106
3 An Introduction to Surface Waves
storm surges observed in the North Sea caused serious flooding and the loss
of lives in the Netherlands and England. The deep depression, travelling eastwards the north of the British Isles and then south-eastwards into the North
Sea, raised the water level in the southern part of the North Sea. The amplitude of storm surge on the eastern coast of England reached about 2.75 m,
while in some places in the Dutch coast it was greater than 3.95 m.
3.9 Rossby Waves
Fluid moving on the Earth's surface possesses vorticity about a vertical axis as
a result of the Earth's rotation at any location other than the Equator. This is
the planetary vorticity, and its magnitude is equal to the Corio lis parameter, f.
Planetary vorticity has to be distinguished from a small scale of fluid element
discussed in Sect. 2.6 and Appendix C.l. Following Mann and Lazier (1996),
let us consider the eastward flowing current. Water element, besides moving
east, is rotating around to the left (in the Northern Hemisphere) with the
rotation of the Earth at a rate of f = 2wEsin¢ (see Sect. 5.3.1). When water
is deflected northward, the vertical component of the rotation increases and
water is moving faster as the Corio lis parameter increases.
In the reference frame attached to the Earth, water coming from south is
rotating to the right or back toward its initial latitude and it can even pass
this latitude arriving in the region where the rate of rotation f is less than the
water in the current. Then the water appears to turn to the left and relative to
the local vertical and again head backward toward its original latitude. These
large, slow, horizontal oscillations in the open ocean are known as Rossby
waves. Their amplitudes are of hundreds of kilometres, their wavelengths can
be as long as hundreds to thousands of kilometres, and periods are of the order
of days.
Using the similar arguments as above, it can be shown that the Rossby waves
cannot be formed on a westward flowing current. However, they can be formed
when the vorticity is changed due to change in depth. The explanation of these
topographic Rossby waves is given by Tomczak and Godfrey (1994) and comprehensive mathematical treatment of the Rossby waves is done by Pedlosky
(1979). As will be shown in Chap. 7, the Rossby waves play important role in
the low-frequency variations in the Equatorial Pacific that lead to El Nino.
3 An Introduction to Surface Waves
storm surges observed in the North Sea caused serious flooding and the loss
of lives in the Netherlands and England. The deep depression, travelling eastwards the north of the British Isles and then south-eastwards into the North
Sea, raised the water level in the southern part of the North Sea. The amplitude of storm surge on the eastern coast of England reached about 2.75 m,
while in some places in the Dutch coast it was greater than 3.95 m.
3.9 Rossby Waves
Fluid moving on the Earth's surface possesses vorticity about a vertical axis as
a result of the Earth's rotation at any location other than the Equator. This is
the planetary vorticity, and its magnitude is equal to the Corio lis parameter, f.
Planetary vorticity has to be distinguished from a small scale of fluid element
discussed in Sect. 2.6 and Appendix C.l. Following Mann and Lazier (1996),
let us consider the eastward flowing current. Water element, besides moving
east, is rotating around to the left (in the Northern Hemisphere) with the
rotation of the Earth at a rate of f = 2wEsin¢ (see Sect. 5.3.1). When water
is deflected northward, the vertical component of the rotation increases and
water is moving faster as the Corio lis parameter increases.
In the reference frame attached to the Earth, water coming from south is
rotating to the right or back toward its initial latitude and it can even pass
this latitude arriving in the region where the rate of rotation f is less than the
water in the current. Then the water appears to turn to the left and relative to
the local vertical and again head backward toward its original latitude. These
large, slow, horizontal oscillations in the open ocean are known as Rossby
waves. Their amplitudes are of hundreds of kilometres, their wavelengths can
be as long as hundreds to thousands of kilometres, and periods are of the order
of days.
Using the similar arguments as above, it can be shown that the Rossby waves
cannot be formed on a westward flowing current. However, they can be formed
when the vorticity is changed due to change in depth. The explanation of these
topographic Rossby waves is given by Tomczak and Godfrey (1994) and comprehensive mathematical treatment of the Rossby waves is done by Pedlosky
(1979). As will be shown in Chap. 7, the Rossby waves play important role in
the low-frequency variations in the Equatorial Pacific that lead to El Nino.