Eigenvalue spectra of spatial stability for shear flows

<p indent="0mm">For fluid dynamics, it is undoubtedly very important to obtain and achieve the insights into the eigenvalue spectra of disturbances of flow fields. In this paper, the Arnoldi method is employed to numerically solve the eigenvalue spectra and eigenfunction of the spatial linear stability equation for shear flows. Specifically, four classical compressible and incompressible shear flows are numerically treated. This work obtains the spectra of their eigenvalues in spatial stability, and then analyzes the characteristics of continuous and discrete spectra. In addition, the eigenfunctions of each branch spectrum are solved and analyzed. The results indicate that compared to the temporal mode, there are more complex spectra of eigenvalues and more spectral branches in the spatial mode.