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

Abstract

Two well-known turbulence models that describe the energy spectrum in the inertial and dissipative ranges simultaneously are by Pao~(1965) and Pope~(2000). In this paper, we compute the energy spectrum $E(k)$ and energy flux $\Pi (k)$ using direct numerical simulations on grids up to $4096^3$, and show consistency between the numerical results and the predictions by the aforementioned models. We also construct a model for laminar flows that predicts $E(k)\sim k^{-1}\exp (-k)$ and $\Pi (k)\sim k\exp (-k)$. Our model predictions match with the numerical results. We emphasize differences on the energy transfers in the two flows---they are {\em local} in the turbulent flows, and {\em nonlocal} in laminar flows.

References in corpus (4)

• Phenomenology of buoyancy-driven turbulence: recent results
• Non-local interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws
• Anisotropy in Quasi-Static Magnetohydrodynamic Turbulence
• A systematic bias in the calculation of spectral density from a 3D spatial grid

Cited by in corpus (6)

• Energy and enstrophy spectra and fluxes for the inertial-dissipation range of two-dimensional turbulence
• Variable energy flux in turbulence
• Analysis of the dissipative range of the energy spectrum in grid turbulence and in direct numerical simulations
• Asymmetric energy transfers in driven nonequilibrium systems and arrow of time
• Prandtl number dependence of the small-scale properties in turbulent Rayleigh-Bénard convection
• Enstrophy transfers in helical turbulence