using Matlab How to plot eigenfunction and perturbed argument of an Orr-Sommerfeld equation

%How to plot normalized eigenfunction and its argument of an orr sommerfeld equation also the its epsilon pseudospectra plot .%

Answer 1

[Nipun]

Hi Kavitha,

I understand that you want to plot the normalized eigenfunction and its argument for the Orr-Sommerfeld equation, as well as its epsilon pseudospectra. Here's a basic approach using MATLAB:

1. Solve the Orr-Sommerfeld equation:

• Use appropriate boundary conditions and discretization to solve for eigenvalues and eigenfunctions.

2. Normalize the eigenfunction:

• Normalize the eigenfunction by dividing by its maximum value.

3. Plot the normalized eigenfunction:

• Plot the real and imaginary parts against the argument.

4. Compute and plot epsilon pseudospectra:

• Use the "eig" function and numerical techniques to compute and visualize the pseudospectra.

Refer to the following MathWorks documentation for more information on:

1. Eigenvalues and Eigenvectors in MATLAB: https://www.mathworks.com/help/matlab/ref/eig.html
2. Plotting 2D and 3D data in MATLAB: https://www.mathworks.com/help/matlab/ref/plot.html
3. Pseudospectrum using eigenvector method in MATLAB: https://www.mathworks.com/help/signal/ref/peig.html

Hope this helps.

Regards,

Nipun

[Kavitha G N]

I am thankful for your grnerosity Nipun.