Localness of energy cascade in hydrodynamic turbulence, II. Sharp spectral filter [electronic resource].
- Washington, D.C. : United States. Dept. of Energy, 2009.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
- Additional Creators:
- Los Alamos National Laboratory, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information
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- Free-to-read Unrestricted online access
- We investigate the scale-locality of subgrid-scale (SGS) energy flux and interband energy transfers defined by the sharp spectral filter. We show by rigorous bounds, physical arguments, and numerical simulations that the spectral SGS flux is dominated by local triadic interactions in an extended turbulent inertial range. Interband energy transfers are also shown to be dominated by local triads if the spectral bands have constant width on a logarithmic scale. We disprove in particular an alternative picture of 'local transfer by nonlocal triads,' with the advecting wavenumber mode at the energy peak. Although such triads have the largest transfer rates of all individual wavenumber triads, we show rigorously that, due to their restricted number, they make an asymptotically negligible contribution to energy flux and log-banded energy transfers at high wavenumbers in the inertial range. We show that it is only the aggregate effect of a geometrically increasing number of local wavenumber triads which can sustain an energy cascade to small scales. Furthermore, nonlocal triads are argued to contribute even less to the space-average energy flux than is implied by our rigorous bounds, because of additional cancellations from scale-decorrelation effects. We can thus recover the -4/3 scaling of nonlocal contributions to spectral energy flux predicted by Kraichnan's abridged Lagrangian-history direct-interaction approximation and test-field model closures. We support our results with numerical data from a 512³ pseudospectral simulation of isotropic turbulence with phase-shift dealiasing. We also discuss a rigorous counterexample of Eyink [Physica D 78, 222 (1994)], which showed that nonlocal wavenumber triads may dominate in the sharp spectral flux (but not in the SGS energy flux for graded filters). We show that this mathematical counter example fails to satisfy reasonable physical requirements for a turbulent velocity field, which are employed in our proof of scale locality. We conclude that the sharp spectral filter has a firm theoretical basis for use in large-eddy simulation modeling of turbulent flows.
- Report Numbers:
- E 1.99:la-ur-09-06200
E 1.99: la-ur-09-6200
- Other Subject(s):
- Published through SciTech Connect.
Physics of Fluids 21 11 FT
Eyink, Gregory L; Aluie, Hussein.
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