  As a minimal mathematical model generating cascade analogous to that of the
Navier-Stokes turbulence in the inertial range, we propose a one-dimensional
partial-differential-equation model that conserves the integral of the squared
vorticity analogue (enstrophy) in the inviscid case. With a large-scale forcing
and small viscosity, we find numerically that the model exhibits the enstrophy
cascade, the broad energy spectrum with a sizable correction to the
dimensional-analysis prediction, peculiar intermittency and self-similarity in
the dynamical system structure.
