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7 Ocean Currents
Very often the depth, hE, is compared to the depth of the upper mixed layer.
However, it should be noted that the mixed layer depth is the result of longterm history of the wind action in a given area. On the other hand, the Ekman's
depth is influenced much more by even short periods of strong winds at the
time of observation, and it should be much smaller than the mixed-layer depth.
The total Ekman's surface current velocity depends on the wind stress at the
surface through the expression:
v27rT0
V o = - - -
hEPw ifi'
(7.21 )
in which TO is given by Eq. (7.9). When ClO ::::; 1.4 X 10- 3 and VoIVlO rv
(0.013-0.030), the Ekman's depth, hE, is typically between 200 m (for VlO = 20
mls and Equation (7.19) indicates that at the sea surface (z = 0), the current speeds
are:
u(O)
(7.22)
v(O)
This means that the surface current flows at 45° to the right (left) of the wind
direction in the Northern (Southern) Hemisphere.
At the depth z = -hE, which is given by Eq. (7.20), it is seen that:
(7.23)
This shows that at z = -hE the current vector has decreased to the value
exp( -7r) times the surface speed (rv 0.043Uo), and that the current direction
is exactly opposite to the surface current direction.
The Ekman's spiral is illustrated in Fig. 7.7 for the Northern Hemispheres.
Figure 7.7a shows the perspective view of the current velocity decreasing and
rotating clockwise with increasing depth, and Fig. 7.7b gives the plan view of
velocities at equal depth intervals (~z = hEllO) and the Ekman's spiral.
Of special importance is the total vertically integrated horizontal water volume or mass transport in wind-driven currents. The total mass transport is
obtained by integrating Eq. (7.19) over the depth between z = 0 and z = -2hE,
after multiplication by the constant water density, Pw. The lower level was chosen deep enough such that the influence of the wind driven current would be
essentially zero i. e. z = - 2hE where the speed is exp( - 27r) = 0.002 of that
7 Ocean Currents
Very often the depth, hE, is compared to the depth of the upper mixed layer.
However, it should be noted that the mixed layer depth is the result of longterm history of the wind action in a given area. On the other hand, the Ekman's
depth is influenced much more by even short periods of strong winds at the
time of observation, and it should be much smaller than the mixed-layer depth.
The total Ekman's surface current velocity depends on the wind stress at the
surface through the expression:
v27rT0
V o = - - -
hEPw ifi'
(7.21 )
in which TO is given by Eq. (7.9). When ClO ::::; 1.4 X 10- 3 and VoIVlO rv
(0.013-0.030), the Ekman's depth, hE, is typically between 200 m (for VlO = 20
mls and Equation (7.19) indicates that at the sea surface (z = 0), the current speeds
are:
u(O)
(7.22)
v(O)
This means that the surface current flows at 45° to the right (left) of the wind
direction in the Northern (Southern) Hemisphere.
At the depth z = -hE, which is given by Eq. (7.20), it is seen that:
(7.23)
This shows that at z = -hE the current vector has decreased to the value
exp( -7r) times the surface speed (rv 0.043Uo), and that the current direction
is exactly opposite to the surface current direction.
The Ekman's spiral is illustrated in Fig. 7.7 for the Northern Hemispheres.
Figure 7.7a shows the perspective view of the current velocity decreasing and
rotating clockwise with increasing depth, and Fig. 7.7b gives the plan view of
velocities at equal depth intervals (~z = hEllO) and the Ekman's spiral.
Of special importance is the total vertically integrated horizontal water volume or mass transport in wind-driven currents. The total mass transport is
obtained by integrating Eq. (7.19) over the depth between z = 0 and z = -2hE,
after multiplication by the constant water density, Pw. The lower level was chosen deep enough such that the influence of the wind driven current would be
essentially zero i. e. z = - 2hE where the speed is exp( - 27r) = 0.002 of that