We study the propagation of localised disturbances in a turbulent, but
momentarily quiescent and unforced shell model (an approximation of the
Navier-Stokes equations on a set of exponentially spaced momentum shells).
These disturbances represent bursts of turbulence travelling down the inertial
range, which is thought to be responsible for the intermittency observed in
turbulence. Starting from the GOY shell model, we go to the limit where the
distance between succeeding shells approaches zero (``the zero spacing limit'')
and helicity conservation is retained. We obtain a discrete field theory which
is numerically shown to have pulse solutions travelling with constant speed and
with unchanged form. We give numerical evidence that the model might even be
exactly integrable, although the continuum limit seems to be singular and the
pulses show an unusual super exponential decay to zero as exp(−constσn) when n→∞, where σ is the {\em
golden mean}. For finite momentum shell spacing, we argue that the pulses
should accelerate, moving to infinity in a finite time. Finally we show that
the maximal Lyapunov exponent of the GOY model approaches zero in this limit.Comment: 27 pages, submitted for publicatio