Issue |
EPL
Volume 95, Number 2, July 2011
|
|
---|---|---|
Article Number | 24005 | |
Number of page(s) | 5 | |
Section | Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics | |
DOI | https://doi.org/10.1209/0295-5075/95/24005 | |
Published online | 05 July 2011 |
Mixed flux-equipartition solutions of a diffusion model of nonlinear cascades
1
Mathematics Institute, University of Warwick - Coventry CV4 7AL, UK, EU
2
Warwick Centre for Complexity Science, University of Warwick - Coventry CV4 7AL, UK, EU
3
York Plasma Institute, Department of Physics, University of York - Heslington, York YO10 5DD, UK, EU
Received:
18
April
2011
Accepted:
7
June
2011
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.
PACS: 47.27.E- – Turbulence simulation and modeling / 05.45.-a – Nonlinear dynamics and chaos / 47.56.+r – Flows through porous media
© EPLA, 2011
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.