Streamline pattern of a solitary wave?

[hanson]

Hi all!
How shall a streamline pattern of a solitary wave look like?
I can hardly find people plotting and discussing this, how this is the case?
It shall be reasonable to ask for the streamline pattern of a solitary wave, isn't it?
If I want to plot the velocity field of the solitary wave, all I basically need is to work out the velocity field after obtaining the surface evolution equation, isn't it?

 

[Chris Hillman]

Are you asking for the velocity field of a shallow water wave corresponding to a traveling wave solution of the KdV equation? I already pointed out that the sech solitons are not the only wave solutions. See Drazin and Johnson.

 

[tacman]

The streamline pattern of a solitary wave is a topic that has been studied by many researchers in the field of fluid dynamics. However, it is not a widely discussed topic because it is a complex phenomenon that requires advanced mathematical and computational techniques to accurately model and understand.

The streamline pattern of a solitary wave will depend on various factors such as the shape and initial conditions of the wave, the properties of the medium it is propagating through, and the surrounding environment. In general, the streamline pattern of a solitary wave will consist of curved lines that follow the direction of the wave motion, with the highest velocity occurring at the crest of the wave and decreasing towards the trough.

It is understandable that there may be a lack of readily available information and discussions on this topic, as it requires specialized knowledge and techniques to accurately study and visualize. However, it is certainly a valid and important question to ask about the streamline pattern of a solitary wave.

In order to plot the velocity field of a solitary wave, one would indeed need to work out the velocity field after obtaining the surface evolution equation. This can be a challenging task, but with the use of advanced mathematical and computational techniques, it is possible to accurately model and visualize the velocity field of a solitary wave.

In conclusion, the streamline pattern of a solitary wave is a complex and fascinating phenomenon that has been studied by many researchers. While it may not be a widely discussed topic, it is certainly a valid and important question to ask about the behavior of these waves. With the use of advanced techniques and methods, it is possible to accurately model and understand the streamline pattern of a solitary wave.