Kardar-Parisi-Zhang asymptotics for the two-dimensional noisy Kuramoto-Sivashinsky equation

TL;DR

This study numerically investigates the two-dimensional noisy Kuramoto-Sivashinsky equation, demonstrating that KPZ scaling emerges as the asymptotic behavior under large coupling or system size, highlighting finite size effects and crossover phenomena.

Contribution

The paper provides the first numerical evidence of KPZ asymptotics in 2D noisy KS equations, clarifying the role of finite size effects and crossover behavior.

Findings

KPZ scaling observed in 2D noisy KS equation at large scales.

Finite size effects influence the asymptotic behavior.

Stronger crossover effects in 2D compared to 1D.

Abstract

We study numerically the Kuramoto-Sivashinsky (KS) equation forced by external white noise in two space dimensions, that is a generic model for e.g. surface kinetic roughening in the presence of morphological instabilities. Large scale simulations using a pseudospectral numerical scheme allow us to retrieve Kardar-Parisi-Zhang (KPZ) scaling as the asymptotic state of the system, as in the 1D case. However, this is only the case for sufficiently large values of the coupling and/or system size, so that previous conclusions on non-KPZ asymptotics are demonstrated as finite size effects. Crossover effects are comparatively stronger for the 2D case than for the 1D system.