kitchen table math, the sequel: help desk - Earth Science

Wednesday, January 23, 2008

help desk - Earth Science

Wave Refraction

Most waves approach the shoreline at an angle. Yet when a wave reaches shallow water, it tends to swing around until it approaches the shoreline more or less head on. This swinging or bending is called refraction. Refraction occurs because the end of the wave closest to shore scrapes bottom first and slows down. The end that is still in deeper water continues at its normal speed and catches up. Thus, the wave ends up nearly parallel to the shore.

Wave refraction helps explain why an uneven shoreline with shallow water is eventually worn away to a more even shoreline. etc.

Earth Science by Spaulding & Namowitz
McDougal Littell, p. 345

Barron's gives it a go here:

Wave Refraction

Waves that enter shallow water at an angle to the beach are refracted; their direction of travel is changed. This refraction occurs because one part of the wave reaches shallow water and slows down while the rest of the wave is still in deep water and moving faster. Like a rolling log whose one end hits a tree, causing the whole log to swing around, the faster moving end of the wave swings around when the end in shallow water slows down. etc.


on the other hand...

One page later, in Spaulding/Namowitz, we find an explanation of ....


Shoreline Currents

Waves, like the winds that form them, may come from any direction. Thus, many waves approach the shreline at an angle. When such waves break, large amounts of water and sand are pushed up the beach at an angle. etc.
I'm sorry.

There is really no excuse for this kind of thing.

10 comments:

Doug Sundseth said...

Those aren't contradictory. "...swing around until it approaches the shoreline more or less head on" is compatible with "...Thus, many waves approach the shoreline at an angle. When such waves break, large amounts of water and sand are pushed up the beach at an angle...".

In the open ocean, waves travel in any direction. This continues to be true until the wave amplitude is greater than the depth of the water the wave is moving through.

When the bottom of any part of a wave hits the seafloor, that part of the wave slows down (and the wave build up above where the surface would be in calm seas). When the wave approaches a coastline at an angle, one end of the wave will slow down first, which will tend to make the wave bend (or refract) toward the shoreline. Thus, the wave (in total) will "approach[] the shoreline more or less head on".

If you think about being at the beach, though, you'll remember that it's very common for a wave to begin breaking at one point and for the break to propagate in one or both directions along the shore. You've probably also noted that the wave hits the shore at different times depending on where you are.

Now, to understand how this could result in "water and sand ... pushed up the beach at an angle", consider a snowplow. At every point as the snowplow moves down the road, the direction of movement is parallel to the road. Yet the snow is thrown off to the side of the road because the blade is angled. A wave acts on a shoreline much like a snowplow acts on a road. It hits first at one point and propagates along the shore even though its water is moving almost exactly perpendicular to the shore as it hits.

Catherine Johnson said...

hmmm....

I am still not getting this.

The first passage says waves end up coming in head on.

The second passages says they end up coming in at an angle.

Also, I'm still not getting how the "bottom" of the wave hitting first makes the thing become parallel or head on.

I'm not getting this at all!

aaack!

Catherine Johnson said...

It's 9:17. Time to go upstairs and study Earth Science.

Instructivist said...

[Also, I'm still not getting how the "bottom" of the wave hitting first makes the thing become parallel or head on.]

When the wave comes in at an angle, the part closer to shore hits shallower water (the bottom starts scraping the ground) and slows down. The other end is still in deeper water and continues at a higher speed allowing it to catch up with the now-slower moving end. That reduces the angle and the wave becomes nearly parallel to the shore.

---------- (shore)

- (wave)
-
-
-
-

I can't draw this very well. The angle looks exagerated.

Instructivist said...

Aack.

The program ate the spacebar spaces and my carefully crafted angle is gone. Ignore the drawing as it appears completely!

SteveH said...

Waves that match the shoreline shape are never perfect. Our town beach has shifting sandbars that cause breaks in different areas.

"Waves, like the winds that form them, may come from any direction. Thus, many waves approach the shoreline at an angle. When such waves break, large amounts of water and sand are pushed up the beach at an angle. etc."


I don't like this explanation either. It's not so much the direction of the wave hitting the beach as it is cross-current effects. There are other secondary effects, like riptides that cause problems too.

"Also, I'm still not getting how the "bottom" of the wave hitting first makes the thing become parallel or head on."

The wave is not really hitting the bottom. You would have to look at the equations to get a better feel for that. They are based on potential flow theory and the governing equations are differential in nature.

It makes me wonder what the goal of the textbook is. Fluid dynamics is a complicated subject. You have to be very careful when you simplify it for high school use.

Catherine Johnson said...

The other end is still in deeper water and continues at a higher speed allowing it to catch up with the now-slower moving end. That reduces the angle and the wave becomes nearly parallel to the shore.

This is making slightly more sense, thanks to the phrase "reduces the angle"....

I desperately need an illustration.

The way this unfolds in my mind's eye is that when the front of the wave hits the sand and slows you simply end up with a breaker.

The book's explanation sounds to me like what happens in a head-on collision. The car stops but your body keeps moving forward.

I get "breaker"; I don't get "change in angle."

Catherine Johnson said...

I suspect that oversimplification to the point of meaninglessness and error is probably a standard problem in K-12 science.

Catherine Johnson said...

instructivist, if you're still around, do you think the Holt text is significantly clearer than this?

I ordered the other two you mentioned.

Catherine Johnson said...

Hey!

Instructivist gets the prize!

This sentence, even without the illustration, set me on the right path:

"That reduces the angle and the wave becomes nearly parallel to the shore."

I found this explanation on a web site:

Refraction is the bending of waves because of varying water depths underneath. The part of a wave in shallow water moves slower than the part of a wave in deeper water. So when the depth under a wave crest varies along the crest, the wave bends.

An example of refraction is when waves approach a straight shoreline at an angle. The part of the wave crest closer to shore is in shallower water and moving slower than the part away from the shore in deeper water. The wave crest in deeper water catches up so that the wave crest tends to become parallel to the shore.


Refraction/Diffraction

I was able to figure it out from there.

(At least, I think I was!)