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Authors: C. Cartes, E. Tirapegui, R. Pandit and M. Brachet

Abstract

The one-dimensional Galerkin-truncated Burgers equation, with both dissipation and noise terms included, is studied using spectral methods. When the truncation-scale Reynolds number 𝑅min is varied, from very small values to order 1 values, the scale-dependent correlation time $\tau(k)$ is shown to follow the expected crossover from the short-distance $\tau(k)\sim k^{-2}$ Edwards–Wilkinson scaling to the universal long-distance Kardar–Parisi–Zhang scaling $\tau(k)\sim k^{-3/2}$. In the inviscid limit, $R_{min} \rightarrow \infty$, we show that the system displays another crossover to the Galerkin-truncated inviscid-Burgers regime that admits thermalized solutions with $\tau(k)\sim k^{-1}$. The scaling forms of the time-correlation functions are shown to follow the known analytical laws and the skewness and excess kurtosis of the interface increments distributions are characterized.