Streamline and free surface profile

[hanson]

In a linear shear flow with the free surface being a solitary wave, shall this free surface solitary wave profile coincides with a streamline representing the flow?

I have plotted out the streamline of the flow. The streamlines look like the profile of a solitary wave. However the streamline corresponding to the free surface do not really coincides the solitary wave profile exactly. I am wondering if it is an error with my computation or what.

What comments do you have?

 

[Chris Hillman]

Hi again, hanson,

I see you are quite fascinated by solitons, which are indeed fascinating, but somehow you never provide enough detail for me to figure out what your question is! As far as I can tell, you seem to be reading various books and you seem to be particularly interested in "solitary traveling waves", such as the famous "Russell sech solition", which can arise under appropriate circumstances as shallow water waves. You seem to be asking here about the relationship between the full hydrodynamical equations and the KdV (or some other equations) which arise from appropriate limiting cases. If so, you might try chapter 1 of Soliton Theory and Its Applications, ed. by Gu Chaohao, Springer-Beijing, 1990.

 

[hanson]

Thanks Chris Hillman.
I am sorry for not providing enough information.
Since I am new to this field, I don't have a solid background or good concepts about these things. Thanks for your recommendation.

Indeed, I am looking at the streamline pattern of a solitary traveling wave. I have the streamline determined somehow and used mathematica to plot the streamlines. I am wondering if I could find the amplitude of the solitary traveling wave by reading the streamline?

The streamline pattern is "wave-like" and I am wondering if the wave amplitude can be determined by measuring the height of the streamline relative to the free surface?