geology lap report

Waves

_______________________

(Name)

How do ocean waves form?

“All waves are disturbances of a fluid medium through which energy is moved” (Davis,

1997). Ocean waves travel on the interface between oceans and the atmosphere, and are

produced most commonly by winds. As shown in Figure 1, the crest of a wave is its highest

point while the trough is the lowest. The height of the wave is the vertical distance between the

crest and the trough. The wavelength (λ) is the horizontal distance from crest to crest or from

trough to trough. The steepness is the ratio of its height to λ. When the steepness value reaches

0.143 (i.e., a ratio of 1:7), the crest of the wave breaks. Note that a steepness value less than

0.143 means a stable wave while one larger than 0.143 means an unstable breaking wave.

Figure 1. Key characteristics used to describe ocean waves.

Using Figure 1, please answer all of the following questions.

(1) What is the height of the illustrated wave?

(2) What is the wavelength?

(3) What is the steepness?

(4) Will the wave break given your answer to question (3)? Please briefly explain

your answer.

Using Figure 2, use two different colored pencils and sketch two waves:

Wave “A” has a height of 2 m and a wavelength of 10 m.

Wave “B” has a height of 4m and a wavelength of 6m.

For each wave, label the wavelength, wave height, crest, and trough.

Figure 2. A grid for drawing a wave.

(5) What is the steepness of wave A that you sketched?

(6) Will wave A break?

(7) What is the steepness of wave B that you sketched?

(8) Will wave B break?

When the interface between the oceans and the atmosphere is disturbed by a force, then

waves form. Most commonly that disturbing force is the friction of the wind moving across the

water. Once the wave has formed gravity acts against this disturbance, and attempts to restore the

water/atmosphere interface back to its flat-water position (i.e., a horizontal state). Hence, wind-

generated waves are sometimes referred to as gravity waves. As gravity pulls the crest of a wave

downward, momentum carries the water/atmosphere interface beyond the flat-water position to

form a trough. As a result, a buoy will appear to move up and down without being translated in

the direction that the waves appear to be moving. Such up and down motion will continue as

along as the wind is blowing. When the wind stops blowing, the water/atmosphere interface

returns to its normal flat-water state.

The period of a wave is the time it takes for one wavelength to pass a reference mark.

The periods for normal ocean waves range from a few seconds to about 15 seconds. Note that

this differs from wave celerity which is the speed at which a wave advances or propagates. Deep

water waves are waves that occur in water depth that is greater than one half their wavelength.

(9) If it takes 10 seconds for 1 wavelength of wave “A” from your sketch in Figure 2

to pass the end of Scripps pier, then what is the period of the wave?

(10) What is celerity (speed) of wave “A?”

(11) If the wave passing the end of Scripps pier had the wavelength of wave “B” (from

figure 2), but still took 10 seconds for 1 wavelength to pass, then what would its

period be?

(12) What is the celerity of wave “B?” Did this wave advance faster or slower than the

wave “A?”

The size of a wave increases as the speed, duration, and fetch of the wind increases.

Fetch is the extent of the open water over which the wind travels. A slight breeze over a calm

sea can generate a series of ripples, i.e., waves with a period of less than 1 second. The

generation of ripples provides the wind an elevated surface across which it can push. In so doing

it transfers energy to this surface, and, as a result, the small waves (ripples) begin to grow

increasing their height and period. Wind blowing for many hours and over a great distance (long

fetch) will result in very large and powerful waves.

Though many students think that water is moving in the direction of wave motion, it turns

out that this perception is not correct. If you think about it, you have probably observed things

like fishing boats remaining stationary as a swell passes beneath them, or a fishing bob moving

up and down as small waves or ripples pass beneath along a lake or bay shoreline. If the water

was moving with the waves, then each of these items should have been translated along with the

wave. What actually happens is that water particles within the wave are moving forward on the

crest and backward on the trough, with vertical motion occurring between the two. The exact

path that they follow is circular. For example, shown in Figure 3 are 11 different positions of a

wave that is moving from right to left. The position of a particle of water time 1 (T1) is shown at

the crest of the wave.

As the wave moves to the left at times 2 (T2) – 11 (T11) that same particle will appear to

move downward in a circular path.

On Figure 3 use your colored pencils and show the positions a water particle will occupy if it

starts out in the trough of the wave at time 1 (T1).

Figure 3. Circular path taken by a water particle as a wave moves through a column of water from right to left.

In the open ocean the circular paths followed by water particles decrease systematically

downward until a depth of 0.5*λ. This depth is known as wave base (Figure 3). Below wave base

water particles do not feel the wave. In contrast, as waves approach the shore, the water depth

decreases and results in a dramatic change in the wave character.

(13) Which aspects of waves will change (and in which direction) as they encounter

shallow water?

As deep water waves move toward adjacent shores they progressively encounter

shallower waters. Eventually, they will begin to feel the bottom when the depth of water is less

than one half their wavelength. At this depth the circular orbits that water particles are following

come into contact with the seabed and the wave begins to travel slower as wavelength is reduced,

and wave height increased. In contrast, the wave period remains constant.

The friction produced by the wave encountering the seabed causes the circular paths of

water particles to be squeezed into elliptical forms, and as water depth continues to decrease

these paths eventually become simple back and forth motions parallel to the seaward dipping

seabed. Because the friction between the advancing wave and the seabed is greatest lower in the

wave than higher in the wave, the speed of advancement of the wave at this depth is more greatly

reduced than it is higher in the wave. The contrast in speed of advancement with depth leads to

an unstable wave form with the upper part outracing the lower part, a circumstance that

eventually leads to collapse in a breaker.

When water depth is about 1/20 the wavelength (0.05 * λ) waves are said to be in shallow

water. At this depth water particles follow strongly elliptical back-and-forth motions (see Figure

4).

Figure 4. The change in particle paths as waves encounter shallow water.

(14) If the wavelength is 10 m, wave height is 1 m, and the period 10 sec, then in

Figure 4 at what depth is wave base?

(15) At what depth would the wave be considered to be in shallow water?

Tsunami, like all waves, are a propagation of energy. This activity uses data collected

from DART (Deep-ocean Assessment and Reporting of Tsunamis) stations in the Pacific

following the 2011 tsunami generated off the coast of Japan.

Use the following data to draw the approximate location of the 2011 tsunami wave

front after 5, 10, and 15 hours on the provided map.

Arrival times extracted from raw DART data: http://www.ngdc.noaa.gov/hazard/dart/2011honshu_dart.html

(16) Use your map to estimate when the tsunami arrived at:

Osaka, Japan ___________

Hawaii (station 51407) ___________

Los Angeles ___________

(17) How far (in miles) did the tsunami travel from its source near Japan to Los

Angeles?

(18) How long (in hours) did it take for the tsunami to travel from Japan to Los

Angeles?

(19) Given the total distance and total travel time from the two above questions,

estimate the speed of the tsunami in miles per hour? (please show your work)

(20) Does this method of calculating the average speed of the tsunami provide a good

approximation of the actual speed of the wave at any given point? Why or why

not?

(21) Debris from the 2011 Tsunami did not begin to wash ashore on North American

beaches until late 2012. Why did it take so much longer for the debris to arrive

than the wave?