diverge, resulting in low heights at the shore. (b^/b less than 1-0-)
Similarly, heights will be greater at a headland than m a bay. Since
the wave energy contained between two orthogonals is constant, a larger
part of the total energy expended at the shore is focused on projections
from the shoreline; consequently, refraction straightens an irregular
coast. Bottom topography can be inferred from refraction patterns on
aerial photography. The pattern in Figure 2-17 indicates the presence
of a submarine ridge.
Refraction diagrams can provide a measure of changes in waves
approaching a shore. However, the accuracy of refraction diagrams is
limited by the validity of the theory of construction and the accuracy
of depth data. The orthogonal direction change (Equation 2-78) is
derived for straight parallel contours. It is difficult to carry an
orthogonal accurately into shore over complex bottom features (Munk and
Arthur, 1951). Moreover, the équation is derived for small waves moving
over mild slopes.
Dean (1973) considers the combined effects of refraction and shoaling including nonlinearities applied to a slope with depth contours
parallel to the beach but not necessarily of constant slope. He finds
that non-linear effects can significantly increase (in comparison with
linear theory) both amplification and angular tuming of waves of low
steepness in deep water.
Strict accuracy for height changes cannot be expected for slopes
steeper than 1:10, although model tests hâve shown that direction
changes nearly as predicted even over a vertical discontinu!ty (Wiegel
and Arnold, 1957). Accuracy where orthogonals bend sharply or exhibit
extreme divergence or convergence is questionable because of energy
transfer along the crest. The phenomenon has been studied by Beitinjani
and Brater (1965), Battjes (1968) and Whalin (1971). Where two orthogonals roeet, a caustic -develops.
A caustic is an envelope of orthogonal crossings, caused by convergence of wave energy at the caustic
point. An analysis of wave behavior near a caustic is not available;
however, qualitative analytical results show that wave amplitude decays
exponentially away from a caustic in the shadow zone, and there is a
phase shift of ir/2 across the caustic (Whalin 1971). Wave behavior
near a caustic has also been studied by Pierson (1950), Chao (1970) and
others. Little quantitative information is available for the area
beyond a caustic.
2.328 Refraction of Océan Waves.
océan waves are more complicated.
Unlike Monochromatic waves, actual
r
------------ Their crest lengths are short; their
form does not remain permanent; and their speed, period, and direction
of propagation vary from wave to wave.
2-78
Similarly, heights will be greater at a headland than m a bay. Since
the wave energy contained between two orthogonals is constant, a larger
part of the total energy expended at the shore is focused on projections
from the shoreline; consequently, refraction straightens an irregular
coast. Bottom topography can be inferred from refraction patterns on
aerial photography. The pattern in Figure 2-17 indicates the presence
of a submarine ridge.
Refraction diagrams can provide a measure of changes in waves
approaching a shore. However, the accuracy of refraction diagrams is
limited by the validity of the theory of construction and the accuracy
of depth data. The orthogonal direction change (Equation 2-78) is
derived for straight parallel contours. It is difficult to carry an
orthogonal accurately into shore over complex bottom features (Munk and
Arthur, 1951). Moreover, the équation is derived for small waves moving
over mild slopes.
Dean (1973) considers the combined effects of refraction and shoaling including nonlinearities applied to a slope with depth contours
parallel to the beach but not necessarily of constant slope. He finds
that non-linear effects can significantly increase (in comparison with
linear theory) both amplification and angular tuming of waves of low
steepness in deep water.
Strict accuracy for height changes cannot be expected for slopes
steeper than 1:10, although model tests hâve shown that direction
changes nearly as predicted even over a vertical discontinu!ty (Wiegel
and Arnold, 1957). Accuracy where orthogonals bend sharply or exhibit
extreme divergence or convergence is questionable because of energy
transfer along the crest. The phenomenon has been studied by Beitinjani
and Brater (1965), Battjes (1968) and Whalin (1971). Where two orthogonals roeet, a caustic -develops.
A caustic is an envelope of orthogonal crossings, caused by convergence of wave energy at the caustic
point. An analysis of wave behavior near a caustic is not available;
however, qualitative analytical results show that wave amplitude decays
exponentially away from a caustic in the shadow zone, and there is a
phase shift of ir/2 across the caustic (Whalin 1971). Wave behavior
near a caustic has also been studied by Pierson (1950), Chao (1970) and
others. Little quantitative information is available for the area
beyond a caustic.
2.328 Refraction of Océan Waves.
océan waves are more complicated.
Unlike Monochromatic waves, actual
r
------------ Their crest lengths are short; their
form does not remain permanent; and their speed, period, and direction
of propagation vary from wave to wave.
2-78