Streamline pattern of a solitary wave?

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SUMMARY

The discussion centers on the streamline pattern of solitary waves, specifically in the context of shallow water waves and the Korteweg-de Vries (KdV) equation. Participants emphasize the need to plot the velocity field after deriving the surface evolution equation. The mention of sech solitons indicates that they are not the sole wave solutions, as referenced in the work of Drazin and Johnson. This highlights the complexity and variety of wave solutions in fluid dynamics.

PREREQUISITES
  • Understanding of the Korteweg-de Vries (KdV) equation
  • Familiarity with fluid dynamics concepts, particularly solitary waves
  • Knowledge of plotting velocity fields in fluid mechanics
  • Reference to Drazin and Johnson's work on wave solutions
NEXT STEPS
  • Research the derivation of the surface evolution equation for solitary waves
  • Study the properties of sech solitons and other wave solutions
  • Learn about plotting velocity fields in fluid dynamics using software tools
  • Examine the implications of the KdV equation in real-world shallow water scenarios
USEFUL FOR

Fluid dynamicists, researchers in wave mechanics, and students studying the KdV equation and solitary waves will benefit from this discussion.

hanson
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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?
 
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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.
 

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