Triad interations in shallow water

[floating]

Apparently in shallow water the energy in waves can be redistributed by triad interactions among 3 different wave frequencies that add/subtract to zero.
I can look at the equations but I am not getting the big picture. Can you give me a simple explanation of what is going on? How would this process show up in wave height and period measurements in increasingly shallow water?

[philSweet]

don't quite understand your question, but maybe something here?

http://en.wikipedia.org/wiki/Cnoidal_wave

[floating]

Sorry, I did not explain things very well! The process I am asking about is a non-linear triad interaction that only occurs in very shallow water: Two waves pass energy to a third wave which is either a low frequency (the difference of the first two waves' frequencies) or a high frequency (the sum of the first two waves' frequencies).
I am having trouble picturing and understanding this process and how it would show up in wave height and period measurements. I was hoping someone might be able to explain this.

[philSweet]

try also here-

http://en.wikipedia.org/wiki/Soliton

solitons and cnoidals interfere differently that they taught you in school. Often there is a phase shift involved. I don't think it easy to visualize this because we were taught to think about wave interactions a certain way and we have spent all our lives since then trying to interpret what we see in terms of what we were taught. It really messes things up when you need to relearn the workings of something you've been experiencing for a long time. The only way to work with this is to dig into some genuinely nasty math.

http://en.wikipedia.org/wiki/Kortewe...Vries_equation

[philSweet]

Is this where you were coming from?

http://www.nonlin-processes-geophys....5-137-1998.pdf

[floating]

Here is a reference on the shallow-water triad interactions that I am asking about,
http://books.google.com/books?id=7tF...=triad&f=false
It is an interaction between 2 surface gravity waves that produce a third, either much lower or higher in frequency. It happens in shallow water (surf zone).

[philSweet]

found this, as far as the math goes, starting at ch2.2-

http://spie.org/etop/1997/279_1.pdf

[jehardiman]

Originally Posted by floating

Apparently in shallow water the energy in waves can be redistributed by triad interactions among 3 different wave frequencies that add/subtract to zero.
I can look at the equations but I am not getting the big picture. Can you give me a simple explanation of what is going on? How would this process show up in wave height and period measurements in increasingly shallow water?

What you are looking at is the natural "slumping" of the water. Basicly as the water shoals, the wave slows and grows in height to maintain energy. However, water being a viscous fluid (duh!), it cannot support the height needed and either breaks if crest celerity is sufficient or passes energy off into leading/trailing wavetrains, which necessarily cancel because energy must remain constant. As I stated in your other thread, see Wiegel, this time Chapter 7 and also do a search for wind wave spectra spreading which is a similiar phenomenon.

[floating]

Thanks, now I have something I can picture. For waves close in frequency and propagating onshore, is this cartoon right: due to triad interactions, the steep waves 'slump' and shed high-frequency/slower wavetrains from their back, and low-frequency/faster waves from their 'sides', i.e. alongshore.