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Mixed flux-equipartition solutions of a diffusion model of nonlinear cascades
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Connaughton, Colm and McAdams, Rachel. (2011) Mixed flux-equipartition solutions of a diffusion model of nonlinear cascades. EPL (Europhysics Letters), Vol.95 (No.2). Article no. 24005. ISSN 0295-5075
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Official URL: http://dx.doi.org/10.1209/0295-5075/95/24005
Abstract
We present a parametric study of a nonlinear diffusion equation which generalises Leith's model of a turbulent cascade to an arbitrary cascade having a single conserved quantity. There are three stationary regimes depending on whether the Kolmogorov exponent is greater than, less than or equal to the equilibrium exponent. In the first regime, the large-scale spectrum scales with the Kolmogorov exponent. In the second regime, the large-scale spectrum scales with the equilibrium exponent so the system appears to be at equilibrium at large scales. Furthermore, in this equilibrium-like regime, the amplitude of the large-scale spectrum depends on the small-scale cut-off. This is interpreted as an analogue of cascade nonlocality. In the third regime, the equilibrium spectrum acquires a logarithmic correction. An exact analysis of the self-similar, nonstationary problem shows that time-evolving cascades have direct analogues of these three regimes.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Centre for Complexity Science Faculty of Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Diffusion processes, Cascades (Fluid dynamics) |
| Journal or Publication Title: | EPL (Europhysics Letters) |
| Publisher: | Institute of Physics Publishing Ltd. |
| ISSN: | 0295-5075 |
| Date: | July 2011 |
| Volume: | Vol.95 |
| Number: | No.2 |
| Page Range: | Article no. 24005 |
| Identification Number: | 10.1209/0295-5075/95/24005 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Related URLs: | |
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| URI: | http://wrap.warwick.ac.uk/id/eprint/39485 |
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