Balance between Coriolis and the vertical friction mixing of momentum, or
stress, leads to Ekman currents. Integrating this
balance vertically (in practice over the top few tens of meters) gives us the Ekman* transport*:

_{}

These components of
Ekman transport describe depth integrated flow (in *m ^{2}s^{-1}*) (i.e.
velocity

The units of m^{2}
s^{-1} can be thought of as the total transport (m^{3} s^{-1})
per meter perpendicular to the current.

Conveniently, the
details of the eddy viscosity profile (the vertical rate of momentum mixing)
are irrelevant to this *transport*
result.

In an infinite
ocean, uniform winds would generate uniform Ekman
transports and the ocean currents would be the same everywhere.

But the ocean is
not infinite, and winds are variable, so Ekman
transports are not spatially uniform, which leads to converge and divergence of
the surface currents.

This effect is
dramatic at the coast where winds parallel to the coast cannot drive Ekman transports across the coastline. The details of the
ocean circulation response in this case are complicated, but the dominant
features of the transport patterns can be deduced from mass balance concepts.

Assuming the
upwelling pattern is 2-dimensional and uniform alongshore, the Ekman transport offshore must be balanced by water uplifted
from below.

The zone of active
upwelling can be seen as a band of cold water adjacent to the coast, and this
has a characteristic with determined by the Rossby
radius which depends

_{}

In coastal NJ
waters the scales are roughly h = 10m, density difference of 2 kg m^{-3},
and *f*=10^{-4} s^{-1}.
g =9.81 m s^{-2}, so

R ~ (10 x 10 x 2/1025)^{1/2}
10^{4} = 14 km

The vertical
transport due to upwelling occurs over this horizontal distance next to the
coast, so an average vertical velocity can be estimated from mass conservation.

Mass conservation
also demands that flow feed the upwelling, and this would come from offshore in
the 2-dimensional idealized case, or possibly from a divergence of the along
shelf flow.

There must be an alongshelf flow because of the pressure gradient set up by
horizontal density pattern (geostrophy) which will
come to later.

Q: Recalling what
you know about the global patterns of winds, what latitudes would you expect to
be characterized by converging Ekman transports and
therefore downward Ekman pumping?

A: The region between the Trades and Westerlies

The net influence
of converging or diverging horizontal Ekman
transports can be quantified by considering the conservation of mass equation:

_{}

Figure
3.24 Ocean Circulation: Ekman pumping (convergence
and divergence)

Recall that the Ekman transport components are related to the wind stress:

_{}

Where _{} the Ekman pumping velocity *w _{E}* is
negative, i.e. there is a convergence of Ekman
transports that

This downward Ekman pumping between the Trades and Westerlies
generates a depressed thermocline in the center of
the subtropical gyres.

This is the case in
both hemispheres, because the sign of curl wind stress and *f* both differ, so *w _{e}
< 0.*

The baroclinic pressure gradients associated with this drive
the large scale gyre circulations, and conservation of mass closes the gyre
circulations with intense poleward western boundary
currents.

*Suggested reading: *

·
*Chapters 3.2, 3.3,
3.4 of Ocean Circulation*

·
*Section 9.4 of Pond
and Pickard*

·
*Chapter 9 of
Stewart*