This is an Orr-Sommerfeld operator generated from a spectral method [2]. This discretization results in a matrix of dimension N=99. There are numerous spurious eigenvalues beyond the plotted axis, so the matrix is projected onto an appropriate invariant subspace to accelerate the computation. Pseudospectra of Orr-Sommerfeld operators were first investigated in [1].
[1]: S. C. Reddy, P. J. Schmidt and D. S. Henningson, "Pseudospectra of the Orr-Sommerfeld operator", SIAM J. Appl. Math. 53(1), pp. 15-47, 1993.
[2]: L. N. Trefethen, "Spectral methods in MATLAB", SIAM, 2000.
EigTool EigTool Demos Menu.