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.

More recent equipment: surface drifter a platform designed to move with the ocean current

Surface current observations

Annual Mean Surface Current North Atlantic, Drifting Buoy Data Assembly Center, Miami, Florida Atlantic Oceanographic and Meteorological Laboratory, NOAA

Annual Mean Surface current from surface drifter measurements Indian Ocean, 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.

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

Sverdrup Relation Consider the following balance in an ocean of depth h of flat bottom (1) (2), Differentiating, we have Using continuity equation Integrating vertically from –h to 0, we have (neglecting bottom stress and surface height change) whereand, we have  Sverdrup relation

and Since, we have set x =0 at the eastern boundary, More generally,

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

Alternative derivation of Sverdrup Relation Construct vorticity equation from geostrophic balance (1) (2)  Integrating over the whole ocean depth, we have where is the entrainment rate from the Ekman layer The Sverdrup transport is the total of geostrophic and Ekman transport. The indirectly driven V g may be much larger than V E. at 45 o N

1 Sverdrup (Sv) =10 6 m 3 /s

Ekman layer at bottom Spatially changing sea surface height η and bottom topography z B and pressure p B. Assume atmospheric pressure p η ≈0. Let, Integratingover the vertical column, we have A more general form of the Sverdrup relation, where Taking into account of these factors, the meridional transport can be derived as,

Vorticity Equation In physical oceanography, we deal mostly with the vertical component of vorticity, From horizontal momentum equation, (1) (2) which is notated as Taking, we have

Considering the case of constant ρ. For a shallow layer of water (depth H<<L), u and v are not function of z because the horizontal pressure gradient is not a function of z. (In general, the vortex tilting term, is usually small. Then we have the simplified vorticity equation Since the vorticity equation can be written as (ignoring friction) ζ+f is the absolute vorticity

Using the Continuity Equation For a layer of thickness H, consider a material column We get or Potential Vorticity Equation

In the ocean’s interior, for large-scale movement, we have the differential form of the Sverdrup relation i.e.,ζ<<f