toward deep water. In such cases, a sheaf or fan of orthogonals may be
projected seaward in directions some 5 or 10 degrees apart. See Figure
2-22a. With the deepwater directions thus determined by the individual
orthogonals, companion orthogonals may be projected shoreward on either
side of the seaward projected ones to détermine the refraction coefficient
for the various directions of wave approach. (See Figure 2-22b.)
2.325 Other Graphical Methods of Refraction Analysis. Another graphical
method for the construction of refraction diagrams is the wave-front
method (Johnson, et al., 1948). This method is particularly applicable
to very long waves where the crest alignment is also desired. The method
is not presented here, where many diagrams are required, because, where
many diagrams are required, it is overbalanced by the advantages of the
orthogonal method. The orthogonal method permits the direct construction
of orthogonals and détermination of the refraction coefficient without the
intermediate step of first constructing successive wave crests. Thus,
when the wave crests are not required, significant time is saved by using
the orthogonal method.
2.326 Computer Methods for Refraction Analysis. Harrison and Wilson (1964)
developed a method for the numerical calculation of wave refraction by use
of an electronic computer. Wilson (1966) extended the method so that, in
addition to the numerical calculation, the actual plotting of refraction
diagrams is accomplished automatically by use of a computer. Numerical
methods are a practical means of developing wave refraction diagrams when
an extensive refraction study of an area is required, and when they can
be relied upon to give accurate results. However, the interprétation of
computer output requires care, and the limitations of the particular scheme
used should be considered in the évaluation of the results. For a discussion of some of these limitations, see Coudert and Raichlen (1970).
For additional references, the reader is referred to the Works of Keller
(1958), Mehr (1962), Griswold (1963), Wilson (1966), Lewis, et al., (1967),
Dobson (1967), Hardy (1968), Chao (1970), and Keulegan and Harrison (1970),
in which a number of availabié computer programs for calculation of refraction diagrams are presented. Most of these programs are based on an algorithm derived by Munk and Arthur (1951) and, as such, are fundamentally
based on the geometrical optics approximation.
(Fermât’s Principle.)
2.327 Interprétation of Results and Diagram Limitations. Some general
observations of refraction phenomena are illustrated in Figures 2-23, 24,
and 25. These figures show the effects of several common bottom features
on passing waves. Figure 2-23 shows the effect of a straight beach with
parallel evenly spaced bottom contours on waves approaching from an angle.
Wave crests turn toward alignment with the bottom contours as the waves
approach shore. The refraction effects on waves normally incident on a
beach fronted by a submarine ridge or submarine dépréssion are illustrated
in Figure 2-24a and 2-24b. The ridge tends to focus wave action toward
the section of beach where the ridge line meets the shoreline. The orthogonals in this région are more closely spaced; hence-^bo/b' is greater
than 1.0 and the waves are higher than they would be if no refraction
occurred. Conversely, a submarine dépréssion will cause orthogonals to
2-75
projected seaward in directions some 5 or 10 degrees apart. See Figure
2-22a. With the deepwater directions thus determined by the individual
orthogonals, companion orthogonals may be projected shoreward on either
side of the seaward projected ones to détermine the refraction coefficient
for the various directions of wave approach. (See Figure 2-22b.)
2.325 Other Graphical Methods of Refraction Analysis. Another graphical
method for the construction of refraction diagrams is the wave-front
method (Johnson, et al., 1948). This method is particularly applicable
to very long waves where the crest alignment is also desired. The method
is not presented here, where many diagrams are required, because, where
many diagrams are required, it is overbalanced by the advantages of the
orthogonal method. The orthogonal method permits the direct construction
of orthogonals and détermination of the refraction coefficient without the
intermediate step of first constructing successive wave crests. Thus,
when the wave crests are not required, significant time is saved by using
the orthogonal method.
2.326 Computer Methods for Refraction Analysis. Harrison and Wilson (1964)
developed a method for the numerical calculation of wave refraction by use
of an electronic computer. Wilson (1966) extended the method so that, in
addition to the numerical calculation, the actual plotting of refraction
diagrams is accomplished automatically by use of a computer. Numerical
methods are a practical means of developing wave refraction diagrams when
an extensive refraction study of an area is required, and when they can
be relied upon to give accurate results. However, the interprétation of
computer output requires care, and the limitations of the particular scheme
used should be considered in the évaluation of the results. For a discussion of some of these limitations, see Coudert and Raichlen (1970).
For additional references, the reader is referred to the Works of Keller
(1958), Mehr (1962), Griswold (1963), Wilson (1966), Lewis, et al., (1967),
Dobson (1967), Hardy (1968), Chao (1970), and Keulegan and Harrison (1970),
in which a number of availabié computer programs for calculation of refraction diagrams are presented. Most of these programs are based on an algorithm derived by Munk and Arthur (1951) and, as such, are fundamentally
based on the geometrical optics approximation.
(Fermât’s Principle.)
2.327 Interprétation of Results and Diagram Limitations. Some general
observations of refraction phenomena are illustrated in Figures 2-23, 24,
and 25. These figures show the effects of several common bottom features
on passing waves. Figure 2-23 shows the effect of a straight beach with
parallel evenly spaced bottom contours on waves approaching from an angle.
Wave crests turn toward alignment with the bottom contours as the waves
approach shore. The refraction effects on waves normally incident on a
beach fronted by a submarine ridge or submarine dépréssion are illustrated
in Figure 2-24a and 2-24b. The ridge tends to focus wave action toward
the section of beach where the ridge line meets the shoreline. The orthogonals in this région are more closely spaced; hence-^bo/b' is greater
than 1.0 and the waves are higher than they would be if no refraction
occurred. Conversely, a submarine dépréssion will cause orthogonals to
2-75