2.422 Waves Passing a Gap of Width Less than Five Wavelengths at Normal
Ineidenc'e. The solution of this problem is more complex than that for a
single breakwater, and it is not possible to construct a single diagram
for ail conditions. A separate diagram must be drawn for each ratio of
gap width to wavelength B/L. The diagram for a B/L-ratio of 2 is shown
in Figure 2-42 which also illustrâtes its use. Figures 2-43 through 2-52
(Johnson, 1953) show Unes of equal diffraction coefficient for B/L-ratios
of 0.50, 1.00, 1.41, 1.64, 1.78, 2.00, 2.50, 2.95, 3.82 and 5.00. A
sufficient number of diagrams hâve been included to represent most gap
widths encountered in practice. In ail but Figure 2-48 (B/L = 2.00), the
wave icrest lines hâve been omitted. Wave crest lines are usually of use
only for illustrative purposes. They are, however, required for an
accurate estimate of the combined effects of refraction and diffraction.
In such cases, wave crests may be approximated with sufficient accuracy
by circular arcs. For a single breakwater, the arcs will be centered on
the breakwater tip. That part of the wave crest extending into unprotected
water beyond the K' =0.5 line may be approximated by a straight line.
For a breakwater gap, crests that are more than eight wavelengths behind
the breakwater may be approximated by an arc centered at the middle of
the gap; crests to about six wavelengths may be approximated by two arcs,
centered on the two ends of the breakwater and may be connected by a
smooth curve (approximated by a circular arc centered at the middle of
the gap). Only one-half of the diffraction diagram is presented on the
figures since the diagrams are symmetrical about the line x/L = 0.
2.423 Waves Passing a Gap of Width Greater Than Five Wavelengths at
Normal Incidence. Where the breakwater gap width is greater than five
wavelengths, the diffraction effects of each wing are nearly independent,
and the diagram (Figure 2-33) for a single breakwater with a 90° wave
approach angle may be used to define the diffraction characteristic in
the lee of both wings (See Figure 2-53.)
2-424 Diffraction at a Gap-Oblique Incidence. When waves approach at an
angle to the axis of a breakwater, the diffracted wave characteristics
differ from those resulting when waves approach normal to the axis. An
approximate détermination of diffracted wave characteristics may be
obtained by considering the gap to be as wide as its projection in the
direction of incident wave travel as shown in Figure 2-54. Calculated
diffraction diagrams for wave approach angles of 0°, 15°, 30° 45°, 60°
and 75 are shown in Figures 2-55, 56 and 57. Use of these diagrams will
give more accurate results than the approximate method. A comparison of
a 45 incident wave using the approximate method and the more exact diagram
method is shown in Figure 2-58.
2-43 REFRACTION AND DIFFRACTION COMBINED
Usually the bottom seaward and shoreward of a breakwater is not
,12k^h!ref°^e’JrefraCti0n occurs in addition to diffraction. Although
int U?k 16
tbe tW0 bas not
been developed, some innicturi
PI?b em ls Presented by Battjes (1968). An approximate
picture of wave changes may be obtained by: (a) constructing a refraction
2-98
Ineidenc'e. The solution of this problem is more complex than that for a
single breakwater, and it is not possible to construct a single diagram
for ail conditions. A separate diagram must be drawn for each ratio of
gap width to wavelength B/L. The diagram for a B/L-ratio of 2 is shown
in Figure 2-42 which also illustrâtes its use. Figures 2-43 through 2-52
(Johnson, 1953) show Unes of equal diffraction coefficient for B/L-ratios
of 0.50, 1.00, 1.41, 1.64, 1.78, 2.00, 2.50, 2.95, 3.82 and 5.00. A
sufficient number of diagrams hâve been included to represent most gap
widths encountered in practice. In ail but Figure 2-48 (B/L = 2.00), the
wave icrest lines hâve been omitted. Wave crest lines are usually of use
only for illustrative purposes. They are, however, required for an
accurate estimate of the combined effects of refraction and diffraction.
In such cases, wave crests may be approximated with sufficient accuracy
by circular arcs. For a single breakwater, the arcs will be centered on
the breakwater tip. That part of the wave crest extending into unprotected
water beyond the K' =0.5 line may be approximated by a straight line.
For a breakwater gap, crests that are more than eight wavelengths behind
the breakwater may be approximated by an arc centered at the middle of
the gap; crests to about six wavelengths may be approximated by two arcs,
centered on the two ends of the breakwater and may be connected by a
smooth curve (approximated by a circular arc centered at the middle of
the gap). Only one-half of the diffraction diagram is presented on the
figures since the diagrams are symmetrical about the line x/L = 0.
2.423 Waves Passing a Gap of Width Greater Than Five Wavelengths at
Normal Incidence. Where the breakwater gap width is greater than five
wavelengths, the diffraction effects of each wing are nearly independent,
and the diagram (Figure 2-33) for a single breakwater with a 90° wave
approach angle may be used to define the diffraction characteristic in
the lee of both wings (See Figure 2-53.)
2-424 Diffraction at a Gap-Oblique Incidence. When waves approach at an
angle to the axis of a breakwater, the diffracted wave characteristics
differ from those resulting when waves approach normal to the axis. An
approximate détermination of diffracted wave characteristics may be
obtained by considering the gap to be as wide as its projection in the
direction of incident wave travel as shown in Figure 2-54. Calculated
diffraction diagrams for wave approach angles of 0°, 15°, 30° 45°, 60°
and 75 are shown in Figures 2-55, 56 and 57. Use of these diagrams will
give more accurate results than the approximate method. A comparison of
a 45 incident wave using the approximate method and the more exact diagram
method is shown in Figure 2-58.
2-43 REFRACTION AND DIFFRACTION COMBINED
Usually the bottom seaward and shoreward of a breakwater is not
,12k^h!ref°^e’JrefraCti0n occurs in addition to diffraction. Although
int U?k 16
tbe tW0 bas not
been developed, some innicturi
PI?b em ls Presented by Battjes (1968). An approximate
picture of wave changes may be obtained by: (a) constructing a refraction
2-98