[Rime]

Hi
this is what I found on the internet

"The shallow water equations can be thought of as an approximation to the Navier Stokes equations and are solved more readily"

Can you give me the advantages of using the Shallow water equations instead of the Navier-Stokes equations.

I do not find a clear view.

Thank u

[truffaldino]

Originally Posted by Rime

Can you give me the advantages of using the Shallow water equations instead of the Navier-Stokes equations.

The advantage is lower dimension (3d NS reduces to 2d shalow water and 2d NS to 1d shallow water)

[Rime]

Thank u for the reply

They have the same accuracy??

[truffaldino]

Originally Posted by Rime

Thank u for the reply

They have the same accuracy??

Since shallow water equations are approximations, they are less accurate.

However, as wavelength goes to infinity they become more and more accurate.

It also worthy to note importance of 1d shallow water equation for waves of moderate amplitude, called Korteveg de Vries equation, which is exactly solvable and very important example of continuous integrable system.

There are several more examples of further simlifications of shallow water equations (e.g. KP equation for 2d shallow water waves) which are integrable and are important for mathematic theory of non-linear PDEs.