Question: Why 45 o, physics or math? andare perpendicular to each other 45 o relation holds for boundary layer solution Physics: Coriolis force is balanced by vertical mixing (friction) for Ekman flow If A z is constant, 45 o relation is not likely to hold Only if B=0, i.e., as z  - 

Question: Why 45 o, physics or math? andare not likely perpendicular to each other Physics: Coriolis force is balanced by vertical mixing (friction) for Ekman flow If A z is not constant, 45 o 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&S The data are much sparse.

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 Reference: Lumpkin, R. and Z. Garraffo, 2005: Evaluating the Decomposition of Tropical Atlantic Drifter Observations. J. Atmos. Oceanic Techn. I 22, Lumpkin, R. and S. L. Garzoli, 2005: Near-surface Circulation in the Tropical Atlantic Ocean. Deep-Sea Res. I 52(3), , /j.dsr

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

Annual Mean Surface Current Pacific Ocean, 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 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) where (3) (4) are total zonal and meridional transport of mass sum of geostrophic and ageostropic transports

Differentiating, we have DefineWe 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 35 o N,  -4 s -1,  2  m -1 s -1, assume  x  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) =10 6 m 3 /s

A More General Form of Sverdrup Equation Surface stress curl Bottom stress curl Bottom topography effect Vanish if the bottom is flat Or flow follows topographic contour