This represents the expenditure of
ft-lb
sec
. ,
5120 ----- X 3600 — = 18.55 X 106 ft-lbs ,
sec
hr
of energy each hour on each foot of beach.
*********** **************
The mean rate of energy transmission associated with waves propagating
into an area of calm water provides a better physical description of the
concept of group velocity. An excellent treatment of this subject is given
by Sverdrup and Munk (1947) and is repeated here.
Quoting from the Beach Erosion Board Technical
Report No. 2, (1942): "As the first wave in the group
advances one wave length, its form induces corresponding velocities in the previously undisturbed water and
the kinetic energy corresponding to those velocities
must be drawn from the energy flowing ahead with the
form. If there is equipartition of energy in the wave,
half of the potential energy which advanced with the
wave must be given over to the kinetic form and the
wave loses height. Advancing another wave length
another half of the potential energy is used to supply
kinetic energy to the undisturbed liquid. The process
continues until the first wave is too small to identify.
The second, third, and subséquent waves move into water
already disturbed and the rate at which they lose height
is less than for the first wave. At the rear of the
group, the potential energy might be imagined as moving
ahead, leaving a fiat surface and half of the total
energy behind as kinetic energy. But the velocity
pattern is such that flow converges toward one section
thus developing a crest and diverges from another
section forming a trough. Thus the kinetic energy is
converted into potential and a wave develops in the
rear of the group."
This concept can be interpreted in a quantitative
manner, by taking the following example from R. Gatewood
(Gaillard 1904, p. 50). Suppose that in a very long
trough containing water originally at rest, a plunger
at one end is suddenly set into harmonie motion and
starts generating waves by periodically imparting an
energy E/2 to the water. After a time interval of n
periods there are n waves présent. Let m be the position of a particular wave in this group such that tt?=1
refers to the wave which has just been generated by
the plunger, m=(n+l')/2 to the center wave, and m=n to
the wave furthest advanced. Let the waves travel with
constant velocity C, and neglect friction.
2-31
ft-lb
sec
. ,
5120 ----- X 3600 — = 18.55 X 106 ft-lbs ,
sec
hr
of energy each hour on each foot of beach.
*********** **************
The mean rate of energy transmission associated with waves propagating
into an area of calm water provides a better physical description of the
concept of group velocity. An excellent treatment of this subject is given
by Sverdrup and Munk (1947) and is repeated here.
Quoting from the Beach Erosion Board Technical
Report No. 2, (1942): "As the first wave in the group
advances one wave length, its form induces corresponding velocities in the previously undisturbed water and
the kinetic energy corresponding to those velocities
must be drawn from the energy flowing ahead with the
form. If there is equipartition of energy in the wave,
half of the potential energy which advanced with the
wave must be given over to the kinetic form and the
wave loses height. Advancing another wave length
another half of the potential energy is used to supply
kinetic energy to the undisturbed liquid. The process
continues until the first wave is too small to identify.
The second, third, and subséquent waves move into water
already disturbed and the rate at which they lose height
is less than for the first wave. At the rear of the
group, the potential energy might be imagined as moving
ahead, leaving a fiat surface and half of the total
energy behind as kinetic energy. But the velocity
pattern is such that flow converges toward one section
thus developing a crest and diverges from another
section forming a trough. Thus the kinetic energy is
converted into potential and a wave develops in the
rear of the group."
This concept can be interpreted in a quantitative
manner, by taking the following example from R. Gatewood
(Gaillard 1904, p. 50). Suppose that in a very long
trough containing water originally at rest, a plunger
at one end is suddenly set into harmonie motion and
starts generating waves by periodically imparting an
energy E/2 to the water. After a time interval of n
periods there are n waves présent. Let m be the position of a particular wave in this group such that tt?=1
refers to the wave which has just been generated by
the plunger, m=(n+l')/2 to the center wave, and m=n to
the wave furthest advanced. Let the waves travel with
constant velocity C, and neglect friction.
2-31