Numerical simulation and linear analysis of turbulent-like dynamical systems

Abstract

Turbulence is characterized by unsteady perturbations and chaotic behavior. Turbulent flows also display a wide range of spatial and frequency scales. The simulation of turbulent flows requires accurate numerical schemes with minimal artificial dissipation and dispersion in order to capture the transient features of these flows. While the numerical simulations provide a detailed evolution of the flow features, their analysis can be compromised due to the inherent complex dynamics. In order to provide a better understanding of flow evolution, linear techniques have been applied to study the physics of transition to turbulence including the growth of flow instabilities. In this work, we will combine techniques for the numerical simulation of nonlinear model equations with chaotic behavior similar to that observed in turbulent flows. These models are useful for testing numerical methods and interpreting intermittent behavior in dynamic systems. Linear techniques will also be employed to understand the impact of non-normality and transient growth in model equations such as the complex Ginzburg-Landau and Kuramoto-Sivashinsky equations. (AU)