Dave Kruger wrote, in response to my earlier post: [I subscribe to thre digest, so it's easier for me to use cut and paste in replying. Thus Dave's words don't have any preceding ">", and I've indicated my replies with "BW>"] Don't have access to any fluid dynamics books so I'm stuck with my physical intuition ... which tells me that other properties of a fluid are involved here also -- not just viscosity, per se. What I'm thinking about is that it is the visco-elastic restoring forces which affect gravity wave propagation, and those BW> No. They're called gravity waves because the restoring force is gravity. At very short wave lengths(a few cm or less), the restoring force is surface tension, which is the only way in which inter-molecular forces can affect the wave motion. Remember, since we're talking about waves, we're talking about what is happening _away_ from the boat. Viscous drag is not a part of wavemaking. In fact you can see the capillary waves, those in which the restoring force is surface tension, in front of your bow wave, if the water is otherwise smooth enough. As we know, gravity waves are faster when the wavelength is longer; capillary waves are the opposite. So on the leading edge of the cusp on top of your bow wave, you can see very small waves running ahead, with the shorter-wavelength ones leading. Once you recognize them, you can see where the wind is putting capillary waves on top of gravity waves, which will eventually make the gravity waves bigger. Or you can see them around the beetles swimming on the (fresh-water) surface, who use them instead of vision. will be a function of the medium. Tightly coupled molecules should respond to a wave disturbance differently than ones that are not tightly coupled, giving lesser amplitude for a given disturbance, but greater speed of gravity wave propagation ... and that might give a different "ideal angle" for the bow wave. Hmmmmm ... "more tightly coupled" may just translate into "more viscous." BW> I suspect so. Maybe I'm all wet! If the oceans were made of alcohol, gravity waves would travel at a lesser speed, and could the bow wave angle be different than it is in water? (I assume the viscoelastic resotoring forces in sea water are pretty close to those in fresh water, though the density is some 3 % different.) BW> No. The critical thing is that the wavelength is proportional to the square of the frequency. The constant of proportionality, i.e., the strength of gravity, drops out. This discussion may be more than most Paddlewisers want to know ... BW> Maybe, but E. Sullivan very much enjoyed looking at her boat waves, and with any natural phenomenon, the more clearly you understand them, the more things you see in them to appreciate. Bruce Winterbon bwinterb_at_magma.ca http://magma.ca:80/~bwinterb A non-indexed pension is a fraud. *************************************************************************** PaddleWise Paddling Mailing List - All postings copyright the author and not to be reproduced/forwarded outside PaddleWise without author's permission Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************Received on Tue Oct 10 2000 - 19:08:19 PDT
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