Spatial Dimensions: L (Wavelength) [m] Temporal Dimension: T (Period - time between successive crests measured by fixed observer) [s] Anatomy of an Ideal Wave

Restoring Force: Gravity Initial Perturbation: Astronomical Forcing, Wind, Seismic, etc. Two Key Ratios control wave dynamics: 1.) h/L The ratio of depth to wavelength 2.) H/L The ratio of amplitude to wavelength Ocean Surface Gravity Waves

We maintain our small amplitude approximation and look at the limits of h/L L/2 < h (“deep wave”)L/20 > h (“shallow wave”) Wave cannot feel bottom Orbits are circular Dispersive: speed dependent on wavelength Wave interacts with bottom (can suspend sediment) Non-dispersive Orbits are elliptical (flat) Deep vs Shallow Waves

Los Angeles Harbor at San Pedro, Ca Wind Wave Generation Wind Duration = time during which wind blows Wind Fetch = distance over which wind blows 1 nm = 1.15 miles = 1.85 km 1 knot = 1 nm/hour = 1.85 km/hour

1. The distance from San Pedro, California, to Avalon, on Santa Catalina Island, is about 25 nautical miles (nm). The island is almost due south (180°) from the Los Angeles Harbor at San Pedro (see Figure 7-15). (a) What is the minimum northerly (from the north) wind speed needed to set- up a fully-developed sea in this channel? ____________ knots _____________kilometers/hour. (HINT: Interpolate between fetch distances 10 nm and 70 nm in Table 7-1 above and round your answer to nearest whole number). (b) How long must a northerly wind blow in order to generate a fully-developed sea in this channel? __________________________hour. (HINT: A Table 7-1 interpolation is required here also.)

Assume :

c. d.

(2 days = 48 hours!)

NE S W Offshore waves Storm waves

Exercise 2: Imagine waves heading towards shore, with a crest that is initially parallel to the thick black line shown on each of the panels in Figure In the panels on the left assume the waves are initially at an angle of 45 o with respect to the shoreline, and have relatively small wave heights. In the panels on the right, assume the waves have a relatively large wave height and that they propagate from deep water directly towards the shore. Please sketch the following directly onto Figure 7-17 Please sketch the following directly onto Figure 7-17: Mapping Wave Refraction For each of the cases (that is, in each panel), draw in a few wave lines to represent wave crests as the wave approaches the shore. Mapping Beach Erosion For each of the three panels on the right (large waves), sketch the configuration of the shore (using a dashed line) as you guess it might be deformed by the erosive effects of large waves during a storm. Label areas of deposition and erosion.

45 degrees

QUESTIONS 1.How does the orientation (angle of approach) of the incoming waves determine the orientation of the waves as they strike the beach? 2. Which areas were subjected to the most severe erosion? …and why? 3. What areas were subjected to the larger deposition? …..why?

Some Reminders  This is a tough homework. Get help right away if you need it.  Read the background carefully. Most of what you need for the homework exercises are found there.  Homework 7 is due to 8 th November