Elliptical motion of surface buoy.

[mathfeel]

Failed at Googling. Can anyone point me to a simple model derivation on elliptical motion of a buoy on surface gravity wave?

 

[Andy Resnick]

A place to start may be here:

http://web.ics.purdue.edu/~braile/edumod/waves/WaveDemo.htm

There are at least two types of surface waves: Rayleigh and Love. Advected motion for a Rayleigh wave is elliptical.

Hang on... I failed to realize how complex the problem is. Segel's "mathematics applied to continuum mechanics" has *several* chapters on surface waves, and apparently draws a distinction between Rayleigh/Love waves (surface waves that exist in an *elastic* medium) and surface waves that propagate in a fluid. Slattery's "Interfacial transport phenomena" has an impenetrable section at the end... ugh.

I would start with the website, and if that's unsatisfactory, go to Segel's book (it's excellent), or alternatively, if you find a decent book or paper devoted to wave motion:

https://www.amazon.com/dp/9812389490/?tag=pfamazon01-20
http://www.ams.org/journals/bull/2007-44-03/S0273-0979-07-01159-7/home.html
http://iopscience.iop.org/0951-7715/21/5/012/
http://aimsciences.org/journals/pdfs.jsp?paperID=6943&mode=full

Good luck...

 

[Bill_K]

"Water Waves" by J J Stoker is the standard reference. You can find it online here.

 

[Andy Resnick]

"Water Waves" by J J Stoker is the standard reference. You can find it online here.

Fantastic- thanks!

 

[Andy Resnick]

Sure enough- the results are found on page 41 of Stoker's book (eqn. 3.1.20), which also has a a set of images taken from the literature clearly showing the motion.