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Updated: Aug 26, 2026

Evolution of Staircase Structures in Diffusive Convection
Published on: September 5, 2018
Warm cascades and anomalous scaling in a diffusion model of turbulence
Colm Connaughton1, Sergey Nazarenko
1Laboratoire de Physique Statistique de l'Ecole Normale Supérieur, associé au CNRS, 24 Rue Lhomond, 75231 Paris Cedex 05, France.
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.
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