Elliptical motion of surface buoy.

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Discussion Overview

The discussion revolves around the elliptical motion of a buoy on surface gravity waves, exploring theoretical models and references for understanding this phenomenon. Participants seek derivations and resources related to the motion of buoys influenced by different types of surface waves.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests a simple model derivation for the elliptical motion of a buoy on surface gravity waves.
  • Another participant suggests starting with a specific website and mentions the complexity of the problem, noting distinctions between Rayleigh and Love waves and their relation to surface waves in elastic media versus fluids.
  • References to several books and papers are provided, including Segel's "Mathematics Applied to Continuum Mechanics" and Slattery's "Interfacial Transport Phenomena," indicating the depth of the topic.
  • Multiple participants mention "Water Waves" by J J Stoker as a standard reference, with one noting specific results found in the book.

Areas of Agreement / Disagreement

Participants generally agree on the complexity of the topic and the utility of certain references, but there is no consensus on a single model or derivation for the elliptical motion of the buoy.

Contextual Notes

Participants express uncertainty regarding the distinctions between types of waves and their implications for the motion of buoys, as well as the accessibility of the referenced materials.

Who May Find This Useful

This discussion may be useful for those interested in fluid dynamics, wave mechanics, and the mathematical modeling of surface waves, particularly in the context of buoy motion.

mathfeel
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Failed at Googling. Can anyone point me to a simple model derivation on elliptical motion of a buoy on surface gravity wave?
 
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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...
 
"Water Waves" by J J Stoker is the standard reference. You can find it online here.
 
Bill_K said:
"Water Waves" by J J Stoker is the standard reference. You can find it online here.

Fantastic- thanks!
 
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.
 

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