A New Methodology for Linear Asymptotic Stability Analysis of Fluid Flows in a Continuous-Time Domain

In this talk, we present a new approach for analyzing linear asymptotic stability of fluid flow systems, which is not based on a conventional eigenvalue analysis. In particular, the methodology is formulated in a continuous-time domain and makes no assumption on the form of the perturbations (that is, without resorting to a normal-mode assumption on the perturbations). By analyzing all time-varying perturbations and not only the ones restricted to a specific functional form, the developed stability test provides a stronger condition with regard to the system stability. The new methodology is applied to analyze stability of linearized Navier-Stokes equations in two-dimensional and three-dimensional channel and pipe geometries. Stability results of the new continuous-time formulation are compared with a traditional eigenvalue-based analysis, demonstrating that the developed methodology indeed represents a stricter (sufficient) condition for stability.