Talk:Shallow water equations

Untitled

Good Evening,

I have suppressed a link in this page to the topic "Shallow Water and Waves". The reason why, altough this may seem disturbing, is that both topics are not related one to the other. Shallow water equations are based on the fact that the wave length of the phenomenon they are supposed to model is much bigger than the depth of the river/lake/ocean where the phenomenon takes place (I'll try to had a brief comment about this). Tides are a good example of a valid use of shallow water equations on any case because the wave length of tides is always much bigger than the depth, even in a very deep ocean. A very deep ocean is actually "shallow" from the point of view of tides. The page "Shallow Water and Waves" refers to high frequency breaking waves such as the ones used for surfing, which is the exact contrary of phenomenon that can be modeled with shallow water equations.

Any comments welcome: <email address removed>

Cheers, robin_de_vaucelles—Preceding unsigned comment added by Robin de vaucelles (talk • contribs) 21:44, 22 May 2007

Sounds 100% valid to me. Thanks for catching this! Awickert (talk) 17:34, 7 March 2009 (UTC)

Hello Shallow Water;

Very nice, concise article. I believe that there are some typos in the equations that could be easily fixed. The first three equations have eta where I believe you meant h = H + eta, the layer thickness. I would write the sixth equation in the material derivative form, also.

Regards, Jim Price. —Preceding unsigned comment added by 128.128.28.248 (talk) 15:25, 7 October 2010 (UTC)

Merger proposal

The recently created entry 1-D Saint Venant equation is a duplicate/extension of the existing entry Shallow water equations. Both pages should be merged, so that users find the information about the SV/SW equation collected on one page. — Preceding unsigned comment added by Pia novice (talk • contribs) 12:05, 25 July 2013 (UTC)

Looks like there's no consensus, so I'm removing the tag for now. KJ ^Discuss? 23:59, 24 August 2014 (UTC)

I agree that the articles should be merged – the 1-D SV equation is merely a special case of the SWE, with the same physical interpretations. --jftsang 21:22, 15 June 2015 (UTC)

 Done

File:Shallow water waves.gif to appear as POTD

Hello! This is a note to let the editors of this article know that File:Shallow water waves.gif will be appearing as picture of the day on May 3, 2015. You can view and edit the POTD blurb at Template:POTD/2015-05-06. If this article needs any attention or maintenance, it would be preferable if that could be done before its appearance on the Main Page. Thanks! — Crisco 1492 (talk) 23:42, 14 April 2015 (UTC)

Picture of the day

Output from a shallow water equation model of water in a bathtub. The water experiences five splashes which generate surface gravity waves that propagate away from the splash locations and reflect off the bathtub walls.

The shallow water equations are a set of hyperbolic partial differential equations that describe the flow below a pressure surface in a fluid. They are derived from depth-integrating the Navier–Stokes equations in cases where the horizontal length scale is much greater than the vertical length scale. The shallow water equations can also be simplified to the commonly used 1-D Saint Venant equation.Animation: Dan Copsey

Issues with the section “Non-conservative form”

Hi there,

I noticed that the set of equations in the "Non-conservative form" are based on different assumptions as in "conservative form" equations, and although most of them are briefly stated, this is not a great way to present these equations. I think we should keep the assumptions same, so that it can be more accessible to new learners.

Moreover, there is at least one assumption that is not made explicit there. Clearly, the set of equations listed there are written in a system where the Coriolis force is along the z direction; or, the Coriolis force along the horizontal direction can be neglected compared to the vertical component. Plus, I think the "traditional approximation" in GFD is also applied here; it neglects a few quadratic terms in the momentum equations. One can refer to classic GFD textbooks on the traditional approxiamtion (e.g. Geoffrey Vallis Chapter 2, I think). These are sound, common approximations for many practical fluid systems, especially for large scale planetary motions, but they still need to be stated if you want to write them down.

I would suggest just keeping the assumptions in the two sections the same. To make life easier, we can write the "Non-conservative form" equations in a non-rotating system and ignore friction and viscosity. Then, we can write another section introducing the equations in a shallow-water system that has a constant Coriolis frequency along z axis, and is affected by viscosity &friction.

Let me know what you think. Han

Contradicting notation

Hello,

I have noticed that the notation used for the elevation, bathymetry and total water depth used in this article don't correspond to what I used daily as a researcher (which is fine), but is also completely different to the rest of the sources that I have looked at. (trying to see if my research group was the anomaly)

I went and looked at the 5 first sources of the article and top ~10 articles from google, plus some of the models that we use frequently (NEMO, ROMS, SLIM).

Here is the summary of what people use:

• Elevation : η(8), ζ(3), h(1), h_s(1)
• Bathymetry : b(2), h(2), H(2), h_f(1)
• Total water depth : a(1), h*(1), h(5), H(3)

Apart from the first two textbooks cited in the article, which use (h, ?, a) and (h_s, h_f, h*) for the (elevation, bathymetry, depth), nobody uses h for elevation and nobody uses η for the water depth. In fact η is only ever used for the elevation.

Currently, this article uses

• Elevation : h : I think that this is wrong and should change
• Bathymetry : H : it's debatable. I would prefer b or h.
• Total water depth : η : I think that this is also wrong and should change.

I propose:

• Elevation : η
• Bathymetry : h or b (H is ok)
• Total water depth : H (h is ok)

For reference, here is what I use (image).

Let me know what you think. If the community agrees I can do the edits and a replacement figure. Sparallel (talk) 23:18, 21 March 2024 (UTC)