EXAMPLE PROBLEM III-2-5

FIND:

Calculate (a) the average (over the directional band) wave height *H*mo and determine an equivalent

significant wave height *H*sig, (b) wave approach angle in the sediment transport coordinate system,

(c) percentage of the total wave data represented by this wave directional angle band, (d) average peak

spectral wave period *T*p, (e) breaking wave height *H*b and angle *α*b, and (f) potential longshore sand

transport rate.

GIVEN:

Wave statistics presented in Table III-2-2. The water depth at which the wave statistics were

developed is 27 m. The azimuth angle (from north) of the outward normal to the beach of interest is

approximately 102o. The sediment is quartz-density sand, and *K*sig = 0.39. Assume κ = 1.0 for

simplicity.

SOLUTION:

(a) Weighting the average wave height in each wave height band with the total number of

observations in that band, calculate an average wave height, *H*mo = 0.93 m; that is:

Hmo = [(0.5)(12858) + (1.5)(4777) + (2.5)(1133) + (3.5)(288) + (4.5)(45) + (5.5)(3) + (6.5)(2)] / 19106

= 0.93 m

As discussed in Part II-1, *H*s and *H*mo are approximately equal when irregular wave profiles are

sinusoidal in shape. However, as depth decreases and waves shoal prior to breaking, they become

nonlinear and peaked in shape rather than sinusoidal. According to Part II-1, the two parameters are

within 10 percent of each other if the depth (in meters) is greater than or equal to 0.0975 *T*p2. In the

example, 27 m is greater than 0.0975 (8.5 sec)2 = 7.1 m; therefore, the average significant wave *H*sig

may be said to be approximately equal to *H*mo.

(b) The data in Table III-2-2 represent the angle band that is centered around WIS angle = 135o.

However, the shoreline outward normal angle is 102o (from north), which means that the angle

associated with transport calculations *α *= 102o - 135o = -33o.

(c) WIS RAL2 data are presented every 3 hr for a 20-year time period, totalling 58,440 data points

for each station (in all wave direction angle bands). The total number of occurrences listed in

Table III-2-2 for the 45o direction band centered around 135o equals 19,106, which means that the

percentage of the total data represented by this angle band equals 19,106/58,440 x 100 percent =

32.7 percent. Scanning the other data for this station (Hubertz et al. 1993, p. A-288 - A-289), this

angle band constitutes the dominant wave direction in terms of number of occurrences for station 72.

(Continued)

Longshore Sediment Transport

III-2-23

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