- #1
TriKri
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Hi,
Has there to your knowledge been developed any wave equation for for water waves?
Has there to your knowledge been developed any wave equation for for water waves?
Bill_K said:So it sounds like you want to do a Fast Fourier Transform f(x) -> F(k), propagate each wavelength according to its phase velocity, then FFT back again. FFT algorithms are O(N ln N).
vanhees71 said:A very nice treatment can be found in the excellent book
A. Sommerfeld, Lectures on Theoretical Physics, Vol. II
SteamKing said:The U.S. Army Corps of Engineers publishes a volume in their Coastal Engineering Manual series which discusses water waves in deep and shallow water quite completely. Volume II can be downloaded from the link below in Acrobat format:
"[URL
I have taken a look in it, and it looks quite comprehensive, but I think that it is going to take a long time for me to find what I'm looking for by simply browsing through the documents or browsing through the tables of contents. Is there any specific equation or section in some of the documents you can hint about?
The wave equation for water waves is a mathematical equation that describes the behavior of water waves. It is a partial differential equation that takes into account factors such as the water's depth, gravity, and surface tension.
The wave equation for water waves is derived by applying the principles of fluid dynamics and using the Navier-Stokes equations. These equations describe the conservation of mass and momentum in a fluid, which can then be applied to water waves.
The wave equation for water waves is significant because it allows scientists and engineers to accurately model and predict the behavior of water waves. This is important for understanding and predicting ocean currents, tides, and other water-related phenomena.
Yes, there are limitations to the wave equation for water waves. It assumes an idealized scenario and does not take into account factors such as wind, temperature, and water density variations. It also assumes a uniform and unobstructed body of water, which may not always be the case in the real world.
The wave equation for water waves is used in various practical applications, such as predicting wave heights and patterns for marine structures like offshore oil platforms, designing ships and boats to withstand rough seas, and understanding the impact of tsunamis and other natural disasters on coastal areas.