Speaker: Xinyu Zhao, McMaster University
Date: April 4, 2024
Title: On instability of the Taylor-Green vortex in 2D Euler flows
Abstract: The 2D incompressible Euler equations are globally well-posed, but the stability of even very simple equilibrium solutions has not been fully understood due to the subtle interplay between the point spectrum and the essential spectrum of the corresponding linear operator. In this talk, we will present a numerical study of the instability of the 2D Taylor-Green vortex and showcase the presence of unstable eigenvalues embedded within the essential spectrum. Moreover, we will apply a PDE optimization approach to find non-modal perturbation growth related to the essential spectrum. This is an ongoing joint work with Bartosz Protas and Roman Shvydkoy.
Location: Residents of Lewis Hall can attend talks in the Wan Conference Room (Lewis 208) at 11:30am. The talk will also be streamed live via Zoom.