Casimir preserving spectrum of two-dimensional turbulence

Paolo Cifani; Milo Viviani; Erwin Luesink; Klas Modin; Bernard J. Geurts

doi:10.1103/PhysRevFluids.7.L082601

Casimir preserving spectrum of two-dimensional turbulence

Paolo Cifani, Milo Viviani, Erwin Luesink, Klas Modin, Bernard J. Geurts

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Abstract

We present predictions of the energy spectrum of forced two-dimensional turbulence obtained by employing a structure-preserving integrator. In particular, we construct a finite-mode approximation of the Navier-Stokes equations on the unit sphere, which, in the limit of vanishing viscosity, preserves the Lie-Poisson structure. As a result, integrated powers of vorticity are conserved in the inviscid limit. We obtain robust evidence for the existence of the double energy cascade, including the formation of the
−
3
scaling of the inertial range of the direct cascade. We show that this can be achieved at modest resolutions compared to those required by traditional numerical methods.

Original language	English
Article number	L082601
Journal	Physical review fluids
Volume	7
Issue number	8
DOIs	https://doi.org/10.1103/PhysRevFluids.7.L082601
Publication status	Published - 24 Aug 2022

Keywords

Turbulence simulation
Geometric integration
Lie-Poisson system
Energy spectrum

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10.1103/PhysRevFluids.7.L082601

PhysRevFluids.7.L082601Final published version, 733 KB

11 Citations
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Casimir preserving spectrum of two-dimensional turbulence
Cifani, P., Viviani, M., Luesink, E., Modin, K. & Geurts, B. J., 25 Apr 2022, ArXiv.org.
Research output: Working paper › Preprint › Academic

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title = "Casimir preserving spectrum of two-dimensional turbulence",

abstract = "We present predictions of the energy spectrum of forced two-dimensional turbulence obtained by employing a structure-preserving integrator. In particular, we construct a finite-mode approximation of the Navier-Stokes equations on the unit sphere, which, in the limit of vanishing viscosity, preserves the Lie-Poisson structure. As a result, integrated powers of vorticity are conserved in the inviscid limit. We obtain robust evidence for the existence of the double energy cascade, including the formation of the −3 scaling of the inertial range of the direct cascade. We show that this can be achieved at modest resolutions compared to those required by traditional numerical methods.",

keywords = "Turbulence simulation, Geometric integration, Lie-Poisson system, Energy spectrum",

author = "Paolo Cifani and Milo Viviani and Erwin Luesink and Klas Modin and Geurts, \{Bernard J.\}",

note = "Funding Information: This publication is part of the project SPRESTO which is financed by the Dutch Research Council (NWO). This work was also supported by the Swedish Research Council Grant No. 2017-05040, and the Knut and Alice Wallenberg Foundation Grant No. WAF2019.0201. Simulations were carried out on the Dutch national e-infrastructure with the support of SURF Cooperative. We wish to thank Prof. Guido Boffetta for his valuable suggestions in the setup of the simulations. Publisher Copyright: {\textcopyright} 2022 American Physical Society.",

year = "2022",

month = aug,

day = "24",

doi = "10.1103/PhysRevFluids.7.L082601",

language = "English",

volume = "7",

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issn = "2469-990X",

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T1 - Casimir preserving spectrum of two-dimensional turbulence

AU - Cifani, Paolo

AU - Viviani, Milo

AU - Luesink, Erwin

AU - Modin, Klas

AU - Geurts, Bernard J.

N1 - Funding Information: This publication is part of the project SPRESTO which is financed by the Dutch Research Council (NWO). This work was also supported by the Swedish Research Council Grant No. 2017-05040, and the Knut and Alice Wallenberg Foundation Grant No. WAF2019.0201. Simulations were carried out on the Dutch national e-infrastructure with the support of SURF Cooperative. We wish to thank Prof. Guido Boffetta for his valuable suggestions in the setup of the simulations. Publisher Copyright: © 2022 American Physical Society.

PY - 2022/8/24

Y1 - 2022/8/24

N2 - We present predictions of the energy spectrum of forced two-dimensional turbulence obtained by employing a structure-preserving integrator. In particular, we construct a finite-mode approximation of the Navier-Stokes equations on the unit sphere, which, in the limit of vanishing viscosity, preserves the Lie-Poisson structure. As a result, integrated powers of vorticity are conserved in the inviscid limit. We obtain robust evidence for the existence of the double energy cascade, including the formation of the −3 scaling of the inertial range of the direct cascade. We show that this can be achieved at modest resolutions compared to those required by traditional numerical methods.

AB - We present predictions of the energy spectrum of forced two-dimensional turbulence obtained by employing a structure-preserving integrator. In particular, we construct a finite-mode approximation of the Navier-Stokes equations on the unit sphere, which, in the limit of vanishing viscosity, preserves the Lie-Poisson structure. As a result, integrated powers of vorticity are conserved in the inviscid limit. We obtain robust evidence for the existence of the double energy cascade, including the formation of the −3 scaling of the inertial range of the direct cascade. We show that this can be achieved at modest resolutions compared to those required by traditional numerical methods.

KW - Turbulence simulation

KW - Geometric integration

KW - Lie-Poisson system

KW - Energy spectrum

U2 - 10.1103/PhysRevFluids.7.L082601

DO - 10.1103/PhysRevFluids.7.L082601

M3 - Letter

SN - 2469-990X

VL - 7

JO - Physical review fluids

JF - Physical review fluids

IS - 8

M1 - L082601

ER -

Casimir preserving spectrum of two-dimensional turbulence

Abstract

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Casimir preserving spectrum of two-dimensional turbulence

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