HOMEWORK #1

1. Problems 1, 5, and 16 from Chapter 5 of Komar.

2. We would like to calculate the wave characteristics for a southwest-facing beach on the south end of Whidbey Island. The beach is ‘typical’ of Puget Sound, in that it is relatively steep dropping into the central basin (depth ~ 250 m). The fetch in exposed directions is as follows:

South = 40 km

Southwest = 4 km

West = 4 km

Northwest = 9 km

For strong winds, we know the spatial probability of each direction based on past records is:

South = 0.75

North = 0.25

All other directions = 0

Based on the same records, the probability a wind speed U will exceed U_a during a given year roughly obeys an exponential distribution given by:

, where U and U_a are in m/s.

The recurrence interval R_t is generally defined by .

a. Calculate the R_t = 10 year H_0.1 and the Airy wave-orbital velocity for that wave at 10 m water depth, using SMB and JONSWAP and a Rayleigh distribution for the waves.

b. How good is the assumption of linear wave theory for this wave?

c. How well will the wind-wave models predict the wave-field (both direction and magnitude)? That is, how accurate are the assumptions contained within those models for the Puget Sound?

Be sure to defend your answers and state any assumptions you make.