Spectra of operators associated with flow around an infinite cylinder

Numerical approximations of the spectrum of the Oseen operator and the spectrum of the linearised Navier-Stokes operator for flow around a cylinder in two dimensions have been studied for Reynolds numbers in the range 2 to 40. By using a spectral method featuring basis functions covering the entire exterior domain, it is possible to obtain a numerical approximation to the continuous spectrum and the point spectrum. The numerical approximation of the spectra seems to agree with the expected rigorous results. Namely a parabolic tongue containing the continuous spectra for the Oseen operator and for the linearised Navier--Stokes operator a parabolic tongue containing the continuous part of the spectrum plus a finite number of isolated eigenvalues.