Energy Spectra and Fluxes in Dissipation Range of Turbulent and Laminar Flows

M. K. Verma, A. Kumar, P. Kumar, S. Barman, A. G. Chatterjee, Ravi Samtaney, R. A. Stepanov

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Two well-known turbulence models to describe the energy spectrum in the inertial and dissipative ranges simultaneously are by Pao (1965) and Pope (2000). In this paper, we compute energy spectrum E(k) and energy flux Π(k) using direct numerical simulations on grids up to 40963, and show consistency between the numerical results and predictions by the aforementioned models for turbulence flows. We also consider the laminar flow in which viscosity dominates over nonlinearity. For this case we suggest a modified model that predicts E(k) ~ k−1 exp(−k) and Π(k) ~ k exp(−k) in dissipation range of scales and verify it using numerical simulations. We emphasize the difference revealing local energy transfer for the turbulent flows and nonlocal one for the laminar flows at low Reynolds number.
Original languageEnglish (US)
Pages (from-to)862-873
Number of pages12
JournalFluid Dynamics
Volume53
Issue number6
DOIs
StatePublished - Feb 22 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We thank Mohammad Anas for a valuable feedback on ¯kd. Our numerical simulations were performed on Cray XC40 Shaheen II at KAUST supercomputing laboratory, Saudi Arabia and Chaos cluster of IIT Kanpur. This work was supported by the research grants PLANEX/PHY/2015239 from Indian Space Research Organisation India, INT/RUS/RSF/P-03 by the Department of Science and Technology India, and RSF-16-41-02012 by Russian Science Foundation for the Indo-Russian project.

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