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October 4, 2022, 05:36 
meaning of this formula

#1 
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Hello everybody~!
I have a question about turbulence. I'm taking turbulence lecture but actually I have not taken Engineering mathematics 2 before. So I have no idea of many theories those are built by Fourier. But I should take this lecture. https://www.youtube.com/watch?v=izdE...X2o4TX&index=6 I don't know meaning of this formula. I've read wiki about Orr–Sommerfeld equation briefly and I've seen below equation. . I think this is equation that describes disturbance but I have no idea of meaning, especially for exponential function. Can you let me know meaning of this formula? Thank you! 

October 4, 2022, 11:21 

#2  
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Filippo Maria Denaro
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I don't know the notes where you read this formula but: 1) if psi is a real function, in the RHS you must have a real function. Therefore phi should be complex but I don't understand why depends on y. 2) The argument (xct) stands for a linear wave solution with constant velocity c. That is the function simply shifts at speed c. 

October 4, 2022, 16:52 

#3 
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The function psi is a complex waveform, with the function phi being the real magnitude and the complex part representing the phase. The dependence on y for phi is typically representative of the behavior expected in flat plate boundary layers, with y being the coordinate normal to the plate. At least that's what I remember from the OrrSommerfeld derivations I worked through a long time ago.


October 4, 2022, 17:43 

#4 
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Lucky
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October 6, 2022, 00:14 

#5 
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am writing a thesis on open channel axial water turbine simulation.
As for the setup, i am using transient, VOF (air and water) open channel, ke RNG model, standard wall fn. I have set up everything else normally such as the free surface level and boundary conditions such as pressure inlet, pressure outlet, and another pressure outlet at the top surface. For geometry, I have 2 domains, one stationary and one rotating domain for the turbine. Both are set with numerical beach, with the stationary domain using frame motion and the rotating domain using mesh motion with the setup seen in the picture 

October 8, 2022, 03:57 

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Thank you guys. 

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