Help understanding BASIC fluid dynamics behind faraday waves

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The discussion focuses on understanding the fluid dynamics behind Faraday waves observed in an experiment where water is vertically shaken. Key points include the sudden onset of Faraday waves compared to their gradual decay, raising questions about the underlying mechanisms. The concept of "primary Faraday instability" is mentioned, suggesting a connection to instability phenomena. A qualitative explanation indicates that viscous forces maintain stability during growth, but once a critical amplitude is reached, these forces dissipate, leading to a hysteresis effect. Overall, the conversation emphasizes the nonlinear nature of the mechanisms involved in the formation and decay of Faraday waves.
piareround
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Dear Sir and Mam,



So recently, I have been doing an experiment with Faraday waves. I feel like there are some critical things I don't understand about fluid dynamics (they don't offer it as a course where I go to school), so I was wondering if anyone on pf was good with fluid dynamics and help me understand the qualitative side of Faraday Waves.

In the experiment we vertically shake water with speaker-like device. At certain critical amplitude and frequency, we observe Faraday waves like in Fig. 1 below.

On of the things that really mystify's me is difference the growth of Faraday waves vs. the decay of Faraday waves. For example, let say I introduce a constant sinusodial variation to the speaker. If I plot the acceleration of the speaker vs. the magnitude out put of the Faraday wave, I get something like Fig. 2. Here it easy to see how the onset of the Faraday is quiet sudden vs. the long decrease in Faraday waves.


Can anyone explain qualitatively how or why an oscillation grow differently than its decay?
I have heard some paper use the word "primary Faraday instability". Could it have anything to do with an instability?



https://www.youtube.com/watch?v=<iframe width="420" height="315" src="http://www.youtube.com/embed/v-XEhY4OThs" frameborder="0" allowfullscreen></iframe>
Fig. 1: The following youtube video is


BifRamp60.png

Fig 2: A picture of the Amplitude vs. acceleration graph. It shows how the growth and decay behavior of a Faraday Wave are different.
 
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Well the whole thing has to do with an instability. The whole mechanism is nonlinear, so without going and doing the math behind it, I would say you are most likely dealing with a hysteresis effect.
 
If I had to give you a qualitative explanation without any prior experience with Faraday waves, I would say that during the growth that viscous forces keep the fluid stable, but then upon the sudden growth in amplitude the viscous forces are diffused and this leads to the hysteresis.

Essentially, fluid stays stable as long as it can, but then it becomes unstable and these instabilities "feed themselves."
 

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