3.5 Wind-Generated Waves
97
wind
Fig. 3.12: Waves are propagated from the shoreline in various directions; lengths of
arrows are roughly proportional to amount of energy transported in a given direction
the spectrum curve is a measure of the total wave energy per unit sea surface,
z. e.:
E = l a
OQ S(w )dw.
(3.17)
It is clear that for the same fetch, X, but different wind speed, Vw , the wave
energy will be different. This is illustrated in Fig. 3.11 for three different wind
speeds; 10 mls (~ 20 knots), 15 mls (~ 30 knots) and 20 mls (~ 40 knots),
but for the same fetch of 200 km. It is interesting to note the shift of the
peak frequency, w p , towards lower frequencies when wind speed increases. This
means that for the same fetch, higher wind speeds generate longer waves. For
the case shown in Fig. 3.11, the wavelength associated with the peak frequency
is 91 m, 119 m, and 145 m, respectively. Also the wave energy, proportional to
total area under curve S (w), is greater for highest wind speed.
As the dimension of energy E is [N. m], the dimension of spectrum, S(w),
should be [N· m· s]. If we take into account that E ~ pgH2 and drop the
constant pg, the dimension of energy becomes [m 2 ] and subsequently the dimension of spectrum S(w) is [m 2 ·s], which is frequently used in professional
oceanographical literature.
When observing surface ocean waves, we notice their multidirectionality;
waves travel in many directions, resulting in an apparently confused sea. Consider the simple case of a long coastline extending in the north-south direction,
with a wind of constant speed blowing from the shore normal to shoreline
(Fig. 3.12). Due to the continuity of water mass, and due to the interactions
between waves, waves do not propagate only in the direction in which the wind
is blowing, but spread in the sector of ± 90° from the wind direction. However,
the amount of energy carried by waves in a particular direction depends on the
angle, e, between the wind and wave directions. The highest portion of energy
97
wind
Fig. 3.12: Waves are propagated from the shoreline in various directions; lengths of
arrows are roughly proportional to amount of energy transported in a given direction
the spectrum curve is a measure of the total wave energy per unit sea surface,
z. e.:
E = l a
OQ S(w )dw.
(3.17)
It is clear that for the same fetch, X, but different wind speed, Vw , the wave
energy will be different. This is illustrated in Fig. 3.11 for three different wind
speeds; 10 mls (~ 20 knots), 15 mls (~ 30 knots) and 20 mls (~ 40 knots),
but for the same fetch of 200 km. It is interesting to note the shift of the
peak frequency, w p , towards lower frequencies when wind speed increases. This
means that for the same fetch, higher wind speeds generate longer waves. For
the case shown in Fig. 3.11, the wavelength associated with the peak frequency
is 91 m, 119 m, and 145 m, respectively. Also the wave energy, proportional to
total area under curve S (w), is greater for highest wind speed.
As the dimension of energy E is [N. m], the dimension of spectrum, S(w),
should be [N· m· s]. If we take into account that E ~ pgH2 and drop the
constant pg, the dimension of energy becomes [m 2 ] and subsequently the dimension of spectrum S(w) is [m 2 ·s], which is frequently used in professional
oceanographical literature.
When observing surface ocean waves, we notice their multidirectionality;
waves travel in many directions, resulting in an apparently confused sea. Consider the simple case of a long coastline extending in the north-south direction,
with a wind of constant speed blowing from the shore normal to shoreline
(Fig. 3.12). Due to the continuity of water mass, and due to the interactions
between waves, waves do not propagate only in the direction in which the wind
is blowing, but spread in the sector of ± 90° from the wind direction. However,
the amount of energy carried by waves in a particular direction depends on the
angle, e, between the wind and wave directions. The highest portion of energy