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A mathematical and physical Study of multiscale deconvolution models of turbulence
Author(s) -
Dunca Argus Adrian,
Kohler Kara E.,
Neda Monika,
Rebholz Leo G.
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2514
Subject(s) - enstrophy , energy cascade , turbulence , cascade , homogeneous isotropic turbulence , microscale chemistry , statistical physics , reynolds number , dissipation , mathematics , turbulence kinetic energy , kinetic energy , kolmogorov microscales , isotropy , k omega turbulence model , physics , classical mechanics , mechanics , direct numerical simulation , vorticity , thermodynamics , chemistry , mathematics education , chromatography , quantum mechanics , vortex
This work presents a rigorous analysis of mathematical and physical properties for solutions of multiscale deconvolution turbulence models. We show that solutions of these models exactly conserve model quantities for the integral invariants of fundamental physical importance: kinetic energy, helicity, and (in two dimensions) enstrophy. The kinetic energy conservation is the key that allows us to next apply the phenomenology of homogeneous, isotropic turbulence to establish the existence of a model energy cascade and, in particular, that the cascade exhibits enhanced energy dissipation in a secondary accelerated cascade, which ends at the model's microscale (which we establish is larger than the Kolmogorov microscale). We also prove that the model dissipates energy at the same rate as true turbulent flow, ∼ O ( U 3 ∕ L ), independent of Reynolds number. Lastly, we prove the existence of global attractors for the model solutions; the proof of which also shows that solutions are actually one degree of regularity higher than previously known. Copyright © 2012 John Wiley & Sons, Ltd.