Refraction may be treated analytically at a straight shoreline with
parallel offshore contours, by using Snell's law directly:
/C \
sin a = I — | sin a
\Co
°
(2-78a)
where a is the angle between the wave crest and the shoreline, and a0
is the angle between the deepwater wave crest and the shoreline.
For example, if ao = 30° and the period and depth of the wave
are such that C/C^ = 0.5, then
a = sin"1 [0.5 (0.5)] = 14.5 degrees
cos a = 0.968
and
cosao = 0.866
Vj*
[ cos^\*
/ 0.866
b /
\ cos a )
\ 0.968 /
= 0.945
Figure 2-19 shows the relationships between a, clo, period, depth, and
Kj? in graphical form.
2.321 Procedures in Refraction Diagram Construction - Orthogonal Method.
Charts showing the bottom topography of the study area are obtained. Two
or more charts of differing scale may be required, but the procedures are
identical for charts of any scale. Underwater contours are drawn on the
chart, or on a tracing paper overlay, for various depth intervals. The
depth intervals chosen dépend on the degree of accuracy desired. If
overlays are used, the shoreline should be traced for reference. In
tracing contours, small irregularities must be smoothed out, since bottom
features that are comparâtively small in respect to the wavelength do not
affect the wave appreciably.
The range of wave periods and wave directions to be investigated is
determined by a hindcasting study of historical weather charts or from
other historical records relating to wave period and direction. For each
wave period and direction selected, a separate diagram must be prepared.
C1/C2 values for each contour interval may then be marked between contours
The method of computing C1/C2 is illustrated by Table 2-2; a tabulation
of Ci/C2 for various contour intervals and wave periods is given in
Table C-4 of Appendix C.
To construct orthogonals from deep to shallow water, the deepwater
direction of wave approach is first determined. A deepwater wave front
(crest) is drawn as a straight line perpendicular to this wave direction,
2-69
parallel offshore contours, by using Snell's law directly:
/C \
sin a = I — | sin a
\Co
°
(2-78a)
where a is the angle between the wave crest and the shoreline, and a0
is the angle between the deepwater wave crest and the shoreline.
For example, if ao = 30° and the period and depth of the wave
are such that C/C^ = 0.5, then
a = sin"1 [0.5 (0.5)] = 14.5 degrees
cos a = 0.968
and
cosao = 0.866
Vj*
[ cos^\*
/ 0.866
b /
\ cos a )
\ 0.968 /
= 0.945
Figure 2-19 shows the relationships between a, clo, period, depth, and
Kj? in graphical form.
2.321 Procedures in Refraction Diagram Construction - Orthogonal Method.
Charts showing the bottom topography of the study area are obtained. Two
or more charts of differing scale may be required, but the procedures are
identical for charts of any scale. Underwater contours are drawn on the
chart, or on a tracing paper overlay, for various depth intervals. The
depth intervals chosen dépend on the degree of accuracy desired. If
overlays are used, the shoreline should be traced for reference. In
tracing contours, small irregularities must be smoothed out, since bottom
features that are comparâtively small in respect to the wavelength do not
affect the wave appreciably.
The range of wave periods and wave directions to be investigated is
determined by a hindcasting study of historical weather charts or from
other historical records relating to wave period and direction. For each
wave period and direction selected, a separate diagram must be prepared.
C1/C2 values for each contour interval may then be marked between contours
The method of computing C1/C2 is illustrated by Table 2-2; a tabulation
of Ci/C2 for various contour intervals and wave periods is given in
Table C-4 of Appendix C.
To construct orthogonals from deep to shallow water, the deepwater
direction of wave approach is first determined. A deepwater wave front
(crest) is drawn as a straight line perpendicular to this wave direction,
2-69