Igor Khavkine
Jun1-07, 05:01 AM
Consider the following situation. There is a lake of width L and depth
h. Generally, L >> h. The water in the lake is gently sloshing from one
side of the lake to the other. Incidentally, this sloshing motion is
called a "seiche". The challenge is to estimate the frequency of this
sloshing motion as a function of L, h, and g (acceleration due to
gravity).
Now, I know of a very high brow way to approach this problem. It
involves setting up hydrodynamic equations for an incompressible fluid
in a rectangular tank, linearizing them about the equilibrium
configuration, and extracting the frequency of the slowest oscillating
mode.
This method yields what appears to be the correct answer. However, I'd
like to know if there is a quick and dirty way to get a reasonably
accurate estimate of this frequency, without invoking detailed
hydrodynamic calculations.
Can you find one?
Igor
h. Generally, L >> h. The water in the lake is gently sloshing from one
side of the lake to the other. Incidentally, this sloshing motion is
called a "seiche". The challenge is to estimate the frequency of this
sloshing motion as a function of L, h, and g (acceleration due to
gravity).
Now, I know of a very high brow way to approach this problem. It
involves setting up hydrodynamic equations for an incompressible fluid
in a rectangular tank, linearizing them about the equilibrium
configuration, and extracting the frequency of the slowest oscillating
mode.
This method yields what appears to be the correct answer. However, I'd
like to know if there is a quick and dirty way to get a reasonably
accurate estimate of this frequency, without invoking detailed
hydrodynamic calculations.
Can you find one?
Igor