Hydrodynamics of the Kuramoto-Sivashinsky Equation in Two Dimensions
Bruce Boghosian, Carson C. Chow, and Terence Hwa
TL;DR
This paper investigates the large-scale hydrodynamic behavior of the two-dimensional Kuramoto-Sivashinsky equation, revealing that its spatiotemporal chaos likely belongs to the KPZ universality class through coarse graining and numerical analysis.
Contribution
It introduces an explicit coarse graining scheme and derives intermediate equations to connect small-scale structures with large-scale hydrodynamics in 2D KS equation.
Findings
Supports the KPZ universality class for 2D KS equation
Derives intermediate equations describing scale interactions
Numerical results align with KPZ predictions
Abstract
The large scale properties of spatiotemporal chaos in the 2d Kuramoto-Sivashinsky equation are studied using an explicit coarse graining scheme. A set of intermediate equations are obtained. They describe interactions between the small scale (e.g., cellular) structures and the hydrodynamic degrees of freedom. Possible forms of the effective large scale hydrodynamics are constructed and examined. Although a number of different universality classes are allowed by symmetry, numerical results support the simplest scenario, that being the KPZ universality class.
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