Some Interesting Wave Science

General Discussion
1

I was fortunate enough to attend a short hour long presentation tonight by a science teacher/surfer who used to teach at my highschool in Marin. Anyways, he presented some interesting facts and equations I thought all of you might have some fun with if you didn’t already know about them. I already knew most of the basic theories he presented but I also found a lot of it really interesting in the whole scheme of waves and how they work/why. so here’s what I learned…in no particular order…

Wave Train (Set) Speed Equation

Speed=1/2(speed of wave)

this means that what we call a set of waves, or wave train, moves 1/2 the speed of an individual wave in that set.

Deep Water Wave Speed = 5 * (Period/timed distance between crests)

Shallow Water Wave Speed = 3.1 * (the square root of the depth)

Interesting Fact: deep water waves don’t “feel” the ocean floor - this is why surfable waves or shallow water waves are created when the deep water waves reach shallower water. The energy is pushed up.

In order for a wave to be a ‘deep water wave’, the depth it travels through must be more than or equal to 1/2 * the period

or in equation form: d [greater than or equal to] 1/2(period)

In order for a wave to be an ‘intermediate water wave’, the depth it travels through must be more than or equal to 1/20 * the period and less than or equal to 1/2 * the period

or in equation form:

1/2(period) [greater than and equal to] d [greater than or = to] 1/20(period)

In order for a wave to be a ‘shallow water wave’ (the waves we surf) the depth it travels through must be less than or equal to 1/20 * the period

or in equation form: d [less than or equal to] 1/20(period)

so, just some interesting equations and such. It’s pretty interesting once you start thinking about it on a more scientific level. it sort of begins to make some sense. If there’s anything to add, take away, or change, feel more than free.

thanks!

-jeremy

2

All tsunamis are shallow water waves, due to their wavelength being so incredibly long, which is why they also travel so fast accross oceans.

The craziest thing is how a wave train travels - the wave in front “dissapears” and the 2nd wave becomes the front wave, and a new one “appears” in the back. Really weird to watch after seeing diagrams of it in textbooks. Still not sure why/how that works out.

3

You can see the front wave disappearing in a wave train in boat wakes. It is a strange phenomena. Also, the leading and trailing waves in a wave packet are smaller than the other waves in the packet/set.

JSS

4

You just combine the momentum equation with the wave equation and VOILA! there it is…

What was the ex-science teacher’s name?

I wrote this page a few years ago to try to show the basics of wave forecasting to others…

http://www.blakestah.com/surf/oldprediction.html

5

surferstar - yes, the presenter talked about the ‘disappearing’ wave so to speak and it is really fascinating. It’s an explaination for how a wave train is able to travel across so many miles of open deep water.

6

blakestah - what is the momentum equation? is it one of the ones listed on this post or the one from my 8th grade physics class? if so, what exactly is it again and what would the two equations look like together?

the ex-Marin Academy science teacher’s name is Don Alexander

I’d be really interested to read the page you wrote if you could rummage it up?

-jeremy

7

I’m sure this book has been mentioned in previous discussions, but for those who missed it, a really great book for surfers interested in simple wave physics and coastal processes is the classic “Waves and Beaches” by Willard Bascom.

8
Quote:

……

Shallow Water Wave Speed = 3.1 * (the square root of the depth)

……

This equation is a good approximation for a wave with a small amplitude (i.e. wave height << water depth).

When the wave height becomes comparable to the water depth (i.e. near the point where the wave begins to break on a sloping beach), a better approximation for the motion at the crest of the wave is:

V(crest) = square-root (g x (water depth + 0.75 x wave height))

g = gravitational acceleration = 32.2 ft/sec^2

A wave breaking over a sloping bottom commonly breaks in a water depth comparable to the wave height (typical ratio varies from 0.85 to 1.15, and depends on the slope of the bottom and the deep water slope of the wave face). Assuming this ratio to be 1, the equation above increases the speed of the crest at the breaking point by about 32 percent.

(From: Oceanography and Seamanship, William G. Van Dorn. Dodd, Mead & Company, NY. ISBN 0-396-06888-X. …I highly recommend this book as the next step up from Willard Bascom’s “Waves and Beaches”)