  According to Richardson's cascade description of turbulence, large vortices
break up to form smaller ones, thereby transferring kinetic energy towards
smaller scales. Energy dissipation occurs at the smallest scales due to
viscosity. We study this energy cascade in a phenomenological model of vortex
breakdown. The model is a binary tree of decreasing masses connected by
softening springs, with dampers acting on the lowest level. The masses and
stiffnesses between levels change according to a power law. The different
levels represent different scales, enabling the definition of "mass
wavenumbers". The eigenvalue distribution of the model exhibits a devil's
staircase self-similarity. The energy spectrum of the model (defined as the
energy distribution among the different mass wavenumber) is derived in the
asymptotic limit. A decimation procedure is applied to replace the model with
an equivalent chain oscillator. We show that for a range of stiffness parameter
the energy spectrum is qualitatively similar to the Kolmogorov spectrum of 3D
homogeneous, isotropic turbulence and find the stiffness parameter for which
the energy spectrum has the well-known -5/3 scaling exponent.
