Effects of base flow uncertainty on Couette flow stability

• Published in: Computers & fluids Vol. 43; no. 1; pp. 82 - 89
• Main Authors: Ko, Jordan, Lucor, Didier, Sagaut, Pierre
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Kidlington Elsevier Ltd 01.04.2011; Elsevier
• Subjects: Base flow; Computational methods in fluid dynamics; Computer simulation; Correlation; Couette flow; Engineering Sciences; Exact sciences and technology; Flow stability; Fluid dynamics; Fluids mechanics; Fundamental areas of phenomenology (including applications); Generalized Polynomial Chaos method; Hydrodynamic stability; Instability of shear flows; Mathematical models; Mechanics; Perturbation methods; Physics; Random field; Stability; Stability analysis; Uncertainty quantification; Flow stability; Uncertainty quantification; Random field; Generalized Polynomial Chaos method; Chaos; Projection method; Modal analysis; Digital simulation; Hydrodynamic instability; Disturbances; Couette flow; Modelling; Karhunen-Loeve transforms; Orthogonal polynomial; Parallel plate
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2010.09.029

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.