question: why 45 o, physics or math? andare perpendicular to each other 45 o relation holds for...
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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-
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