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shallow water VS deep water

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Old   August 26, 2004, 10:33
Default shallow water VS deep water
  #1
Paul
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Is there any rigorous definition of shallow water and deep water in terms of depth of the water?

thanks!
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Old   August 26, 2004, 11:33
Default Re: shallow water VS deep water
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Jon
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Depends how tall you are.
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Old   August 26, 2004, 11:36
Default Re: shallow water VS deep water
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Paul
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interesting argument.

I mean the explorsion in the shallow water or the deep water.
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Old   August 26, 2004, 11:36
Default Re: shallow water VS deep water
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Jarmo Monttinen
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Seem to recall that this would have to do something with the waves... try these links:

http://www.google.com/search?hl=en&l...TF-8&q=shallow+water+approximation

-- Jarmo
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Old   August 27, 2004, 04:24
Default Re: shallow water VS deep water
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Tom
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As Jarmo points out it is defined in terms of waves. Specifically for a layer of fluid of depth H the dispersion relation linking the frequency and wavenumber is (in the absense of surface tension)

w = sqrt( g.k.tanh(kH) )

where g is the acceleration due to gravity. For deep water, where kH >> 1, w ~ sqrt(gk) and the depth of the layer is much greater than the length of the surface waves which propagate on it. For shallow water the surface waves are much longer than the depth of the layer so that kH << 1 and w ~ sqrt(gH)k (which are non dispersive),

Tom.
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Old   August 27, 2004, 05:20
Default Re: shallow water VS deep water
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Kel
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Tom, that means the symbol "k" in your formula?
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Old   August 27, 2004, 07:19
Default Re: shallow water VS deep water
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Tom
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It's the wavenumber = 2.pi/wavelength
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Old   August 27, 2004, 15:56
Default Re: shallow water VS deep water
  #8
Wen Long
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Shallow water approximation or deep water approximation are two ends of asymptotic approximation in water wave theory.

For shallow water, when h/L is less than 1/20, it's called shallow water, when 1/20<h/L<1/2 it's called imtermediate depth water, when h/L > 1/2 it's called deep water.

where h is depth, L is wave length(distance between to adjecent wave crests)

for ocean, say h=1000m, if wave length > 20 km is still called shallow water though 1000m is not that shallow at all.

For commonly seeng waves with L =10m, h <10/20=0.5m is called shallow water, h>10/2=5m is called deep water. We see that shallow water is really shallow, and deep water is not horriblely deep.

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Old   August 27, 2004, 15:58
Default Re: shallow water VS deep water
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Wen Long
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Shallow water approximation or deep water approximation are two ends of asymptotic approximation in water wave theory.

For shallow water, when h/L is less than 1/20, it's called shallow water, when h/L larger than 1/20 but less than 1/2, it's intemediate depth water. When h/L larger than 1/2, it's called deep water.

where h is depth, L is wave length(distance between to adjecent wave crests)

for ocean, say h=1000m, if wave length > 20 km is still called shallow water though 1000m is not that shallow at all.

For commonly seeng waves with L =10m, h <10/20=0.5m is called shallow water, h>10/2=5m is called deep water. We see that shallow water is really shallow, and deep water is not horriblely deep.

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Old   August 30, 2004, 06:41
Default Re: shallow water VS deep water
  #10
Kel
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Hello, I also write a fortran code for simple (linear) equations of 2-D shallow water. Unknown functions are u,v, and ksi (ksi is the free surface elevation over a reference plane). Can anybody suggest some test example for program debugging? Thanks.
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Old   August 30, 2004, 11:56
Default Re: shallow water VS deep water
  #11
Wen Long
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Go to the following website and download the Funwave, there are many examples in the documents.

http://chinacat.coastal.udel.edu/~kirby/programs/

I think one of the best is Berkhoff Shoaling, for weakly nonlinear waves,

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