4.2 Wave Parameters Based on Small Amplitude Wave Theory
119
z
z
________________________________ )!WL_
p..,g[1-Klz)] ~ (dynamic)
total
pressure
total
pressure
Fig. 4.9: Vertical profiles of wave-induced pressure
p..,g[1-Klz)] ~
(dynamic)
The first term on the right-hand side represents a hydrostatic pressure due to
submergence and surface displacement. The second term is the dynamic part
of the total pressure, and its contribution to the resulting pressure depends on
wave phase. A more detailed discussion of wave-induced pressure is given in
Appendix C.S.4 and a final vertical profile of wave induced pressure below both
a wave crest and a trough is illustrated in Fig. 4.9. The computer program
D.44 (Appendix D) calculates pressure for an arbitrary submergence, under
wave crest and wave trough.
Wave Energy. From classical physics it is known that a displacement of some
mass, m, from a position of equilibrium against a gravitational field results in
the generation of potential energy. This principle is used in various facilities
to generate energy. Water falling from a reservoir through a turbine eventually
generates electricity. As in surface waves, the water mass has been displaced
from an equilibrium position, and it possesses a potential energy. Even when
there are no waves, potential energy exists because the centre of gravity of the
water mass is above the sea bottom which can be considered as a reference
surface (see Fig. C.7).
Water particles in wave motion are not only displaced from their equilibrium
positions, but they move along circular or elliptical paths. Thus, their velocity
is not zero and therefore they possess some kinetic energy. The total wave energy, per unit area, is the sum of the potential and kinetic energy (see Appendix
C.S for derivation):
( 4.37)
Waves Propagating in an Arbitrary Direction. Consider a top view
of surface waves as in Fig. 4.10. Wave crests are perpendicular to the wave
119
z
z
________________________________ )!WL_
p..,g[1-Klz)] ~ (dynamic)
total
pressure
total
pressure
Fig. 4.9: Vertical profiles of wave-induced pressure
p..,g[1-Klz)] ~
(dynamic)
The first term on the right-hand side represents a hydrostatic pressure due to
submergence and surface displacement. The second term is the dynamic part
of the total pressure, and its contribution to the resulting pressure depends on
wave phase. A more detailed discussion of wave-induced pressure is given in
Appendix C.S.4 and a final vertical profile of wave induced pressure below both
a wave crest and a trough is illustrated in Fig. 4.9. The computer program
D.44 (Appendix D) calculates pressure for an arbitrary submergence, under
wave crest and wave trough.
Wave Energy. From classical physics it is known that a displacement of some
mass, m, from a position of equilibrium against a gravitational field results in
the generation of potential energy. This principle is used in various facilities
to generate energy. Water falling from a reservoir through a turbine eventually
generates electricity. As in surface waves, the water mass has been displaced
from an equilibrium position, and it possesses a potential energy. Even when
there are no waves, potential energy exists because the centre of gravity of the
water mass is above the sea bottom which can be considered as a reference
surface (see Fig. C.7).
Water particles in wave motion are not only displaced from their equilibrium
positions, but they move along circular or elliptical paths. Thus, their velocity
is not zero and therefore they possess some kinetic energy. The total wave energy, per unit area, is the sum of the potential and kinetic energy (see Appendix
C.S for derivation):
( 4.37)
Waves Propagating in an Arbitrary Direction. Consider a top view
of surface waves as in Fig. 4.10. Wave crests are perpendicular to the wave