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Evanescent waves, line breaks (4).

Dear colleagues,


In the following, I will try to explain why I think that evanescent liquid-sound-pressure waves occur near oscillating underwater resonators. These waves are standing convection waves. They are predicted to occur also in strictly incompressible and non-viscous liquids. The wave is limited to a certain region of the liquid. Such waves play a role in cochlear mechanics.


A horizontal cut through a wine glass standing on a table is circular. If one hits the glass horizontally with a spoon from the north, say, then that circle is initially deformed into an ellipse. The distance-from-centre is small at the north (N) and south (S), and is large at the east (E) and west (W). There are 4 knots, at NW, SW, SE, and NE.


If the glass is filled with water, then approximately horizontal curved streamlines go through the water, e.g., from NNW to WNW. Liquid particles with no-wave position on the streamline move back and forth sinusoidally on the streamline. Since that line is fairly long, typically about equal to the radius of the mentioned circle, the drop in resonance frequency caused by filling the glass is large; the corresponding frequency factor is ~0.6.


If the glass is submerged completely, then there are even longer streamlines on its outside; now the mentioned frequency factor is ~0.4.


As mentioned before, I am looking for published papers on these evanescent liquid-sound-pressure waves. 


Unwanted line breaks: My problem is not yet solved completely, I fear. As mentioned, I now use hyper-text markup language, and I do carriage returns at the end of paragraphs only. At the end of each paragraph, I do two consecutive carriage returns, in order to insert one empty line between paragraphs. In my own sent-messages folder, and also in what comes back to me from Canada, the result is as desired. In responses from List members to me, however, my line breaks are doubled, so that there are three empty lines between paragraphs instead of one. Interestingly, in my signature (see below), my line breaks are not doubled, probably because the lines are very short. 



Reinhart Frosch,
Dr. phil. nat.,
r. PSI and ETH Zurich,
Sommerhaldenstr. 5B,
CH-5200 Brugg.
Phone: 0041 56 441 77 72.
Mobile: 0041 79 754 30 32.
E-mail: reinifrosch@xxxxxxxxxx .