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 Paul August 26, 2004 11:33

shallow water VS deep water

Is there any rigorous definition of shallow water and deep water in terms of depth of the water?

thanks!

 Jon August 26, 2004 12:33

Re: shallow water VS deep water

Depends how tall you are.

 Paul August 26, 2004 12:36

Re: shallow water VS deep water

interesting argument.

I mean the explorsion in the shallow water or the deep water.

 Jarmo Monttinen August 26, 2004 12:36

Re: shallow water VS deep water

Seem to recall that this would have to do something with the waves... try these links:

-- Jarmo

 Tom August 27, 2004 05:24

Re: shallow water VS deep water

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.

 Kel August 27, 2004 06:20

Re: shallow water VS deep water

Tom, that means the symbol "k" in your formula?

 Tom August 27, 2004 08:19

Re: shallow water VS deep water

It's the wavenumber = 2.pi/wavelength

 Wen Long August 27, 2004 16:56

Re: shallow water VS deep water

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.

 Wen Long August 27, 2004 16:58

Re: shallow water VS deep water

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.

 Kel August 30, 2004 07:41

Re: shallow water VS deep water

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.

 Wen Long August 30, 2004 12:56

Re: shallow water VS deep water

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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