CFD Online Discussion Forums - The wavenumber in the jet flow

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

is the numerical differential operator in the radial direction. In the finite difference discretization scheme for the operator

, I have a normalization factor $\frac{1}{dy^2}$ , 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 $\alpha$ 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

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.