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The wavenumber in the jet flow

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Old   March 28, 2015, 06:04
Default The wavenumber in the jet flow
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Hi all,

I have the following question.

I am doing the stability analysis of a jet flow, which assumes a profile like U=sech(y).^2, where y is the cooridinate. The 2D flow is assumed to be x-periodic, so I can perform Fourier Transform to reduce the problem to 1D. And the reference length in the problem is the distance between the jet centerline and the radial position where its velocity is half maximum jet velocity.

In the numerical method for the stability analysis, I need to evaluate the laplacian of the variables, the numerical laplacian being D^2-\alpha^2, where \alpha is the wavenumber in the x direction and D is the numerical differential operator in the radial direction. In the finite difference discretization scheme for the operator D^2, I have a normalization factor \frac{1}{dy^2}, where dy is the grid space.

My doubts arise when I consider different confinements of jet, which means that the max(y)=L could change. If I fix the grid number, this means that the dy would change, leading to that D^2 would change. But \alpha is still the same (since I doesn't change the reference length.) In short, it seems to me that when I change L, the relative "amplitude" between D^2 and \alpha is changing, which doesn't make a sense to me.

Do you have any suggestions? I think I must get something wrong. Thanks.
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Old   March 28, 2015, 06:29
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D is a numerical operator for derivative, right?
In no way D changes depending on the size of the grid step...you simply have a smaller truncation error of the operator....
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