I'm new here. I have been reading articles on Navier-Stokes equation and the stability analysis by studying different modes. However I am still confused by what is meant by modes as in the context of Navier-Stokes equations, how are they computed, how are they differentiated (hydrodynamic and non-hydrodynamic modes), and how these are linked to linearization + stability analysis. Most books seem to dive straight into the formulas without enough background info. I am also familiar with the Fourier analysis/Fourier transform; it is just that it hasn't clicked in my head how all these things are related together and where to start from.
What I am looking for is: not exactly looking for detailed mathematical derivations, just a relatively easy explanation on how all these concepts relate together, and then I can go on from there and continue the research myself.
Thank you all in advance for any help/advice/links! Let me know if I am missing info or if I should rephrase my question, still learning :D