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

C. Cartes; E. Tirapegui; R. Pandit; M. Brachet

doi:10.1098/rsta.2021.0090

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

C. Cartes, E. Tirapegui, R. Pandit, M. Brachet^*

^*Autor correspondiente de este trabajo

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13 Citas (Scopus)

Resumen

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)'.

Idioma original	Inglés
Número de artículo	20210090
Publicación	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volumen	380
N.º	2219
DOI	https://doi.org/10.1098/rsta.2021.0090
Estado	Publicada - 2022

Nota bibliográfica

Funding Information:
This work was supported by the French Agence nationale de la recherche (ANR QUTE-HPC project no. ANR-18-CE46-0013). Acknowledgements

Funding Information:
This work was granted access to HPC resources of MesoPSL financed by Region Ile de France and the project Equip@Meso (reference ANR-10-EQPX-29-01) of the programme Investissements d’Avenir supervised by Agence Nationale pour la Recherche. M.B. and R.P. thank the Indo-French Centre for Applied Mathematics for financial support. R.P. also thanks CSIR, UGC and DST India for support and Dipankar Roy for discussions. C.C., E.T. and M.B. acknowledge the support of the Laboratoire International Associé ‘Matière: Structure et Dynamique’ LIA-MSD. C.C. wishes to acknowledge the support of FONDECYT (CL), no. 1200357 and Universidad de los Andes (CL) through FAI initiatives. Uriel Frisch has been a leader in research on turbulence for several decades. He has inspired many researchers in this area, especially M.B. and R.P., who have worked closely with him. We wish him many more years of active research and we look forward to working with him.

Publisher Copyright:
© 2022 The Author(s).

Palabras clave

Crossover
Kardar-Parisi-Zhang universality
Truncated Burgers equation

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The Galerkin-truncated Burgers equation: crossover from inviscid-thermalized to Kardar-Parisi-Zhang scaling. / Cartes, C.; Tirapegui, E.; Pandit, R. et al.
En: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 380, N.º 2219, 20210090, 2022.

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

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N2 - 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)'.

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

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