Warm cascades and anomalous scaling in a diffusion model of turbulence.
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.
Laboratoire de Physique Statistique de l'Ecole Normale Supérieur, associé au CNRS, 24 Rue Lhomond, 75231 Paris Cedex 05, France.
Colm
C
Connaughton
Sergey
S
Nazarenko