  A 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.
