Effective Viscosity and Time Correlation for the Kuramoto-Sivashinsky Equation

Details Effective Viscosity and Time Correlation for the Kuramoto-Sivashinsky Equation Effective Viscosity and Time Correlation for the Kuramoto-Sivashinsky Equation

2002-04-16

arxiv.org/abs/nlin/0204034v1

Nonlinear Sciences

Chaotic Dynamics

6 figures

Scientific paper

10.1143/PTP.107.879

A shock-like structure appears in a time-averaged pattern produced by the Kuramoto-Sivashinsky equation and the noisy Burgers equation with fixed boundary conditions. We show that the effective viscosity computed from the width of the time-averaged shock structure is consistent with that computed from the time correlation of the fluctuations. The effective viscosity depends on the lengthscale, although our system size is not sufficiently large to satisfy the asymptotic dynamic scaling law. We attempt to determine the effective viscosity in a finite size system with the projection operator method.

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