I How does a free surface flow cause non-linearity?

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Free surface flow causes non-linearity primarily through boundary conditions, influencing flow dynamics. Thicker films exhibit greater boundary layer flow velocity, allowing surface waves to gather more fluid from thinner films, leading to breaking waves. The discussion emphasizes the mathematical aspects rather than physical explanations, prompting inquiries about specific equations involved. Reference is made to "Free-surface flow: shallow-water dynamics" by Nikolaos D. Katopodes for further insights. Understanding these dynamics is crucial for analyzing fluid behavior in various applications.
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Free surface flow , non linearity
How does a free surface flow cause non-linearity , is it through the boundary conditions ? Which one and how ? Thanks
 
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binbagsss said:
How does a free surface flow cause non-linearity , is it through the boundary conditions ...
Boundary layer flow velocity is greater for thicker films. A surface wave catches up with, and collects more fluid from thinner films, until it builds into a breaking wave, that rushes across the wet surface.
 
Baluncore said:
Boundary layer flow velocity is greater for thicker films. A surface wave catches up with, and collects more fluid from thinner films, until it builds into a breaking wave, that rushes across the wet surface.
in terms of the equations sorry, not physically, thanks
 
binbagsss said:
in terms of the equations sorry, not physically, thanks
Which situation and which equations.

I refer you to chapters 2 and 3 of;
Title: Free-surface flow: shallow-water dynamics
Author(s): Katopodes, Nikolaos D.
Publisher: Elsevier Science & Technology, Year: 2019
 
Thread 'Why higher speeds need more power if backward force is the same?'

Thread 'Why higher speeds need more power if backward force is the same?'

Power = Force v Speed Power of my horse = 104kgx9.81m/s^2 x 0.732m/s = 1HP =746W Force/tension in rope stay the same if horse run at 0.73m/s or at 15m/s, so why then horse need to be more powerfull to pull at higher speed even if backward force at him(rope tension) stay the same? I understand that if I increase weight, it is hrader for horse to pull at higher speed because now is backward force increased, but don't understand why is harder to pull at higher speed if weight(backward force)...
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