  In this paper, we study the inviscid limit of the Sabra shell model of
turbulence, which is considered as a particular case of a viscous conservation
law in one space dimension with a nonlocal quadratic flux function. We present
a theoretical argument (with a detailed numerical confirmation) showing that a
classical deterministic solution before a finite-time blowup, $t < t_b$, must
be continued as a stochastic process after the blowup, $t > t_b$, representing
a unique physically relevant description in the inviscid limit. This theory is
based on the dynamical system formulation written for the logarithmic time
$\tau = \log(t-t_b)$, which features a stable traveling wave solution for the
inviscid Burgers equation, but a stochastic traveling wave for the Sabra model.
The latter describes a universal onset of stochasticity immediately after the
blowup.
