Let ,
,
where is stream function.
Problem: only one boundary condition can be satisfied.
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1 Sverdrup (Sv) =106 m3/s
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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