  We present results from a systematic numerical study of structural properties
of an unforced, incompressible, homogeneous, and isotropic three-dimensional
turbulent fluid with an initial energy spectrum that develops a cascade of
kinetic energy to large wavenumbers. The results are compared with those from a
recently studied set of power-law initial energy spectra [C. Kalelkar and R.
Pandit, Phys. Rev. E, {\bf 69}, 046304 (2004)] which do not exhibit such a
cascade. Differences are exhibited in plots of vorticity isosurfaces, the
temporal evolution of the kinetic energy-dissipation rate, and the rates of
production of the mean enstrophy along the principal axes of the strain-rate
tensor. A crossover between non-`cascade-type' and `cascade-type' behaviour is
shown numerically for a specific set of initial energy spectra.
