Decay of sinusoidal velocity wave (kolmogorov flow)

In summary, the problem is to find the velocity field u(x,t) with given conditions such as constant density, boundary conditions, and partial differential equations. The solution attempts have been unsuccessful after hours of research. It is suggested to approach the problem similarly to unsteady couette flow.
  • #1
OldStudent0382
14
1

Homework Statement


Find the velocity field [itex]u(x,t)[/itex]

Homework Equations


[itex]\rho = constant[/itex]
[itex]u(0,t)=0[/itex]
[itex]u(0,L)=0[/itex]

[itex]\frac{\partial u}{\partial t} = \nu \frac{\partial ^{2}u}{\partial x^{2}}[/itex]

[itex]u(x,0)=U_{o}[sin(\frac{3\pi x}{L})+0.7sin(\frac{9\pi x}{L})][/itex]

upload_2015-5-2_13-1-11.png

The Attempt at a Solution



I have absolutely no idea how to start this problem (again) and I'm embarrassed to admit that I've been looking at it and searching for two hours -- and I have nothing to show for it.

Thank you in advance!
 
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  • #2
Would this be approached similarly to unsteady couette flow? I spent a few more hours trying to research the problem (and the topic) and I'm either not finding anything relevant or I'm just so far lost that I'm not finding the connection between this assignment and what I've been reading.
 

Related to Decay of sinusoidal velocity wave (kolmogorov flow)

1. What is the Decay of Sinusoidal Velocity Wave?

The Decay of Sinusoidal Velocity Wave, also known as Kolmogorov Flow, is a phenomenon in fluid mechanics where a sinusoidal velocity wave gradually decreases in amplitude over time due to the effects of viscosity.

2. What causes the Decay of Sinusoidal Velocity Wave?

The Decay of Sinusoidal Velocity Wave is primarily caused by the presence of viscosity in a fluid. Viscosity is a measure of a fluid's resistance to flow, and as the fluid particles move in a sinusoidal pattern, they experience friction with the surrounding particles, resulting in a gradual decrease in velocity.

3. How is the Decay of Sinusoidal Velocity Wave measured?

The Decay of Sinusoidal Velocity Wave can be measured using a variety of techniques, such as laser Doppler anemometry or hot wire anemometry. These methods involve measuring the velocity at different points in the fluid and plotting it over time to observe the decay of the sinusoidal wave.

4. What are the practical implications of the Decay of Sinusoidal Velocity Wave?

The Decay of Sinusoidal Velocity Wave has implications in various fields, such as oceanography, meteorology, and astrophysics. It can affect the dynamics of ocean currents, atmospheric waves, and stellar winds. Understanding this phenomenon is crucial in predicting and modeling these systems accurately.

5. Can the Decay of Sinusoidal Velocity Wave be prevented or reversed?

No, the Decay of Sinusoidal Velocity Wave is a natural process that occurs due to the fundamental properties of fluids. It cannot be prevented or reversed, but its effects can be minimized by reducing the viscosity of the fluid or altering the flow conditions.

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