Effects of base flow uncertainty on Couette flow stability

Linear stability analysis of a Couette flow subject to an internal random perturbation is carried out via a stochastic spectral projection method. The uncertain base flow perturbation, which need not be infinitesimally small, is modeled as a Gaussian random field of prescribed correlation length. The approach leads to the prediction of the response surface of the eigenmodes of the linearized stability problem, and therefore to a probabilistic extension of the usual stability analysis. It is observed that small perturbations in the mean velocity profile can lead to substantial changes in the eigenspectrum of the linearized problem, introducing significant changes in the transient behaviour of the system induced by the non-normality of the governing equations.