# Bulletin of the American Physical Society

# 64th Annual Meeting of the APS Division of Fluid Dynamics

## Volume 56, Number 18

## Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland

### Session D12: Turbulence Simulation II

2:10 PM–4:07 PM,
Sunday, November 20, 2011

Room: 315

Chair: Dale Pullin, California Institute of Technology

Abstract ID: BAPS.2011.DFD.D12.6

### Abstract: D12.00006 : On the Lagrangian Power Spectrum of Turbulence Energy in Isotropic Turbulence

3:15 PM–3:28 PM

Preview Abstract Abstract

#### Authors:

Francesco Lucci

(Aerothermochem. and Combustion Systems Laboratory, ETH, Zurich, Switzerland)

Victor L'vov

(Dept. of Chem. Phys., The Weizmann Institute of Science, Rehovot 76100, Israel)

Antonino Ferrante

(Dept. of Aeronautics \& Astronautics, Univ. of Washington, Seattle, WA 98195)

Said Elghobashi

( Dept. of Mech. \& Aerospace Engineering, Univ. of California, Irvine, CA 92697)

We present, for the first time, a derivation of the transport equation of the Lagrangian frequency power spectrum, ${ E_{L}(t,\omega)}$, of turbulence energy in isotropic turbulence starting from the autocorrelation of the Lagrangian velocity. The new equation is: ${\partial E_L (t,\omega)} \big / {\partial t} = $ $ {\mathcal T}_L (t,\omega) -$ $ \varepsilon_L (t,\omega) +$ $ \Psi_L (t,\omega) $, where $ {\mathcal T}_{L} (t,\omega)$ is the transfer rate of ${ E_{L}(t,\omega)}$ across the frequency spectrum, $\varepsilon_{L} (t,\omega)$ is the viscous dissipation rate of ${ E_{L}(t,\omega)}$, and $ \Psi_L (t,\omega)$ is the external forcing rate. Our DNS shows that $\varepsilon_{L} (\omega)$ is maximum at low frequencies and vanishes at high frequencies. We also performed an analytical study which confirms the DNS result and shows that $\varepsilon_{L}(\omega) \sim (\omega_{\eta} - \omega)$, i.e. there is non-locality for {$\varepsilon_{L}(\omega)$} in the $\omega$ domain, whereas $E_{L}(\omega) \sim (1/\omega^2 - 1/\omega_{\eta}^2)$, i.e. the locality is valid for $E_{L}(\omega)$, where $\omega_{\eta}$ is the Kolmogorov scale frequency.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.DFD.D12.6

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