(1) Most of the interior boundaries of many harbors are lined with structures such as bulkheads or reveted

slopes. Recent laboratory investigations (Seelig and Ahrens 1981; Seelig 1983; Allsop and Hettiarachchi

1988) indicate that the reflection coefficients for most structure forms can be given by the following

2

(II-7-8)

2

where the values of coefficients *a *and *b *depend primarily on the structure geometry and to a smaller extent

on whether waves are monochromatic or irregular. The Iribarren number employs the structure slope and the

wave height at the toe of the structure.

(2) Table II-7-1 presents values for the coefficients *a *and *b *collected from the above references.

Plane slope-monochromatic waves

1.0

5.5

Plane slope-irregular waves

1.1

5.7

Rubble-mound breakwaters1

0.6

6.6

Dolos-armored breakwaters - monochromatic waves

0.56

10.0

Tetrapod-armored breakwaters - irregular waves

0.48

9.6

1

This is an average conservative value. Seelig and Ahrens (1981) recommend a range of values for *a *and *b *that depend on the

number of stone layers, the relative water depth (*d*/*L*), and the ratio of incident wave height to breaker height.

EXAMPLE PROBLEM II-7-4

FIND:

The height of the reflected wave.

GIVEN:

A wave in deep water has a height of 1.8 m and a period of 6 sec. It propagates toward shore without

refracting or diffracting to reflect from a rubble-mound breakwater located in water 5 m deep. The breakwater

front slope is 1:1.75 (29.7 deg).

SOLUTION:

From linear wave theory shoaling calculations (Part II-1) the wave height at the structure would be 1.70 m

(this is *H*i). From the linear wave theory, the deepwater wave length is *L*0 = 56.2 m. Then, from Equation II-7-6,

the Iribarren number is

tan 29.7o

' 3.28

1.70 / 56.2

For the coefficient values *a *= 0.6 and *b *= 6.6 (from Table II-7-1), Equation II-7-8 yields

0.6 (3.28)2

' 0.37

6.6 % (3.28)2

Thus, the reflected wave height *H*r = *C*rHi = 0.37(1.70) = 0.63 m.

II-7-28

Harbor Hydrodynamics

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