Oscillations in Fluids

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Main Question or Discussion Point

I am a layman with very little experience in math and physics and recently I became curious about how to analyze dampened oscillations occurring in fluid mediums, such as those following a disturbance in a pool of water. What sort of math and physics is required to understand this phenomenon and what sort of textbooks will cover things like this?
 

Answers and Replies

  • #3
jasonRF
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Yes, there are gravity waves and capillary waves on the surface of water. Capillary waves are the very short wavelength waves that depend on surface tension, while the larger gravity waves are the longer wavelength waves.

How much math and physics you need depends on what your goals are. If you really want to understand the derivation and solutions of the equations, then you need at least the following:
a calculus sequence through multivariable and vector calculus, ordinary differential equations
2 semesters of intro physics

Then you will probably be ready to start looking at "physics of waves" kinds of books such as
http://farside.ph.utexas.edu/teaching/315/315.html

The actual equations of interest are partial differential equations, and while it might be nice to learn partial differential equations first, many students learn about them as needed in physics or engineering courses. It might help to also learn some linear algebra. For some of the relevant math (beyond the calculus sequence) one possible reference is
http://www.physics.miami.edu/~nearing/mathmethods/

If you just want a simple pictorial understanding, then I recommend googling to see what you find. Learning the derivation and solution of the partial differential equations won't necessarily yield any more understanding than you would get from a good qualitative description. It will, however, provide you will skills that are useful if you want to go further in science/engineering/mathematics.

jason
 
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