Linear flow stability beyond eigenmodes: some recent examples
Speaker: Dr. Cristobal Arratia, (EFPL, Lausanne, Switzerland)
Time: 2:00PM
Date: Wednesday, January 08th 2014
Location: Seminar Room (G24), Ground Floor, NexusUCD, University College Dublin. Blocks 9 & 10, Belfield Office Park
Abstract:
The field of hydrodynamic stability has seen a great deal of development during the last decades. Many advances have come through the recognition of the shortcomings of classical linear stability analyses, which focus on the study of eigenmodes and their eigenvalues. In this talk, concepts and methodologies that extend the classical modal stability will be introduced, and recent results from their applications will be shown. A first example will deal with the well known phenomena of vortex shedding past an obstacle; it will be shown that the distinction between absolute and convective instabilities can be used to reconcile with observations the classic point vortex model of von Karman, for over a century known to be temporally unstable. Other examples will involve the computation of 'optimal perturbations', which can produce very large perturbation energy growth even when all the eigenmodes are exponentially decaying. This type of analysis has allowed to capture and characterize ubiquitous instability mechanisms that went for long unnoticed to the community of hydrodynamic stability. In addition, the methodology for computing optimal perturbations is directly applicable when the governing equations depend explicitly on time, allowing us to evaluate the stability of evolving two-dimensional shear layers to three-dimensional perturbations.
Series: Applied and Computational Mathematics Seminar Series
Social Media Links