2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/85254A phenomenological turbulence model in which the energy spectrum obeys a nonlinear diffusion equation is presented. This equation respects the scaling properties of the original Navier-Stokes equations and it has the Kolmogorov -5/3 cascade and the thermodynamic equilibrium spectra as exact steady state solutions. The general steady state in this model contains a nonlinear mixture of the constant-flux and thermodynamic components. Such "warm cascade" solutions describe the bottleneck phenomenon of spectrum stagnation near the dissipative scale. Self-similar solutions describing a finite-time formation of steady cascades are analysed and found to exhibit nontrivial scaling behaviour.April 10 2003 Updated April 22 2003, 9 pages revtex4, 9 figures Added some figures, additional references and corrected typosFluid Dynamicstext