Transition from Markovian to Glassy Dynamics in Damped Kuramoto-Sivashinsky Turbulence

Abstract

In this research, we study Damped Kuramoto-Sivashinsky (DKS) equation, one of the famous nonlinear differential equation which exhibits turbulence. To solve DKS equation, we use Exponential Time Differencing (ETD) scheme which is combined with the Pseudospectral method. To know the effect of damping factor term, we analyze the resulting dynamics using Lyapunov exponent and total autocorrelation function. From that analysis, we elucidate the transition of Markovian to glassy dynamics in DKS equation. We conclude that there is a kind of mixing of several modes in the dynamics of the DKS equation which resulting the glassy dynamics in this system.