Shock Structures and Velocity Fluctuations in the Noisy Burgers and KdV-Burgers Equations

Abstract

Statistical properties of the noisy Burgers and KdV-Burgers equations are numerically studied. It is found that shock-like structures appear in the time-averaged patterns for the case of stepwise fixed boundary conditions. Our results show that the shock structure for the noisy KdV-Burgers equation has an oscillating tail, even for the time averaged pattern. Also, we find that the width of the shock and the intensity of the velocity fluctuations in the shock region increase with system size.