How does a free surface flow cause non-linearity?

• I
• binbagsss
binbagsss
TL;DR Summary
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

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

1. What is a free surface flow?

A free surface flow is a type of fluid flow where the fluid has a free surface exposed to the atmosphere, such as water flowing in an open channel, river, or ocean. This surface can deform and move in response to forces, unlike confined flows where the fluid is completely enclosed by solid boundaries.

2. How does the free surface contribute to non-linearity in fluid flow?

The free surface introduces non-linearity because its shape and position can change dynamically in response to the flow conditions. This creates a feedback loop where the flow affects the surface, and the surface, in turn, affects the flow. This interaction leads to complex behaviors such as waves, turbulence, and varying flow velocities, which are inherently non-linear.

3. What are some examples of non-linear phenomena in free surface flows?

Examples of non-linear phenomena in free surface flows include wave breaking, the formation of vortices, hydraulic jumps, and the development of complex patterns such as ripples and eddies. These phenomena arise due to the interactions between the fluid motion and the changing free surface.

4. Why is it challenging to model free surface flows mathematically?

Modeling free surface flows is challenging because the equations governing the flow (such as the Navier-Stokes equations) become highly complex when accounting for the moving and deforming free surface. Additionally, the boundary conditions at the free surface are non-linear and time-dependent, making analytical solutions difficult and often necessitating advanced numerical methods for accurate simulations.

5. How do engineers and scientists study non-linearity in free surface flows?

Engineers and scientists study non-linearity in free surface flows using a combination of theoretical analysis, laboratory experiments, and numerical simulations. They employ tools such as computational fluid dynamics (CFD) to model the flow and predict behaviors. Experimental setups, such as wave tanks and flumes, are also used to observe and measure the physical phenomena directly, providing data to validate and refine models.

Replies
25
Views
820
Replies
5
Views
1K
Replies
12
Views
903
Replies
6
Views
848
Replies
16
Views
3K
Replies
1
Views
865
Replies
4
Views
922
Replies
7
Views
1K
Replies
14
Views
903
Replies
1
Views
1K