Warm Cascades and Anomalous Scaling in a Diffusion Model of Turbulence
- 27 January 2004
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 92 (4) , 044501
- https://doi.org/10.1103/physrevlett.92.044501
Abstract
A phenomenological turbulence model in which the energy spectrum obeys a nonlinear diffusion equation is analyzed. The general steady state contains a nonlinear mixture of the constant-flux Kolmogorov and fluxless thermodynamic components. Such “warm cascade” solutions describe a bottleneck phenomenon of spectrum stagnation near the dissipative scale. Transient self-similar solutions describing a finite-time formation of steady cascades are analyzed and found to exhibit nontrivial scaling behavior.Keywords
This publication has 7 references indexed in Scilit:
- Non-stationary spectra of local wave turbulencePhysica D: Nonlinear Phenomena, 2003
- A weak turbulence theory for incompressible magnetohydrodynamicsJournal of Plasma Physics, 2000
- Spectral transport model for turbulenceTheoretical and Computational Fluid Dynamics, 1996
- Bottleneck phenomenon in developed turbulencePhysics of Fluids, 1994
- “Waiting-time” Solutions of a Nonlinear Diffusion EquationSIAM Journal on Applied Mathematics, 1982
- Diffusion Approximation for Turbulent Scalar FieldsPhysics of Fluids, 1968
- Diffusion Approximation to Inertial Energy Transfer in Isotropic TurbulencePhysics of Fluids, 1967