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

TL;DR

This paper numerically investigates the statistical properties of the noisy Burgers and KdV-Burgers equations, revealing shock-like structures, oscillating tails, and size-dependent fluctuations in velocity profiles.

Contribution

It demonstrates the emergence of shock structures and their characteristics in noisy nonlinear equations, providing new insights into their statistical behavior.

Findings

Shock-like structures appear in time-averaged patterns.

Oscillating tails are present in the KdV-Burgers shock structures.

Shock width and velocity fluctuation intensity grow with system size.

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.