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March 28, 2015, 06:04 |
The wavenumber in the jet flow
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#1 |
Member
Join Date: Feb 2011
Posts: 41
Rep Power: 15 |
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 , where is the wavenumber in the x direction and is the numerical differential operator in the radial direction. In the finite difference discretization scheme for the operator , I have a normalization factor , where 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 would change, leading to that would change. But 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 and 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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March 28, 2015, 06:29 |
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#2 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,760
Rep Power: 71 |
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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