OCEANOGRAPHY 793
each latitude circle over many years. Figure 2 illustrates the
resulting, long-term averaged wind characteristics. The fol-
lowing patterns are apparent:1) Between latitudes 30N and 30S, there is a zone
of easterly (from the east) winds, with an equa-
torward component, commonly referred to as the
“Trade Winds”.
2) Between latitudes 30N and 60N, and 30S and
60 S, there exists zones of westerly winds, each
with a poleward component.
3) Near each pole, there exists a zone of easterly
winds, each with an equatorward component.We note that the Trade Winds are a fairly consistent
feature of the overall wind field, whereas the winds in the
northern and southern zones are highly variable and often
associated with large, transient storm systems. For this
reason, the zones of westerly winds north and south of
the Trade Wind zone are often referred to as the “Roaring
Forties”. Along the equator, at the convergence of the two
components of the Trade Winds, lies a region of relatively
light winds, commonly referred to as the “Doldrums”.
Note that at the wind divergence located at 30N and the
wind convergence at 60S, we can expect regions of anti-
cyclonic (clockwise) wind gyres, whereas in the vicinity of
60 N and 30S, we expect cyclonic (anticlockwise) gyres, as
illustrated in Figure 2.The long-term averaged surface circulation of the world’s
oceans bears a strong resemblance to the above described
pattern of atmospheric motion, with some modifications due
to the influence of the continental landmasses. The main
features of this circulation are illustrated in Figure 3. Note
especially the presence of wind-induced surface current
gyres, as expected from our description of the atmospheric
circulation.
We here depart from what has been up to now a purely
descriptive treatment of the wind-driven motion, to examine
the equations governing this air-sea interaction. For simplicity,
and in the interest of generality, we shall here confine ourselves
to the problem of a steady (constant in time), uniform (constant
in space) surface wind blowing over an infinitely wide, infi-
nitely deep, constant density ocean. For a much more detailed
treatment of the complexities of upper ocean wind-driven
dynamics, the reader is referred to Price et al. (1987).
In physical terms, our problem specification corresponds
to a very large, relatively stationary storm system acting on
the deep ocean (that is, excluding shallow, continental shelf
areas).
The primary forcings acting on our water column, or ver-
tical slice of the water body, are: 1) the surface wind stress;
2) the internal, turbulent shear stresses; and 3) the Coriolis
“force”.
The surface wind stress will be represented as a steady,
uniform shear stress acting in the x-direction: t S. The inter-
nal turbulent shear stresses, which dominate over the viscous
shear stresses, can be defined in a manner analogous to the
viscous stresses, so that:trtrxyAAvvdu
dz
dv
dz,,where our coordinate system is defined in Figure 4. The quan-tities t (^) x , and t (^) y represent the horizontal (x and y) components
of the turbulent shear stress. The quantities u and v are the x
and y components, respectively, of the water velocity. Note
that u and v are functions only of the vertical coordinate,
z, because of our assumption of a steady, horizontally uni-
form wind stress. The constant, A v , represents the turbulent
eddy viscosity coefficient. Strictly speaking, A v is a function
of the turbulent flow field and should be modelled accord-
ingly as another unknown in our system of equations (see,
e.g., Blumberg and Mellor, 1983). In the interest of obtaining
an analytic solution to the governing equations and so obtain
useful information about the gross features of the wind-driven
water motion, we shall here set A v as constant. The quantity,
r , is the (constant) water density.
The Coriolis “force” is not, strictly speaking, a force,
but is rather the result of applying Newton’s second law to
the earth’s rotating reference frame. In physical terms, this
“force” causes a deflection of motion to the right (left) in the
northern (southern) hemisphere.
Doldrums
Easterlies
60° N
Westerlies
Trades
Trades
Westerlies
Easterlies
30° N
0°
30° S
60° S
FIGURE 2 Long-term averaged wind pattern
(Ross, 1982).
C015_001_r03.indd 793C015_001_r03.indd 793 11/18/2005 11:10:01 AM11/18/2005 11:10:01 AM