,, L

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 wavelength2.) H/L The ratio of amplitude to wavelength

Ocean Surface Gravity Waves

Tf

2

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 bottomOrbits 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, CaLos Angeles Harbor at San Pedro, Ca

Wind Wind Wave Wave GenerationGeneration

Wind DurationWind Duration= time during = time during which wind blowswhich wind blows

Wind FetchWind Fetch= distance over = distance over which wind blowswhich wind blows

1 nm = 1.15 miles = 1.85 km1 nm = 1.15 miles = 1.85 km

1 knot = 1 nm/hour = 1.85 km/hour1 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.)

y ya (yb ya )(x xa )

xb xa

Assume :

ya the Fetch at 10nm

yb the Fetch at 70nm

xa the Wind speed at the Fetch of 10nm

xb the Wind speed at the Fetch of 70nm

y the Fetch at 25nm

c.c.

d.d.

(c) Determine the average wave height that would result in the Catalina Channel from

the winds that you determined would set-up a fully-developed sea (answer in part a). _________________feet; _________________meters

(HINT: Use Table 7-2 above)

Would these waves be a problem to boaters in the Catalina Channel?

If not, why not?

(d) Consider the problem of waves encountered by boaters 280 nm off-shore during the winter. What would be the wave height of a fully-developed sea 280nm south of San Pedro due to the effects of a northerly wind?

______________meters ___________feet.

Would this wave height be more or less of a problem for boaters than the wave heights determined in the previous question?

(2 days = 48 hours!)

NN

EE

SS

WW

Offshore waves

Storm waves

3. Scientists at Scripps Institution of Oceanography developed Figure 7-16 for the U.S. Army Corps of Engineers, the government agency that is responsible for shoreline protection and harbor improvement for the entire country, including the Great Lakes.

(a) Which are the largest waves to strike California during the winter? (fig 7-16)

(b) Which are the largest waves to strike California during the summer? (fig 7-16) (surfer nirvana!)

(c) Do these large waves have long, medium, or short periods? (d) How does the direction of these waves change from winter to summer? Why?

4. (a) What is the group speed of storm waves with wave speeds of 100 km/hr? ___________kilometers /hour. (group speed = ½ wave speed) (b) How long would it take such waves to reach the New Jersey shoreline from a storm

center in the Atlantic Ocean 1500 kilometers away? _______________hours. (c) Why are long waves the first to arrive at the coast from an open-ocean distant storm?

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 7-17. In the panels on the left assume the waves are initially at an angle of 45o 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 7-17Please 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 ErosionFor 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 degrees45 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 8th November