The Galerkin-truncated Burgers equation: crossover from inviscid-thermalized to Kardar-Parisi-Zhang scaling

Cartes, C and Tirapegui, E and Pandit, R and Brachet, M (2022) The Galerkin-truncated Burgers equation: crossover from inviscid-thermalized to Kardar-Parisi-Zhang scaling. In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380 (2219).

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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 τ(k) is shown to follow the expected crossover from the short-distance τ(k)∼k-2 Edwards-Wilkinson scaling to the universal long-distance Kardar-Parisi-Zhang scaling τ(k)∼k-3/2. In the inviscid limit, Rmin→∞, we show that the system displays another crossover to the Galerkin-truncated inviscid-Burgers regime that admits thermalized solutions with τ(k)∼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. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Item Type:	Journal Article
Publication:	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publisher:	Royal Society Publishing
Additional Information:	The copyright for this article belongs to the Royal Society Publishing.
Keywords:	Higher order statistics; Partial differential equations; Reynolds number, Burger's equations; Crossover; Kardar-parisi-zhang scaling; Kardar-Parisi-Zhang universalities; Noise terms; One-dimensional; Reynold number; Scalings; Spectral methods; Truncated burger equation, Galerkin methods, article; correlation function
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	08 Jul 2022 10:10
Last Modified:	08 Jul 2022 10:10
URI:	https://eprints.iisc.ac.in/id/eprint/74335

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