Renormalized dissipation in the nonconservatively forced Burgers equation

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A previous calculation of the renormalized dissipation in the nonconservatively forced one-dimensional Burgers equation, which encountered a catastrophic long-wavelength divergence approximately [k min]-3, is reconsidered. In the absence of velocity shear, analysis of the eddy-damped quasi-normal Markovian closure predicts only a benign logarithmic dependence on kmin. The original divergence is traced to an inconsistent resonance-broadening type of diffusive approximation, which fails in the present problem. Ballistic scaling of renormalized pulses is retained, but such scaling does not, by itself, imply a paradigm of self-organized criticality. An improved scaling formula for a model with velocity shear is also given.

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231 Kilobytes pages

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Krommes, J.A. January 19, 2000.

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Description

A previous calculation of the renormalized dissipation in the nonconservatively forced one-dimensional Burgers equation, which encountered a catastrophic long-wavelength divergence approximately [k min]-3, is reconsidered. In the absence of velocity shear, analysis of the eddy-damped quasi-normal Markovian closure predicts only a benign logarithmic dependence on kmin. The original divergence is traced to an inconsistent resonance-broadening type of diffusive approximation, which fails in the present problem. Ballistic scaling of renormalized pulses is retained, but such scaling does not, by itself, imply a paradigm of self-organized criticality. An improved scaling formula for a model with velocity shear is also given.

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231 Kilobytes pages

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INIS; OSTI as DE00750289

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  • Other Information: PBD: 19 Jan 2000

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  • Report No.: PPPL--3422
  • Grant Number: AC02-76CH03073
  • DOI: 10.2172/750289 | External Link
  • Office of Scientific & Technical Information Report Number: 750289
  • Archival Resource Key: ark:/67531/metadc707183

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  • January 19, 2000

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  • Sept. 12, 2015, 6:31 a.m.

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  • April 15, 2016, 7:37 p.m.

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Krommes, J.A. Renormalized dissipation in the nonconservatively forced Burgers equation, report, January 19, 2000; Princeton, New Jersey. (digital.library.unt.edu/ark:/67531/metadc707183/: accessed August 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.